suzanne.soy/scribble-math
1
0
Fork 0
Code Issues 8 Pull Requests 3 Actions Packages Projects Releases Wiki Activity
1ae55396e4
scribble-math/math-scribble/jsxgraph-082rc4/jsxgraphcore.js
Jens Axel Søgaard 1ae55396e4 Inital commit
2012-06-20 17:20:30 +02:00

26 lines
344 KiB
JavaScript
Raw Blame History

/* Version 0.82rc4 */
/*
Copyright 2008-2010
Matthias Ehmann,
Michael Gerhaeuser,
Carsten Miller,
Bianca Valentin,
Alfred Wassermann,
Peter Wilfahrt
This file is part of JSXGraph.
JSXGraph is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
JSXGraph is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with JSXGraph. If not, see <http://www.gnu.org/licenses/>.
*/
var JXG={};(function(){var a,b;JXG.countDrawings=0;JXG.countTime=0;JXG.require=function(c){};JXG.rendererFiles=[];JXG.rendererFiles.svg="SVGRenderer";JXG.rendererFiles.vml="VMLRenderer";JXG.baseFiles=null;JXG.requirePath="";for(a=0;a<document.getElementsByTagName("script").length;a++){b=document.getElementsByTagName("script")[a];if(b.src&&b.src.match(/loadjsxgraphInOneFile\.js(\?.*)?$/)){JXG.requirePath=b.src.replace(/loadjsxgraphInOneFile\.js(\?.*)?$/,"")}}JXG.serverBase=JXG.requirePath+"server/"})();JXG.Math=new Object();JXG.Math.eps=0.000001;JXG.Math.Vector=function(b){var a;this.length=0;if((typeof b!=undefined)&&(b!=null)){for(a=0;a<b.length;a++){this.push(b[a])}}};JXG.Math.Vector.prototype=new Array();JXG.Math.Vector.prototype.n=function(){return this.length};JXG.Math.Vector.prototype.exchange=function(c,b){var a=this[c];this[c]=this[b];this[b]=a};JXG.Math.Matrix=function(g){var e=0,f=false,d,c,a,b;this.length=0;if((typeof g!=undefined)&&(g!=null)){a=g.length;for(d=0;d<a;d++){b=g[d].length;this.push(new Array());if(f){if(e!=b){this.length=0;throw new JXG.DimensionMismatchException("Your array contains arrays with different lengths.")}}for(c=0;c<b;c++){this[d].push(g[d][c])}e=b;f=true}}};JXG.Math.Matrix.prototype=new Array();JXG.Math.Matrix.prototype.m=function(){return this.length};JXG.Math.Matrix.prototype.n=function(){if(this.length>0){return this[0].length}else{return 0}};JXG.Math.Matrix.prototype.exchangeRows=function(c,b){var a=this[c];this[c]=this[b];this[b]=a};JXG.DimensionMismatchException=function(a){if((typeof a!=undefined)&&(a!=null)){this.message=a}else{this.message=null}};JXG.DimensionMismatchException.prototype.what=function(){var a="Matrix has incorrect dimensions";if(this.message!=null){return a+": "+this.message+"."}else{return a+"."}};JXG.SingularMatrixException=function(a){if((typeof a!=undefined)&&(a!=null)){this.message=a}else{this.message=null}};JXG.SingularMatrixException.prototype.what=function(){var a="Matrix is singular";if(this.message!=null){return a+": "+this.message+"."}else{return a+"."}};JXG.Math.matVecMult=function(g,e){var a=g.length,h=e.length,d=[],c,f,b;if(h==3){for(c=0;c<a;c++){d[c]=g[c][0]*e[0]+g[c][1]*e[1]+g[c][2]*e[2]}}else{for(c=0;c<a;c++){f=0;for(b=0;b<h;b++){f+=g[c][b]*e[b]}d[c]=f}}return d};JXG.Math.matMatMult=function(b,a){var d=b.length,c=a[0].length,l=a.length,h=[],g,f,q,e;for(g=0;g<d;g++){h[g]=[]}for(g=0;g<d;g++){for(f=0;f<c;f++){q=0;for(e=0;e<l;e++){q+=b[g][e]*a[e][f]}h[g][f]=q}}return h};JXG.Math.Matrix.transpose=function(f){var c=[],d,b,a,e;a=f.length;e=(f.length>0)?f[0].length:0;for(d=0;d<e;d++){c.push([]);for(b=0;b<a;b++){c[d].push(f[b][d])}}return c};JXG.Math.crossProduct=function(b,a){return[b[1]*a[2]-b[2]*a[1],b[2]*a[0]-b[0]*a[2],b[0]*a[1]-b[1]*a[0]]};JXG.Math.innerProduct=function(d,c,g){var e,f=0;if(typeof g=="undefined"){g=d.length}for(e=0;e<g;e++){f+=d[e]*c[e]}return f};JXG.memoizer=function(b){var a,c;if(b.memo){return b.memo}a={};c=Array.prototype.join;return(b.memo=function(){var d=c.call(arguments);return(typeof a[d]!="undefined")?a[d]:a[d]=b.apply(this,arguments)})};JXG.Math.factorial=JXG.memoizer(function(a){if(a<0){return NaN}if(a==0||a==1){return 1}return a*arguments.callee(a-1)});JXG.Math.binomial=JXG.memoizer(function(e,c){var a,d;if(c>e||c<0){return 0}if(c==0||c==e){return 1}a=1;for(d=0;d<c;d++){a*=(e-d);a/=(d+1)}return a});JXG.Math.round=function(a,d){var c,b;c=a-Math.ceil(a);b=c.toString();if(c<0){b=b.substr(0,d+3)}else{b=b.substr(0,d+2)}c=parseFloat(b);t=parseInt(a.toString());return t+c};JXG.Math.cosh=function(a){return(Math.exp(a)+Math.exp(-a))*0.5};JXG.Math.sinh=function(a){return(Math.exp(a)-Math.exp(-a))*0.5};JXG.Math.pow=function(d,c){if(d==0){if(c==0){return 1}else{return 0}}if(Math.floor(c)==c){return Math.pow(d,c)}else{if(d>0){return Math.exp(c*Math.log(Math.abs(d)))}else{return NaN}}};JXG.Math.normalize=function(c){var a=2*c[3],d=c[4]/(a),e,b;c[5]=d;c[6]=-c[1]/a;c[7]=-c[2]/a;if(d==Infinity||isNaN(d)){e=Math.sqrt(c[1]*c[1]+c[2]*c[2]);c[0]/=e;c[1]/=e;c[2]/=e;c[3]=0;c[4]=1}else{if(Math.abs(d)>=1){c[0]=(c[6]*c[6]+c[7]*c[7]-d*d)/(2*d);c[1]=-c[6]/d;c[2]=-c[7]/d;c[3]=1/(2*d);c[4]=1}else{b=(d<=0)?(-1):(1);c[0]=b*(c[6]*c[6]+c[7]*c[7]-d*d)*0.5;c[1]=-b*c[6];c[2]=-b*c[7];c[3]=b/2;c[4]=b*d}}return c};JXG.Math.Numerics={};JXG.Math.Numerics.INT_TRAPEZ=1;JXG.Math.Numerics.INT_SIMPSON=2;JXG.Math.Numerics.INT_MILNE=3;JXG.Math.Numerics.number_of_nodes=28;JXG.Math.Numerics.integration_type=JXG.INT_MILNE;JXG.Math.Numerics.backwardSolve=function(g,d){var c=d,a,h,f,e;if(g.m){a=g.m();h=g.n()}else{a=g.length;h=(g.length>0)?g[0].length:0}for(f=a-1;f>=0;f--){for(e=h-1;e>f;e--){c[f]-=g[f][e]*c[e]}c[f]/=g[f][f]}return c};JXG.Math.Numerics.Gauss=function(a,l){var q=JXG.Math.eps,c,f,e,d,g,m,h;if(a.n){c=a.n()}else{c=(a.length>0)?a[0].length:0}g=new JXG.Math.Vector();for(f=0;f<c;f++){g.push(f)}for(e=0;e<c;e++){for(f=c-1;f>e;f--){if(Math.abs(a[f][e])>JXG.Math.eps){if(Math.abs(a[e][e])<JXG.Math.eps){a.exchangeRows(f,e);l.exchange(f,e);g.exchange(f,e)}else{a[f][e]/=a[e][e];l[f]-=a[f][e]*l[e];for(d=e+1;d<c;d++){a[f][d]-=a[f][e]*a[e][d]}}}if(Math.abs(a[e][e])<JXG.Math.eps){throw new SingularMatrixException()}}}return JXG.Math.Numerics.backwardSolve(a,l)};JXG.Math.Numerics.Inverse=function(m){var g,f,e,u,q,a,l,d=m.length,c=[],b=[],h=[];for(g=0;g<d;g++){c[g]=[];for(f=0;f<d;f++){c[g][f]=m[g][f]}b[g]=g}for(f=0;f<d;f++){q=Math.abs(c[f][f]);a=f;for(g=f+1;g<d;g++){if(Math.abs(c[g][f])>q){q=Math.abs(c[g][f]);a=g}}if(q<=JXG.Math.eps){return false}if(a>f){for(e=0;e<d;e++){l=c[f][e];c[f][e]=c[a][e];c[a][e]=l}l=b[f];b[f]=b[a];b[a]=l}u=1/c[f][f];for(g=0;g<d;g++){c[g][f]*=u}c[f][f]=u;for(e=0;e<d;e++){if(e!=f){for(g=0;g<d;g++){if(g!=f){c[g][e]-=c[g][f]*c[f][e]}}c[f][e]=-u*c[f][e]}}}for(g=0;g<d;g++){for(e=0;e<d;e++){h[b[e]]=c[g][e]}for(e=0;e<d;e++){c[g][e]=h[e]}}return c};JXG.Math.Numerics.QR=function(c,a){};JXG.Math.Numerics.Jacobi=function(u){var h,f,e,v,a,l,s,r,w=JXG.Math.eps,q=0,m,g,c=u.length,d=[[0,0,0],[0,0,0],[0,0,0]],b=[[0,0,0],[0,0,0],[0,0,0]];for(h=0;h<c;h++){for(f=0;f<c;f++){d[h][f]=0;b[h][f]=u[h][f];q+=Math.abs(b[h][f])}d[h][h]=1}if(c==1){return[b,d]}if(q<=0){return[b,d]}q/=(c*c);do{m=0;g=0;for(f=1;f<c;f++){for(h=0;h<f;h++){a=Math.abs(b[h][f]);if(a>g){g=a}m+=a;if(a<w){continue}else{a=Math.atan2(2*b[h][f],b[h][h]-b[f][f])*0.5;l=Math.sin(a);s=Math.cos(a);for(e=0;e<c;e++){r=b[e][h];b[e][h]=s*r+l*b[e][f];b[e][f]=-l*r+s*b[e][f];r=d[e][h];d[e][h]=s*r+l*d[e][f];d[e][f]=-l*r+s*d[e][f]}b[h][h]=s*b[h][h]+l*b[f][h];b[f][f]=-l*b[h][f]+s*b[f][f];b[h][f]=0;for(e=0;e<c;e++){b[h][e]=b[e][h];b[f][e]=b[e][f]}}}}}while(Math.abs(m)/q>w);return[b,d]};JXG.Math.Numerics.NewtonCotes=function(d,g){var b=0,a=(d[1]-d[0])/this.number_of_nodes,h,e,c;switch(this.integration_type){case JXG.INT_TRAPEZ:b=(g(d[0])+g(d[1]))*0.5;h=d[0];for(e=0;e<this.number_of_nodes-1;e++){h+=a;b+=g(h)}b*=a;break;case JXG.INT_SIMPSON:if(this.number_of_nodes%2>0){throw new Error("JSXGraph: INT_SIMPSON requires JXG.Math.Numerics.number_of_nodes dividable by 2.")}c=this.number_of_nodes/2;b=g(d[0])+g(d[1]);h=d[0];for(e=0;e<c-1;e++){h+=2*a;b+=2*g(h)}h=d[0]-a;for(e=0;e<c;e++){h+=2*a;b+=4*g(h)}b*=a/3;break;default:if(this.number_of_nodes%4>0){throw new Error("JSXGraph: Error in INT_MILNE: JXG.Math.Numerics.number_of_nodes must be a multiple of 4")}c=this.number_of_nodes*0.25;b=7*(g(d[0])+g(d[1]));h=d[0];for(e=0;e<c-1;e++){h+=4*a;b+=14*g(h)}h=d[0]-3*a;for(e=0;e<c;e++){h+=4*a;b+=32*(g(h)+g(h+2*a))}h=d[0]-2*a;for(e=0;e<c;e++){h+=4*a;b+=12*g(h)}b*=2*a/45}return b};JXG.Math.Numerics.splineDef=function(k,h){var a=k.length,c,e,f,g,b,d=new Array(),r=[],m=[],q;if(k.length!=h.length){throw new Error("JSXGraph: Error in JXG.Math.Numerics.splineDef: Input vector dimensions do not match.")}for(e=0;e<a;e++){c={X:k[e],Y:h[e]};d.push(c)}d.sort(function(n,l){return n.X-l.X});for(e=0;e<a;e++){k[e]=d[e].X;h[e]=d[e].Y}for(e=0;e<a-1;e++){r.push(k[e+1]-k[e])}for(e=0;e<a-2;e++){m.push(6*(h[e+2]-h[e+1])/(r[e+1])-6*(h[e+1]-h[e])/(r[e]))}f=new Array();g=new Array();f.push(2*(r[0]+r[1]));g.push(m[0]);for(e=0;e<a-3;e++){b=r[e+1]/f[e];f.push(2*(r[e+1]+r[e+2])-b*r[e+1]);g.push(m[e+1]-b*g[e])}q=new Array();q[a-3]=g[a-3]/f[a-3];for(e=a-4;e>=0;e--){q[e]=(g[e]-(r[e+1]*q[e+1]))/f[e]}for(e=a-3;e>=0;e--){q[e+1]=q[e]}q[0]=0;q[a-1]=0;return q};JXG.Math.Numerics.splineEval=function(f,z,v,B){var g=z.length,k=1,h=false,A,q,m,w,u,s,r,e;if(g!=v.length){throw new Error("JSXGraph: Error in JXG.Math.Numerics.splineEval: Defining vector dimensions do not match.")}if(JXG.isArray(f)){k=f.length;h=true}else{f=[f]}A=new Array();for(q=0;q<k;q++){if((f[q]<z[0])||(z[q]>z[g-1])){return"NaN"}m;for(m=1;m<g;m++){if(f[q]<=z[m]){break}}m--;w=v[m];u=(v[m+1]-v[m])/(z[m+1]-z[m])-(z[m+1]-z[m])/6*(B[m+1]+2*B[m]);s=B[m]/2;r=(B[m+1]-B[m])/(6*(z[m+1]-z[m]));e=f[q]-z[m];A.push(w+(u+(s+r*e)*e)*e)}if(h){return A}else{return A[0]}};JXG.Math.Numerics.generatePolynomialTerm=function(a,f,b,c){var e="",d;for(d=f;d>=0;d--){e+="("+a[d].toPrecision(c)+")";if(d>1){e+="*"+b+"<sup>"+d+"</sup> + "}else{if(d==1){e+="*"+b+" + "}}}return e};JXG.Math.Numerics.lagrangePolynomial=function(d){var a=[];var c="";var b=function(q,e){var g,f,m,n,r,h=0,l=0;m=d.length;if(!e){for(g=0;g<m;g++){a[g]=1;n=d[g].X();for(f=0;f<m;f++){if(f!=g){a[g]*=(n-d[f].X())}}a[g]=1/a[g]}M=[];for(j=0;j<m;j++){M.push([1])}}for(g=0;g<m;g++){n=d[g].X();if(q==n){return d[g].Y()}else{r=a[g]/(q-n);l+=r;h+=r*d[g].Y()}}return h/l};b.getTerm=function(){return c};return b};JXG.Math.Numerics.neville=function(d){var a=[];var c=function(q,e){var g,m,n,r,u=JXG.Math.binomial,l=d.length,f=l-1,h=0,k=0;if(!e){r=1;for(g=0;g<l;g++){a[g]=u(f,g)*r;r*=(-1)}}m=q;for(g=0;g<l;g++){if(m==0){return d[g].X()}else{r=a[g]/m;m--;h+=d[g].X()*r;k+=r}}return h/k};var b=function(q,e){var g,m,n,r,u=JXG.Math.binomial,l=d.length,f=l-1,h=0,k=0;if(!e){r=1;for(g=0;g<l;g++){a[g]=u(f,g)*r;r*=(-1)}}m=q;for(g=0;g<l;g++){if(m==0){return d[g].Y()}else{r=a[g]/m;m--;h+=d[g].Y()*r;k+=r}}return h/k};return[c,b,0,function(){return d.length-1}]};JXG.Math.Numerics.regressionPolynomial=function(e,l,k){var a=[],f=0,b,h,g,c,d="";if(JXG.isPoint(e)&&typeof e.Value=="function"){b=function(){return e.Value()}}else{if(JXG.isFunction(e)){b=e}else{if(JXG.isNumber(e)){b=function(){return e}}else{throw new Error("JSXGraph: Can't create regressionPolynomial from degree of type'"+(typeof e)+"'.")}}}if(arguments.length==3&&JXG.isArray(l)&&JXG.isArray(k)){c=0}else{if(arguments.length==2&&JXG.isArray(l)&&JXG.isPoint(l[0])){c=1}else{throw new Error("JSXGraph: Can't create regressionPolynomial. Wrong parameters.")}}var m=function(E,n){var u,r,A,w,D,q,C,F,z,v=l.length;z=Math.floor(b());if(!n){if(c==1){h=[];g=[];for(u=0;u<v;u++){h[u]=l[u].X();g[u]=l[u].Y()}}if(c==0){h=[];g=[];for(u=0;u<v;u++){if(JXG.isFunction(l[u])){h.push(l[u]())}else{h.push(l[u])}if(JXG.isFunction(k[u])){g.push(k[u]())}else{g.push(k[u])}}}A=[];for(r=0;r<v;r++){A.push([1])}for(u=1;u<=z;u++){for(r=0;r<v;r++){A[r][u]=A[r][u-1]*h[r]}}D=g;w=JXG.Math.Matrix.transpose(A);q=JXG.Math.matMatMult(w,A);C=JXG.Math.matVecMult(w,D);a=JXG.Math.Numerics.Gauss(q,C);d=JXG.Math.Numerics.generatePolynomialTerm(a,z,"x",3)}F=a[z];for(u=z-1;u>=0;u--){F=(F*E+a[u])}return F};m.getTerm=function(){return d};return m};JXG.Math.Numerics.bezier=function(b){var a=0;return[function(d,c){var g=Math.floor(d)*3,f=d%1,e=1-f;if(!c){a=Math.floor(b.length/3)}if(d<0){return b[0].X()}if(d>=a){return b[b.length-1].X()}if(isNaN(d)){return NaN}return e*e*(e*b[g].X()+3*f*b[g+1].X())+(3*e*b[g+2].X()+f*b[g+3].X())*f*f},function(d,c){var g=Math.floor(d)*3,f=d%1,e=1-f;if(!c){a=Math.floor(b.length/3)}if(d<0){return b[0].Y()}if(d>=a){return b[b.length-1].Y()}if(isNaN(d)){return NaN}return e*e*(e*b[g].Y()+3*f*b[g+1].Y())+(3*e*b[g+2].Y()+f*b[g+3].Y())*f*f},0,function(){return Math.floor(b.length/3)}]};JXG.Math.Numerics.D=function(c,d){var b=0.00001,a=1/(b*2);if(arguments.length==1||(arguments.length>1&&typeof arguments[1]=="undefined")){return function(e,f){return(c(e+b,f)-c(e-b,f))*a}}else{return function(e,f){return(c.apply(d,[e+b,f])-c.apply(d,[e-b,f]))*a}}};JXG.Math.Numerics.I=function(a,b){return JXG.Math.Numerics.NewtonCotes(a,b)};JXG.Math.Numerics.newton=function(e,a,g){var b=0,c=0.000001,d=e.apply(g,[a]),k;while(b<50&&Math.abs(d)>c){k=this.D(e,g)(a);if(Math.abs(k)>c){a-=d/k}else{a+=(Math.random()*0.2-1)}d=e.apply(g,[a]);b++}return a};JXG.Math.Numerics.root=function(b,a,c){return this.newton(b,a,c)};JXG.Math.Numerics.riemann=function(l,e,m,c,g){var d,v,k,u,h,s,q,b,a,r;d=[];v=[];h=0;s=c;e=Math.floor(e);d[h]=s;v[h]=0;if(e>0){u=(g-c)/e;a=u*0.01;for(k=0;k<e;k++){if(m=="right"){q=l(s+u)}else{if(m=="middle"){q=l(s+u*0.5)}else{if((m=="left")||(m=="trapezodial")){q=l(s)}else{if(m=="lower"){q=l(s);for(b=s+a;b<=s+u;b+=a){r=l(b);if(r<q){q=r}}}else{q=l(s);for(b=s+a;b<=s+u;b+=a){r=l(b);if(r>q){q=r}}}}}}h++;d[h]=s;v[h]=q;h++;s+=u;if(m=="trapezodial"){q=l(s)}d[h]=s;v[h]=q;h++;d[h]=s;v[h]=0}}return[d,v]};JXG.Math.Numerics.riemannsum=function(h,d,l,c,e){var k,g,s,r,m,b,a,q;k=0;r=c;d=Math.floor(d);if(d>0){s=(e-c)/d;a=s*0.01;for(g=0;g<d;g++){if(l=="right"){m=h(r+s)}else{if(l=="middle"){m=h(r+s*0.5)}else{if(l=="trapezodial"){m=0.5*(h(r+s)+h(r))}else{if(l=="left"){m=h(r)}else{if(l=="lower"){m=h(r);for(b=r+a;b<=r+s;b+=a){q=h(b);if(q<m){m=q}}}else{m=h(r);for(b=r+a;b<=r+s;b+=a){q=h(b);if(q>m){m=q}}}}}}}k+=s*m;r+=s}}return k};JXG.Math.Numerics.Butcher=function(){this.s=0;this.A=[];this.b=[];this.c=[]};JXG.Math.Numerics.predefinedButcher={};JXG.Math.Numerics.predefinedButcher.RK4={s:4,A:[[0,0,0,0],[0.5,0,0,0],[0,0.5,0,0],[0,0,1,0]],b:[1/6,1/3,1/3,1/6],c:[0,0.5,0.5,1]};JXG.Math.Numerics.predefinedButcher.Heun={s:2,A:[[0,0],[1,0]],b:[0.5,0.5],c:[0,1]};JXG.Math.Numerics.predefinedButcher.Euler={s:1,A:[[0]],b:[1],c:[0]};JXG.Math.Numerics.rungeKutta=function(c,G,m,d,F){var n=[],g=[],E=(m[1]-m[0])/d,u=m[0],H,D,C,A,z,B=G.length,v=c.s,b=1000,a=d/b,q=[],w=0;for(H=0;H<B;H++){n[H]=G[H]}for(D=0;D<d;D++){q[w]=[];for(H=0;H<B;H++){q[w][H]=n[H]}w++;A=[];for(C=0;C<v;C++){for(H=0;H<B;H++){g[H]=0}for(z=0;z<C;z++){for(H=0;H<B;H++){g[H]+=(c.A[C][z])*E*A[z][H]}}for(H=0;H<B;H++){g[H]+=n[H]}A.push(F(u+c.c[C]*E,g))}for(H=0;H<B;H++){g[H]=0}for(z=0;z<v;z++){for(H=0;H<B;H++){g[H]+=c.b[z]*A[z][H]}}for(H=0;H<B;H++){n[H]=n[H]+E*g[H]}u+=E}return q};JXG.Math.Statistics={};JXG.Math.Statistics.sum=function(b){var d,a,c=0;for(d=0,a=b.length;d<a;d++){c+=b[d]}return c};JXG.Math.Statistics.prod=function(b){var d,a,c=1;for(d=0,a=b.length;d<a;d++){c*=b[d]}return c};JXG.Math.Statistics.mean=function(a){if(a.length>0){return this.sum(a)/a.length}else{return 0}};JXG.Math.Statistics.median=function(b){var c,a;if(b.length>0){c=b.clone();c.sort(function(e,d){return e-d});a=c.length;if(a%2==1){return c[parseInt(a*0.5)]}else{return(c[a*0.5-1]+c[a*0.5])*0.5}}else{return 0}};JXG.Math.Statistics.variance=function(c){var b,e,d,a;if(c.length>1){b=this.mean(c);e=0;for(d=0,a=c.length;d<a;d++){e+=(c[d]-b)*(c[d]-b)}return e/(c.length-1)}else{return 0}};JXG.Math.Statistics.sd=function(a){return Math.sqrt(this.variance(a))};JXG.Math.Statistics.weightedMean=function(a,b){if(a.length!=b.length){return}if(a.length>0){return this.mean(this.multiply(a,b))}else{return 0}};JXG.Math.Statistics.max=function(b){var d,c,a;if(b.length==0){return NaN}d=b[0];for(c=1,a=b.length;c<a;c++){d=(b[c]>d)?(b[c]):d}return d};JXG.Math.Statistics.min=function(b){var d,c,a;if(b.length==0){return NaN}d=b[0];for(c=1,a=b.length;c<a;c++){d=(b[c]<d)?(b[c]):d}return d};JXG.Math.Statistics.range=function(a){return[this.min(a),this.max(a)]};JXG.Math.Statistics.diff=function(a){return a};JXG.Math.Statistics.min=function(b){var d,c,a;if(b.length==0){return NaN}d=b[0];for(c=1,a=b.length;c<a;c++){d=(b[c]<d)?(b[c]):d}return d};JXG.Math.Statistics.abs=function(b){var d,a,c=[];if(typeof JXG.isArray(arr1)){for(d=0,a=b.length;d<a;d++){c[d]=Math.abs(b[d])}}else{if(typeof b=="number"){return Math.abs(b)}else{c=null}}return c};JXG.Math.Statistics.add=function(c,b){var e,a,d=[];if(typeof JXG.isArray(c)&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]+b}}else{if(typeof c=="number"&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c+b[e]}}else{if(typeof JXG.isArray(c)&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]+b[e]}}else{if(typeof c=="number"&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c+b}}else{d=null}}}}return d};JXG.Math.Statistics.divide=function(c,b){var e,a,d=[];if(typeof JXG.isArray(c)&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]/b}}else{if(typeof c=="number"&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c/b[e]}}else{if(typeof JXG.isArray(c)&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]/b[e]}}else{if(typeof c=="number"&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c/b}}else{d=null}}}}return d};JXG.Math.Statistics.mod=function(c,b){var e,a,d=[];if(typeof JXG.isArray(c)&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]%b}}else{if(typeof c=="number"&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c%b[e]}}else{if(typeof JXG.isArray(c)&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]%b[e]}}else{if(typeof c=="number"&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c%b}}else{d=null}}}}return d};JXG.Math.Statistics.multiply=function(c,b){var e,a,d=[];if(typeof JXG.isArray(c)&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]*b}}else{if(typeof c=="number"&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c*b[e]}}else{if(typeof JXG.isArray(c)&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]*b[e]}}else{if(typeof c=="number"&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c*b}}else{d=null}}}}return d};JXG.Math.Statistics.subtract=function(c,b){var e,a,d=[];if(typeof JXG.isArray(c)&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]-b}}else{if(typeof c=="number"&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c-b[e]}}else{if(typeof JXG.isArray(c)&&typeof JXG.isArray(b)){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c[e]-b[e]}}else{if(typeof c=="number"&&typeof b=="number"){for(e=0,a=Math.min(c.length,b.length);e<a;e++){d[e]=c-b}}else{d=null}}}}return d};JXG.Math.Symbolic={};JXG.Math.Symbolic.generateSymbolicCoordinatesPartial=function(l,e,d,b){function a(k){if(b=="underscore"){return""+d+"_{"+k+"}"}else{if(b=="brace"){return""+d+"["+k+"]"}else{return""+d+""+k}}}var g=e.ancestors;var f=0;var h;for(var m in g){h=0;if(JXG.isPoint(g[m])){for(var c in g[m].ancestors){h++}if(h==0){g[m].symbolic.x=g[m].coords.usrCoords[1];g[m].symbolic.y=g[m].coords.usrCoords[2]}else{f++;g[m].symbolic.x=a(f);f++;g[m].symbolic.y=a(f)}}}if(JXG.isPoint(e)){e.symbolic.x="x";e.symbolic.y="y"}return f};JXG.Math.Symbolic.clearSymbolicCoordinates=function(b){for(var a in b.objects){if(JXG.isPoint(b.objects[a])){b.objects[a].symbolic.x="";b.objects[a].symbolic.y=""}}};JXG.Math.Symbolic.generatePolynomials=function(g,c,d){if(d){this.generateSymbolicCoordinatesPartial(g,c,"u","brace")}var f=c.ancestors,h,e=[],m=[],l,a,b;f[c.id]=c;for(l in f){h=0;e=[];if(JXG.isPoint(f[l])){for(a in f[l].ancestors){h++}if(h>0){e=f[l].generatePolynomial();for(b=0;b<e.length;b++){m.push(e[b])}}}}if(d){this.clearSymbolicCoordinates(g)}return m};JXG.Math.Symbolic.geometricLocusByGroebnerBase=function(e,g,k){var f=this.generateSymbolicCoordinatesPartial(e,g,"u","brace"),a=this.generatePolynomials(e,g);var c=a.join(","),b=new JXG.Coords(JXG.COORDS_BY_USR,[0,0],e),d=new JXG.Coords(JXG.COORDS_BY_USR,[e.canvasWidth,e.canvasHeight],e),h;if(typeof JXG.Server.modules.geoloci=="undefined"){JXG.Server.loadModule("geoloci")}if(typeof JXG.Server.modules.geoloci=="undefined"){throw new Error("JSXGraph: Unable to load JXG.Server module 'geoloci.py'.")}this.cbp=function(l){k(l.datax,l.datay,l.polynomial)};this.cb=JXG.bind(this.cbp,this);JXG.Server.modules.geoloci.lociCoCoA(b.usrCoords[1],d.usrCoords[1],d.usrCoords[2],b.usrCoords[2],f,c,this.cb);this.clearSymbolicCoordinates(e)};JXG.Math.Geometry={};JXG.Math.Geometry.angle=function(f,e,d){var k=[],h=[],g=[],m,l,q,n;if(f.coords==null){k[0]=f[0];k[1]=f[1]}else{k[0]=f.coords.usrCoords[1];k[1]=f.coords.usrCoords[2]}if(e.coords==null){h[0]=e[0];h[1]=e[1]}else{h[0]=e.coords.usrCoords[1];h[1]=e.coords.usrCoords[2]}if(d.coords==null){g[0]=d[0];g[1]=d[1]}else{g[0]=d.coords.usrCoords[1];g[1]=d.coords.usrCoords[2]}m=k[0]-h[0];l=k[1]-h[1];q=g[0]-h[0];n=g[1]-h[1];return Math.atan2(m*n-l*q,m*q+l*n)};JXG.Math.Geometry.trueAngle=function(a,c,b){return this.rad(a,c,b)*57.29577951308232};JXG.Math.Geometry.rad=function(q,n,m){var h,e,x,w,c,b,g,f,l,k,d,u,s,y,r,v,a=0;if(q.coords==null){h=q[0];e=q[1]}else{h=q.coords.usrCoords[1];e=q.coords.usrCoords[2]}if(n.coords==null){x=n[0];w=n[1]}else{x=n.coords.usrCoords[1];w=n.coords.usrCoords[2]}if(m.coords==null){c=m[0];b=m[1]}else{c=m.coords.usrCoords[1];b=m.coords.usrCoords[2]}l=c-x;k=b-w;g=h-x;f=e-w;v=l*g+k*f;d=g*k-f*l;u=Math.sqrt(g*g+f*f);s=Math.sqrt(l*l+k*k);y=v/(u*s);if(y>1){y=1}else{if(y<-1){y=-1}}r=Math.acos(y);if((Math.sin(r)*d)<0){a=6.283185307179586-r}else{a=r}return a};JXG.Math.Geometry.angleBisector=function(f,e,b,k){var c=f.coords.usrCoords,n=e.coords.usrCoords,g=b.coords.usrCoords,q=c[1]-n[1],m=c[2]-n[2],l=Math.sqrt(q*q+m*m),a,r,h;if(typeof k=="undefined"){k=f.board}q/=l;m/=l;a=Math.acos(q);if(m<0){a*=-1}if(a<0){a+=2*Math.PI}q=g[1]-n[1];m=g[2]-n[2];l=Math.sqrt(q*q+m*m);q/=l;m/=l;r=Math.acos(q);if(m<0){r*=-1}if(r<0){r+=2*Math.PI}h=(a+r)*0.5;if(a>r){h+=Math.PI}q=Math.cos(h)+n[1];m=Math.sin(h)+n[2];return new JXG.Coords(JXG.COORDS_BY_USER,[q,m],k)};JXG.Math.Geometry.reflection=function(n,k,c){var e=k.coords.usrCoords,q=n.point1.coords.usrCoords,d=n.point2.coords.usrCoords,b,h,a,f,l,g,m;if(typeof c=="undefined"){c=k.board}l=d[1]-q[1];g=d[2]-q[2];b=e[1]-q[1];h=e[2]-q[2];m=(l*h-g*b)/(l*l+g*g);a=e[1]+2*m*g;f=e[2]-2*m*l;return new JXG.Coords(JXG.COORDS_BY_USER,[a,f],c)};JXG.Math.Geometry.rotation=function(a,n,f,g){var k=n.coords.usrCoords,b=a.coords.usrCoords,e,m,h,q,d,l;if(typeof g=="undefined"){g=n.board}e=k[1]-b[1];m=k[2]-b[2];h=Math.cos(f);q=Math.sin(f);d=e*h-m*q+b[1];l=e*q+m*h+b[2];return new JXG.Coords(JXG.COORDS_BY_USER,[d,l],g)};JXG.Math.Geometry.perpendicular=function(r,n,f){var e=r.point1.coords.usrCoords,d=r.point2.coords.usrCoords,b=n.coords.usrCoords,l,k,h,q,g,c,a,m;if(typeof f=="undefined"){f=n.board}if(n==r.point1){l=e[1]+d[2]-e[2];k=e[2]-d[1]+e[1];h=true}else{if(n==r.point2){l=d[1]+e[2]-d[2];k=d[2]-e[1]+d[1];h=false}else{if(((Math.abs(e[1]-d[1])>JXG.Math.eps)&&(Math.abs(b[2]-(e[2]-d[2])*(b[1]-e[1])/(e[1]-d[1])-e[2])<JXG.Math.eps))||((Math.abs(e[1]-d[1])<=JXG.Math.eps)&&(Math.abs(e[1]-b[1])<JXG.Math.eps))){l=b[1]+d[2]-b[2];k=b[2]-d[1]+b[1];h=true;if(Math.abs(l-b[1])<JXG.Math.eps&&Math.abs(k-b[2])<JXG.Math.eps){l=b[1]+e[2]-b[2];k=b[2]-e[1]+b[1];h=false}}else{q=e[2]-d[2];g=e[1]-d[1];c=d[1]*q-d[2]*g;a=b[1]*g+b[2]*q;m=q*q+g*g;if(Math.abs(m)<JXG.Math.eps){m=JXG.Math.eps}l=(c*q+a*g)/m;k=(a*q-c*g)/m;h=true}}}return[new JXG.Coords(JXG.COORDS_BY_USER,[l,k],f),h]};JXG.Math.Geometry.circumcenterMidpoint=function(h,f,e,d){var c=h.coords.usrCoords,b=f.coords.usrCoords,a=e.coords.usrCoords,n,m,l,k,g;if(typeof d=="undefined"){d=h.board}n=((c[1]-b[1])*(c[1]+b[1])+(c[2]-b[2])*(c[2]+b[2]))*0.5;m=((b[1]-a[1])*(b[1]+a[1])+(b[2]-a[2])*(b[2]+a[2]))*0.5;l=(c[1]-b[1])*(b[2]-a[2])-(b[1]-a[1])*(c[2]-b[2]);if(Math.abs(l)<JXG.Math.eps){l=JXG.Math.eps}k=(n*(b[2]-a[2])-m*(c[2]-b[2]))/l;g=(m*(c[1]-b[1])-n*(b[1]-a[1]))/l;return new JXG.Coords(JXG.COORDS_BY_USER,[k,g],d)};JXG.Math.Geometry.distance=function(e,d){var c=0,b,a;if(e.length!=d.length){return}a=e.length;for(b=0;b<a;b++){c+=(e[b]-d[b])*(e[b]-d[b])}return Math.sqrt(c)};JXG.Math.Geometry.affineDistance=function(b,a){var c;if(b.length!=a.length){return}c=this.distance(b,a);if(c>JXG.Math.eps&&(Math.abs(b[0])<JXG.Math.eps||Math.abs(a[0])<JXG.Math.eps)){return Infinity}else{return c}};JXG.Math.Geometry.intersectLineLine=function(n,m,g){var f=n.point1.coords.usrCoords,d=n.point2.coords.usrCoords,c=m.point1.coords.usrCoords,a=m.point2.coords.usrCoords,e,b,l,k,h;if(typeof g=="undefined"){g=n.board}e=f[1]*d[2]-f[2]*d[1];b=c[1]*a[2]-c[2]*a[1];l=(d[2]-f[2])*(c[1]-a[1])-(f[1]-d[1])*(a[2]-c[2]);if(Math.abs(l)<JXG.Math.eps){l=JXG.Math.eps}k=(e*(c[1]-a[1])-b*(f[1]-d[1]))/l;h=(b*(d[2]-f[2])-e*(a[2]-c[2]))/l;return new JXG.Coords(JXG.COORDS_BY_USER,[k,h],g)};JXG.Math.Geometry.intersectCircleLine=function(k,A,m){var N=A.point1.coords.usrCoords,K=A.point2.coords.usrCoords,e=k.midpoint.coords.usrCoords,E,a,L,J,C,H,F,n,D,B,g,f,G,v,q,c,z,u,I;if(typeof m=="undefined"){m=A.board}E=A.point1.Dist(A.point2);if(E>0){a=k.midpoint.Dist(A.point1);L=k.midpoint.Dist(A.point2);J=((a*a)+(E*E)-(L*L))/(2*E);C=(a*a)-(J*J);C=(C<0)?0:C;H=Math.sqrt(C);F=k.Radius();n=Math.sqrt((F*F)-H*H);D=K[1]-N[1];B=K[2]-N[2];g=e[1]+(H/E)*B;f=e[2]-(H/E)*D;a=(K[1]*B)-(K[2]*D);L=(g*D)+(f*B);G=(B*B)+(D*D);if(Math.abs(G)<JXG.Math.eps){G=JXG.Math.eps}v=((a*B)+(L*D))/G;q=((L*B)-(a*D))/G;c=n/E;z=new JXG.Coords(JXG.COORDS_BY_USER,[v+c*D,q+c*B],m);u=new JXG.Coords(JXG.COORDS_BY_USER,[v-c*D,q-c*B],m);I=k.midpoint.coords.distance(JXG.COORDS_BY_USER,z);if((F<(I-1))||isNaN(I)){return[0]}else{return[2,z,u]}}return[0]};JXG.Math.Geometry.intersectCircleCircle=function(l,k,n){var c={},f=l.Radius(),e=k.Radius(),d=l.midpoint.coords.usrCoords,b=k.midpoint.coords.usrCoords,r,g,w,v,u,q,m;if(typeof n=="undefined"){n=l.board}r=f+e;g=Math.abs(f-e);w=l.midpoint.coords.distance(JXG.COORDS_BY_USER,k.midpoint.coords);if(w>r){return[0]}else{if(w<g){return[0]}else{if(w!=0){c[0]=1;v=b[1]-d[1];u=b[2]-d[2];q=(w*w-e*e+f*f)/(2*w);m=Math.sqrt(f*f-q*q);c[1]=new JXG.Coords(JXG.COORDS_BY_USER,[d[1]+(q/w)*v+(m/w)*u,d[2]+(q/w)*u-(m/w)*v],n);c[2]=new JXG.Coords(JXG.COORDS_BY_USER,[d[1]+(q/w)*v-(m/w)*u,d[2]+(q/w)*u+(m/w)*v],n)}else{return[0]}return c}}};JXG.Math.Geometry.meet=function(d,b,c,e){var a=JXG.Math.eps;if(Math.abs(d[3])<a&&Math.abs(b[3])<a){return this.meetLineLine(d,b,c,e)}else{if(Math.abs(d[3])>=a&&Math.abs(b[3])<a){return this.meetLineCircle(b,d,c,e)}else{if(Math.abs(d[3])<a&&Math.abs(b[3])>=a){return this.meetLineCircle(d,b,c,e)}else{return this.meetCircleCircle(d,b,c,e)}}}};JXG.Math.Geometry.meetLineLine=function(b,a,c,e){var d=JXG.Math.crossProduct(b,a);if(Math.abs(d[0])>JXG.Math.eps){d[1]/=d[0];d[2]/=d[0];d[0]=1}return new JXG.Coords(JXG.COORDS_BY_USER,d,e)};JXG.Math.Geometry.meetLineCircle=function(l,e,r,s){var x,w,v,u,m,h,g,f,q,y;if(e[4]<JXG.Math.eps){return new JXG.Coords(JXG.COORDS_BY_USER,e.slice(1,3),s)}v=e[0];w=e.slice(1,3);x=e[3];u=l[0];m=l.slice(1,3);h=x;g=(w[0]*m[1]-w[1]*m[0]);f=x*u*u-(w[0]*m[0]+w[1]*m[1])*u+v;q=g*g-4*h*f;if(q>=0){q=Math.sqrt(q);y=[(-g+q)/(2*h),(-g-q)/(2*h)];return((r==0)?new JXG.Coords(JXG.COORDS_BY_USER,[-y[0]*(-m[1])-u*m[0],-y[0]*m[0]-u*m[1]],s):new JXG.Coords(JXG.COORDS_BY_USER,[-y[1]*(-m[1])-u*m[0],-y[1]*m[0]-u*m[1]],s))}else{return new JXG.Coords(JXG.COORDS_BY_USER,[NaN,NaN],s)}};JXG.Math.Geometry.meetCircleCircle=function(c,a,b,d){var e;if(c[4]<JXG.Math.eps){if(this.distance(c.slice(1,3),a.slice(1,3))==a[4]){return new JXG.Coords(JXG.COORDS_BY_USER,c.slice(1,3),d)}else{return new JXG.Coords(JXG.COORDS_BY_USER,[NaN,NaN],d)}}if(a[4]<JXG.Math.eps){if(this.distance(a.slice(1,3),c.slice(1,3))==c[4]){return new JXG.Coords(JXG.COORDS_BY_USER,a.slice(1,3),d)}else{return new JXG.Coords(JXG.COORDS_BY_USER,[NaN,NaN],d)}}e=[a[3]*c[0]-c[3]*a[0],a[3]*c[1]-c[3]*a[1],a[3]*c[2]-c[3]*a[2],0,1,Infinity,Infinity,Infinity];e=JXG.Math.normalize(e);return this.meetLineCircle(e,c,b,d)};JXG.Math.Geometry.meetCurveCurve=function(w,v,h,m,q){var n=0,s,r,E,C,A,z,g,y,x,u,D,B,l,k;if(typeof q=="undefined"){q=w.board}if(arguments.callee.t1memo){s=arguments.callee.t1memo;r=arguments.callee.t2memo}else{s=h;r=m}y=w.X(s)-v.X(r);x=w.Y(s)-v.Y(r);u=y*y+x*x;D=w.board.D(w.X,w);B=v.board.D(v.X,v);l=w.board.D(w.Y,w);k=v.board.D(v.Y,v);while(u>JXG.Math.eps&&n<10){E=D(s);C=-B(r);A=l(s);z=-k(r);g=E*z-C*A;s-=(z*y-C*x)/g;r-=(E*x-A*y)/g;y=w.X(s)-v.X(r);x=w.Y(s)-v.Y(r);u=y*y+x*x;n++}arguments.callee.t1memo=s;arguments.callee.t2memo=r;if(Math.abs(s)<Math.abs(r)){return(new JXG.Coords(JXG.COORDS_BY_USER,[w.X(s),w.Y(s)],q))}else{return(new JXG.Coords(JXG.COORDS_BY_USER,[v.X(r),v.Y(r)],q))}};JXG.Math.Geometry.meetCurveLine=function(c,a,r,l){var v,f,e,g,u,b,n,d,q,s,m,k,h;if(typeof l=="undefined"){l=c.board}for(e=0;e<=1;e++){if(arguments[e].elementClass==JXG.OBJECT_CLASS_CURVE){g=arguments[e]}else{if(arguments[e].elementClass==JXG.OBJECT_CLASS_LINE){u=arguments[e]}else{throw new Error("JSXGraph: Can't call meetCurveLine with parent class "+(arguments[e].elementClass)+".")}}}b=function(w){return u.stdform[0]*1+u.stdform[1]*g.X(w)+u.stdform[2]*g.Y(w)};if(arguments.callee.t1memo){m=arguments.callee.t1memo}else{m=g.minX()}v=JXG.Math.Numerics.root(b,m);arguments.callee.t1memo=v;k=g.X(v);h=g.Y(v);if(r==1){if(arguments.callee.t2memo){m=arguments.callee.t2memo;f=JXG.Math.Numerics.root(b,m)}if(!(Math.abs(f-v)>0.1&&Math.abs(k-g.X(f))>0.1&&Math.abs(h-g.Y(f))>0.1)){q=20;s=(g.maxX()-g.minX())/q;d=g.minX();for(e=0;e<q;e++){f=JXG.Math.Numerics.root(b,d);if(Math.abs(f-v)>0.1&&Math.abs(k-g.X(f))>0.1&&Math.abs(h-g.Y(f))>0.1){break}d+=s}}v=f;arguments.callee.t2memo=v}if(Math.abs(b(v))>JXG.Math.eps){n=0}else{n=1}return(new JXG.Coords(JXG.COORDS_BY_USER,[n,g.X(v),g.Y(v)],l))};JXG.Math.Geometry.projectPointToCircle=function(k,a,c){var f=k.coords.distance(JXG.COORDS_BY_USER,a.midpoint.coords),b=k.coords.usrCoords,d=a.midpoint.coords.usrCoords,h,g,e;if(typeof c=="undefined"){c=k.board}if(Math.abs(f)<JXG.Math.eps){f=JXG.Math.eps}e=a.Radius()/f;h=d[1]+e*(b[1]-d[1]);g=d[2]+e*(b[2]-d[2]);return new JXG.Coords(JXG.COORDS_BY_USER,[h,g],c)};JXG.Math.Geometry.projectPointToLine=function(a,b,d){var c=[0,b.stdform[1],b.stdform[2]];if(typeof d=="undefined"){d=a.board}c=JXG.Math.crossProduct(c,a.coords.usrCoords);return this.meetLineLine(c,b.stdform,0,d)};JXG.Math.Geometry.projectPointToCurve=function(c,f,e){if(typeof e=="undefined"){e=c.board}var b=c.X(),g=c.Y(),d=c.position||0,a=this.projectCoordsToCurve(b,g,d,f,e);c.position=a[1];return a[0]};JXG.Math.Geometry.projectCoordsToCurve=function(k,g,m,n,e){var A,w,b,v,a,f,s,z,q,d,r,l=1000000,h,D,B,c,C,u;if(typeof e=="undefined"){e=n.board}if(n.curveType=="parameter"||n.curveType=="polar"){h=function(E){var y=k-n.X(E),x=g-n.Y(E);return y*y+x*x};c=h(m);u=20;C=(n.maxX()-n.minX())/u;D=n.minX();for(r=0;r<u;r++){B=h(D);if(B<c){m=D;c=B}D+=C}m=JXG.Math.Numerics.root(JXG.Math.Numerics.D(h),m);if(m<n.minX()){m=n.maxX()+m-n.minX()}if(m>n.maxX()){m=n.minX()+m-n.maxX()}A=new JXG.Coords(JXG.COORDS_BY_USER,[n.X(m),n.Y(m)],e)}else{if(n.curveType=="plot"){z=l;for(s=0;s<n.numberPoints;s++){w=k-n.X(s);b=g-n.Y(s);q=Math.sqrt(w*w+b*b);if(q<z){z=q;m=s}if(s==n.numberPoints-1){continue}v=n.X(s+1)-n.X(s);a=n.Y(s+1)-n.Y(s);f=v*v+a*a;if(f>=JXG.Math.eps){d=(w*v+b*a)/f;q=Math.sqrt(w*w+b*b-d*(w*v+b*a))}else{d=0;q=Math.sqrt(w*w+b*b)}if(d>=0&&d<=1&&q<z){m=s+d;z=q}}s=Math.floor(m);d=m-s;if(s<n.numberPoints-1){k=d*n.X(s+1)+(1-d)*n.X(s);g=d*n.Y(s+1)+(1-d)*n.Y(s)}else{k=n.X(s);g=n.Y(s)}A=new JXG.Coords(JXG.COORDS_BY_USER,[k,g],e)}else{m=k;k=m;g=n.Y(m);A=new JXG.Coords(JXG.COORDS_BY_USER,[k,g],e)}}return[n.updateTransform(A),m]};JXG.Math.Geometry.projectPointToTurtle=function(m,r,g){var q,s,l,k,c,n=0,f=0,d=1000000,h,a,b,e=r.objects.length;if(typeof g=="undefined"){g=m.board}for(c=0;c<e;c++){a=r.objects[c];if(a.elementClass==JXG.OBJECT_CLASS_CURVE){q=this.projectPointToCurve(m,a);h=this.distance(q.usrCoords,m.coords.usrCoords);if(h<d){l=q.usrCoords[1];k=q.usrCoords[2];s=m.position;d=h;b=a;f=n}n+=a.numberPoints}}q=new JXG.Coords(JXG.COORDS_BY_USER,[l,k],g);m.position=s+f;return b.updateTransform(q)};JXG.Complex=function(a,b){this.isComplex=true;if(typeof a=="undefined"){a=0}if(typeof b=="undefined"){b=0}if(a.isComplex){b=a.imaginary;a=a.real}this.real=a;this.imaginary=b;this.absval=0;this.angle=0};JXG.Complex.prototype.toString=function(){return""+this.real+" + "+this.imaginary+"i"};JXG.Complex.prototype.add=function(a){if(typeof a=="number"){this.real+=a}else{this.real+=a.real;this.imaginary+=a.imaginary}};JXG.Complex.prototype.sub=function(a){if(typeof a=="number"){this.real-=a}else{this.real-=a.real;this.imaginary-=a.imaginary}};JXG.Complex.prototype.mult=function(a){if(typeof a=="number"){this.real*=a;this.imaginary*=a}else{this.real=this.real*a.real-this.imaginary*a.imaginary;this.imaginary=this.real*a.imaginary+this.imaginary*a.real}};JXG.Complex.prototype.div=function(b){var a;if(typeof b=="number"){if(Math.abs(b)<Math.eps){this.real=Infinity;this.imaginary=Infinity;return}this.real/=b;this.imaginary/=b}else{if((Math.abs(b.real)<Math.eps)&&(Math.abs(b.imaginary)<Math.eps)){this.real=Infinity;this.imaginary=Infinity;return}a=b.real*b.real+b.imaginary*b.imaginary;this.real=(this.real*b.real+this.imaginary*b.imaginary)/a;this.imaginary=(this.imaginary*b.real-this.real*b.imaginary)/a}};JXG.C={};JXG.C.add=function(b,a){var c=new JXG.Complex(b);c.add(a);return c};JXG.C.sub=function(b,a){var c=new JXG.Complex(b);c.sub(a);return c};JXG.C.mult=function(b,a){var c=new JXG.Complex(b);c.mult(a);return c};JXG.C.div=function(b,a){var c=new JXG.Complex(b);c.div(a);return c};JXG.AbstractRenderer=function(){this.vOffsetText=8;this.enhancedRendering=true};JXG.AbstractRenderer.prototype.drawPoint=function(a){var b,c=a.visProp.face;if(c=="cross"||c=="x"){b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")}else{if(c=="circle"||c=="o"){b=this.createPrim("circle",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"circle")}else{if(c=="square"||c=="[]"){b=this.createPrim("rect",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"rect")}else{if(c=="plus"||c=="+"){b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")}else{if(c=="diamond"||c=="<>"){b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")}else{if(c=="triangleup"||c=="a"||c=="^"){b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")}else{if(c=="triangledown"||c=="v"){b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")}else{if(c=="triangleleft"||c=="<"){b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")}else{if(c=="triangleright"||c==">"){b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")}}}}}}}}}this.setObjectStrokeWidth(a,a.visProp.strokeWidth);this.setObjectStrokeColor(a,a.visProp.strokeColor,a.visProp.strokeOpacity);this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillOpacity);this.updatePoint(a)};JXG.AbstractRenderer.prototype.updatePoint=function(b){var a=b.visProp.size,c=b.visProp.face;if(isNaN(b.coords.scrCoords[2])||isNaN(b.coords.scrCoords[1])){return}if(this.enhancedRendering){if(!b.visProp.draft){this.setObjectStrokeWidth(b,b.visProp.strokeWidth);this.setObjectStrokeColor(b,b.visProp.strokeColor,b.visProp.strokeOpacity);this.setObjectFillColor(b,b.visProp.fillColor,b.visProp.fillOpacity)}else{this.setDraft(b)}}a*=((!b.board||!b.board.options.point.zoom)?1:Math.sqrt(b.board.zoomX*b.board.zoomY));if(c=="cross"||c=="x"){this.updatePathPrim(b.rendNode,this.updatePathStringPoint(b,a,"x"),b.board)}else{if(c=="circle"||c=="o"){this.updateCirclePrim(b.rendNode,b.coords.scrCoords[1],b.coords.scrCoords[2],a+1)}else{if(c=="square"||c=="[]"){this.updateRectPrim(b.rendNode,b.coords.scrCoords[1]-a,b.coords.scrCoords[2]-a,a*2,a*2)}else{if(c=="plus"||c=="+"){this.updatePathPrim(b.rendNode,this.updatePathStringPoint(b,a,"+"),b.board)}else{if(c=="diamond"||c=="<>"){this.updatePathPrim(b.rendNode,this.updatePathStringPoint(b,a,"diamond"),b.board)}else{if(c=="triangleup"||c=="a"){this.updatePathPrim(b.rendNode,this.updatePathStringPoint(b,a,"A"),b.board)}else{if(c=="triangledown"||c=="v"){this.updatePathPrim(b.rendNode,this.updatePathStringPoint(b,a,"v"),b.board)}else{if(c=="triangleleft"||c=="<"){this.updatePathPrim(b.rendNode,this.updatePathStringPoint(b,a,"<"),b.board)}else{if(c=="triangleright"||c==">"){this.updatePathPrim(b.rendNode,this.updatePathStringPoint(b,a,">"),b.board)}}}}}}}}}this.setShadow(b)};JXG.AbstractRenderer.prototype.changePointStyle=function(a){var b=this.getElementById(a.id);if(b!=null){this.remove(b)}this.drawPoint(a);JXG.clearVisPropOld(a);if(!a.visProp.visible){this.hide(a)}if(a.visProp.draft){this.setDraft(a)}};JXG.AbstractRenderer.prototype.drawLine=function(a){var b=this.createPrim("line",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"lines");this.updateLine(a)};JXG.AbstractRenderer.prototype.updateLine=function(b){var n=new JXG.Coords(JXG.COORDS_BY_USER,b.point1.coords.usrCoords,b.board),l=new JXG.Coords(JXG.COORDS_BY_USER,b.point2.coords.usrCoords,b.board),a,q,f,e,k,d,h,g,c;this.calcStraight(b,n,l);this.updateLinePrim(b.rendNode,n.scrCoords[1],n.scrCoords[2],l.scrCoords[1],l.scrCoords[2],b.board);if(b.image!=null){a=n.scrCoords[1];q=n.scrCoords[2];f=l.scrCoords[1];e=l.scrCoords[2];k=Math.atan2(e-q,f-a);h=250;g=256;c=[[1,0,0],[h*(1-Math.cos(k))+g*Math.sin(k),Math.cos(k),-Math.sin(k)],[g*(1-Math.cos(k))-h*Math.sin(k),Math.sin(k),Math.cos(k)]];b.imageTransformMatrix=c}this.makeArrows(b);if(this.enhancedRendering){if(!b.visProp.draft){this.setObjectStrokeWidth(b,b.visProp.strokeWidth);this.setObjectStrokeColor(b,b.visProp.strokeColor,b.visProp.strokeOpacity);this.setDashStyle(b,b.visProp);this.setShadow(b)}else{this.setDraft(b)}}};JXG.AbstractRenderer.prototype.calcStraight=function(e,n,m){var b,a,k,g,q,d,l,v,h,f,u,r;q=e.visProp.straightFirst;d=e.visProp.straightLast;if(Math.abs(n.scrCoords[0])<JXG.Math.eps){q=true}if(Math.abs(m.scrCoords[0])<JXG.Math.eps){d=true}if(!q&&!d){return}l=[];l[0]=e.stdform[0]-e.stdform[1]*e.board.origin.scrCoords[1]/e.board.stretchX+e.stdform[2]*e.board.origin.scrCoords[2]/e.board.stretchY;l[1]=e.stdform[1]/e.board.stretchX;l[2]=e.stdform[2]/(-e.board.stretchY);if(isNaN(l[0]+l[1]+l[2])){return}v=[];v[0]=JXG.Math.crossProduct(l,[0,0,1]);v[1]=JXG.Math.crossProduct(l,[0,1,0]);v[2]=JXG.Math.crossProduct(l,[-e.board.canvasHeight,0,1]);v[3]=JXG.Math.crossProduct(l,[-e.board.canvasWidth,1,0]);for(h=0;h<4;h++){if(Math.abs(v[h][0])>JXG.Math.eps){for(f=2;f>0;f--){v[h][f]/=v[h][0]}v[h][0]=1}}b=false;a=false;if(!q&&n.scrCoords[1]>=0&&n.scrCoords[1]<=e.board.canvasWidth&&n.scrCoords[2]>=0&&n.scrCoords[2]<=e.board.canvasHeight){b=true}if(!d&&m.scrCoords[1]>=0&&m.scrCoords[1]<=e.board.canvasWidth&&m.scrCoords[2]>=0&&m.scrCoords[2]<=e.board.canvasHeight){a=true}if(Math.abs(v[1][0])<JXG.Math.eps){k=v[0];g=v[2]}else{if(Math.abs(v[0][0])<JXG.Math.eps){k=v[1];g=v[3]}else{if(v[1][2]<0){k=v[0];if(v[3][2]>e.board.canvasHeight){g=v[2]}else{g=v[3]}}else{if(v[1][2]>e.board.canvasHeight){k=v[2];if(v[3][2]<0){g=v[0]}else{g=v[3]}}else{k=v[1];if(v[3][2]<0){g=v[0]}else{if(v[3][2]>e.board.canvasHeight){g=v[2]}else{g=v[3]}}}}}}k=new JXG.Coords(JXG.COORDS_BY_SCREEN,k.slice(1),e.board);g=new JXG.Coords(JXG.COORDS_BY_SCREEN,g.slice(1),e.board);if(!b&&!a){if(!q&&d&&!this.isSameDirection(n,m,k)&&!this.isSameDirection(n,m,g)){return}else{if(q&&!d&&!this.isSameDirection(m,n,k)&&!this.isSameDirection(m,n,g)){return}}}if(!b){if(!a){if(this.isSameDirection(n,m,k)){if(!this.isSameDirection(n,m,g)){r=k;u=g}else{if(JXG.Math.Geometry.affineDistance(m.usrCoords,k.usrCoords)<JXG.Math.Geometry.affineDistance(m.usrCoords,g.usrCoords)){u=k;r=g}else{r=k;u=g}}}else{if(this.isSameDirection(n,m,g)){u=k;r=g}else{if(JXG.Math.Geometry.affineDistance(m.usrCoords,k.usrCoords)<JXG.Math.Geometry.affineDistance(m.usrCoords,g.usrCoords)){r=k;u=g}else{u=k;r=g}}}}else{if(this.isSameDirection(m,n,k)){u=k}else{u=g}}}else{if(!a){if(this.isSameDirection(n,m,k)){r=k}else{r=g}}}if(u){n.setCoordinates(JXG.COORDS_BY_USER,u.usrCoords.slice(1))}if(r){m.setCoordinates(JXG.COORDS_BY_USER,r.usrCoords.slice(1))}};JXG.AbstractRenderer.prototype.isSameDirection=function(g,d,c){var b,a,f,e;b=d.usrCoords[1]-g.usrCoords[1];a=d.usrCoords[2]-g.usrCoords[2];f=c.usrCoords[1]-g.usrCoords[1];e=c.usrCoords[2]-g.usrCoords[2];if(Math.abs(b)<JXG.Math.eps){b=0}if(Math.abs(a)<JXG.Math.eps){a=0}if(Math.abs(f)<JXG.Math.eps){f=0}if(Math.abs(e)<JXG.Math.eps){e=0}if(b>=0&&f>=0){if((a>=0&&e>=0)||(a<=0&&e<=0)){return true}}else{if(b<=0&&f<=0){if((a>=0&&e>=0)||(a<=0&&e<=0)){return true}}}return false};JXG.AbstractRenderer.prototype.updateTicks=function(b,d,a,e,c){};JXG.AbstractRenderer.prototype.removeTicks=function(a){var b=this.getElementById(a.id+"_ticks");this.remove(b)};JXG.AbstractRenderer.prototype.drawArrow=function(a){var b=this.createPrim("line",a.id);this.setObjectStrokeWidth(a,a.visProp.strokeWidth);this.setObjectStrokeColor(a,a.visProp.strokeColor,a.visProp.strokeOpacity);this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillOpacity);this.setDashStyle(a,a.visProp);this.makeArrow(b,a);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"lines");this.updateArrow(a)};JXG.AbstractRenderer.prototype.updateArrow=function(a){if(this.enhancedRendering){if(!a.visProp.draft){this.setObjectStrokeWidth(a,a.visProp.strokeWidth);this.setObjectStrokeColor(a,a.visProp.strokeColor,a.visProp.strokeOpacity);this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillOpacity);this.setShadow(a);this.setDashStyle(a,a.visProp)}else{this.setDraft(a)}}this.updateLinePrim(a.rendNode,a.point1.coords.scrCoords[1],a.point1.coords.scrCoords[2],a.point2.coords.scrCoords[1],a.point2.coords.scrCoords[2],a.board)};JXG.AbstractRenderer.prototype.drawCurve=function(a){var b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path");this.setObjectStrokeWidth(a,a.visProp.strokeWidth);this.setObjectStrokeColor(a,a.visProp.strokeColor,a.visProp.strokeOpacity);this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillOpacity);this.setDashStyle(a,a.visProp);this.updateCurve(a)};JXG.AbstractRenderer.prototype.updateCurve=function(a){if(this.enhancedRendering){if(!a.visProp.draft){this.setObjectStrokeWidth(a,a.visProp.strokeWidth);this.setObjectStrokeColor(a,a.visProp.strokeColor,a.visProp.strokeOpacity);this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillOpacity);this.setDashStyle(a,a.visProp);this.setShadow(a)}else{this.setDraft(a)}}this.updatePathPrim(a.rendNode,this.updatePathStringPrim(a),a.board);this.makeArrows(a)};JXG.AbstractRenderer.prototype.drawCircle=function(a){var b=this.createPrim("ellipse",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"ellipse");this.updateCircle(a)};JXG.AbstractRenderer.prototype.updateCircle=function(b){if(this.enhancedRendering){if(!b.visProp.draft){this.setObjectStrokeWidth(b,b.visProp.strokeWidth);this.setObjectStrokeColor(b,b.visProp.strokeColor,b.visProp.strokeOpacity);this.setObjectFillColor(b,b.visProp.fillColor,b.visProp.fillOpacity);this.setDashStyle(b,b.visProp);this.setShadow(b)}else{this.setDraft(b)}}var a=b.Radius();if(a>0&&!isNaN(b.midpoint.coords.scrCoords[1]+b.midpoint.coords.scrCoords[2])){this.updateEllipsePrim(b.rendNode,b.midpoint.coords.scrCoords[1],b.midpoint.coords.scrCoords[2],(a*b.board.stretchX),(a*b.board.stretchY))}};JXG.AbstractRenderer.prototype.drawPolygon=function(a){var b=this.createPrim("polygon",a.id);a.visProp.fillOpacity=0.3;this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"polygon");this.updatePolygon(a)};JXG.AbstractRenderer.prototype.updatePolygon=function(a){if(this.enhancedRendering){if(!a.visProp.draft){this.setObjectStrokeWidth(a,a.visProp.strokeWidth);this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillOpacity);this.setShadow(a)}else{this.setDraft(a)}}this.updatePolygonePrim(a.rendNode,a)};JXG.AbstractRenderer.prototype.drawText=function(a){var b;if(a.display=="html"){b=this.container.ownerDocument.createElement("div");b.style.position="absolute";b.style.color=a.visProp.strokeColor;b.className="JXGtext";b.style.zIndex="10";this.container.appendChild(b);b.setAttribute("id",this.container.id+"_"+a.id)}else{b=this.drawInternalText(a)}b.style.fontSize=a.board.options.text.fontSize+"px";a.rendNode=b;a.htmlStr="";this.updateText(a)};JXG.AbstractRenderer.prototype.drawInternalText=function(a){};JXG.AbstractRenderer.prototype.updateText=function(a){if(a.visProp.visible==false){return}if(isNaN(a.coords.scrCoords[1]+a.coords.scrCoords[2])){return}this.updateTextStyle(a);if(a.display=="html"){a.rendNode.style.left=(a.coords.scrCoords[1])+"px";a.rendNode.style.top=(a.coords.scrCoords[2]-this.vOffsetText)+"px";a.updateText();if(a.htmlStr!=a.plaintextStr){a.rendNode.innerHTML=a.plaintextStr;if(a.board.options.text.useASCIIMathML){AMprocessNode(a.rendNode,false)}a.htmlStr=a.plaintextStr}}else{this.updateInternalText(a)}};JXG.AbstractRenderer.prototype.updateInternalText=function(a){};JXG.AbstractRenderer.prototype.updateTextStyle=function(b){var a;if(b.visProp.fontSize){if(typeof b.visProp.fontSize=="function"){a=b.visProp.fontSize();b.rendNode.style.fontSize=(a>0?a:0)}else{b.rendNode.style.fontSize=(b.visProp.fontSize)}}};JXG.AbstractRenderer.prototype.drawImage=function(a){};JXG.AbstractRenderer.prototype.updateImage=function(a){this.updateRectPrim(a.rendNode,a.coords.scrCoords[1],a.coords.scrCoords[2]-a.size[1],a.size[0],a.size[1]);if(a.parent!=null){this.transformImageParent(a,a.parent.imageTransformMatrix)}else{this.transformImageParent(a)}this.transformImage(a,a.transformations)};JXG.AbstractRenderer.prototype.drawGrid=function(e){var x=e.gridX,v=e.gridY,s=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],e),f=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e.canvasWidth,e.canvasHeight],e),y=Math.ceil(s.usrCoords[1]),u=0,w,a,q,r,m,h,n,g,b,c,d;e.hasGrid=true;for(w=0;w<=x+1;w++){if(y-w/x<s.usrCoords[1]){u=w-1;break}}y=Math.floor(f.usrCoords[1]);a=0;for(w=0;w<=x+1;w++){if(y+w/x>f.usrCoords[1]){a=w-1;break}}y=Math.ceil(f.usrCoords[2]);r=0;for(w=0;w<=v+1;w++){if(y-w/v<f.usrCoords[2]){r=w-1;break}}y=Math.floor(s.usrCoords[2]);q=0;for(w=0;w<=v+1;w++){if(y+w/v>s.usrCoords[2]){q=w-1;break}}m=Math.round((1/x)*e.stretchX);h=Math.round((1/v)*e.stretchY);n=new JXG.Coords(JXG.COORDS_BY_USER,[Math.ceil(s.usrCoords[1])-u/x,Math.floor(s.usrCoords[2])+q/v],e);g=new JXG.Coords(JXG.COORDS_BY_USER,[Math.floor(f.usrCoords[1])+a/x,Math.ceil(f.usrCoords[2])-r/v],e);b=this.drawVerticalGrid(n,g,m,e);this.appendChildPrim(b,e.options.layer.grid);if(!e.snapToGrid){c=new Object();c.visProp={};c.rendNode=b;c.elementClass=JXG.OBJECT_CLASS_LINE;c.id="gridx";JXG.clearVisPropOld(c);this.setObjectStrokeColor(c,e.gridColor,e.gridOpacity)}else{c=new Object();c.visProp={};c.rendNode=b;c.elementClass=JXG.OBJECT_CLASS_LINE;c.id="gridx";JXG.clearVisPropOld(c);this.setObjectStrokeColor(c,"#FF8080",0.5)}this.setPropertyPrim(b,"stroke-width","0.4px");if(e.gridDash){this.setGridDash("gridx")}b=this.drawHorizontalGrid(n,g,h,e);this.appendChildPrim(b,e.options.layer.grid);if(!e.snapToGrid){c=new Object();c.visProp={};c.rendNode=b;c.elementClass=JXG.OBJECT_CLASS_LINE;c.id="gridy";JXG.clearVisPropOld(c);this.setObjectStrokeColor(c,e.gridColor,e.gridOpacity)}else{c=new Object();c.visProp={};c.rendNode=b;c.elementClass=JXG.OBJECT_CLASS_LINE;c.id="gridy";JXG.clearVisPropOld(c);this.setObjectStrokeColor(c,"#FF8080",0.5)}this.setPropertyPrim(b,"stroke-width","0.4px");if(e.gridDash){this.setGridDash("gridy")}};JXG.AbstractRenderer.prototype.removeGrid=function(a){var b=this.getElementById("gridx");this.remove(b);b=this.getElementById("gridy");this.remove(b);a.hasGrid=false};JXG.AbstractRenderer.prototype.hide=function(a){};JXG.AbstractRenderer.prototype.show=function(a){};JXG.AbstractRenderer.prototype.setObjectStrokeWidth=function(b,a){};JXG.AbstractRenderer.prototype.setObjectStrokeColor=function(c,a,b){};JXG.AbstractRenderer.prototype.setObjectFillColor=function(c,a,b){};JXG.AbstractRenderer.prototype.setDraft=function(b){if(!b.visProp.draft){return}var a=b.board.options.elements.draft.color,c=b.board.options.elements.draft.opacity;if(b.type==JXG.OBJECTT_TYPE_POLYGON){this.setObjectFillColor(b,a,c)}else{if(b.elementClass==JXG.OBJECT_CLASS_POINT){this.setObjectFillColor(b,a,c)}else{this.setObjectFillColor(b,"none",0)}this.setObjectStrokeColor(b,a,c);this.setObjectStrokeWidth(b,b.board.options.elements.draft.strokeWidth)}};JXG.AbstractRenderer.prototype.removeDraft=function(a){if(a.type==JXG.OBJECT_TYPE_POLYGON){this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillColorOpacity)}else{if(a.type==JXG.OBJECT_CLASS_POINT){this.setObjectFillColor(a,a.visProp.fillColor,a.visProp.fillColorOpacity)}this.setObjectStrokeColor(a,a.visProp.strokeColor,a.visProp.strokeColorOpacity);this.setObjectStrokeWidth(a,a.visProp.strokeWidth)}};JXG.AbstractRenderer.prototype.highlight=function(b){var a;if(b.visProp.draft==false){if(b.type==JXG.OBJECT_CLASS_POINT){this.setObjectStrokeColor(b,b.visProp.highlightStrokeColor,b.visProp.highlightStrokeOpacity);this.setObjectFillColor(b,b.visProp.highlightStrokeColor,b.visProp.highlightStrokeOpacity)}else{if(b.type==JXG.OBJECT_TYPE_POLYGON){this.setObjectFillColor(b,b.visProp.highlightFillColor,b.visProp.highlightFillOpacity);for(a=0;a<b.borders.length;a++){this.setObjectStrokeColor(b.borders[a],b.borders[a].visProp.highlightStrokeColor,b.visProp.highlightStrokeOpacity)}}else{this.setObjectStrokeColor(b,b.visProp.highlightStrokeColor,b.visProp.highlightStrokeOpacity);this.setObjectFillColor(b,b.visProp.highlightFillColor,b.visProp.highlightFillOpacity)}}if(b.visProp.highlightStrokeWidth){this.setObjectStrokeWidth(b,b.visProp.highlightStrokeWidth)}}};JXG.AbstractRenderer.prototype.noHighlight=function(b){var a;if(b.visProp.draft==false){if(b.type==JXG.OBJECT_CLASS_POINT){this.setObjectStrokeColor(b,b.visProp.strokeColor,b.visProp.strokeOpacity);this.setObjectFillColor(b,b.visProp.strokeColor,b.visProp.strokeOpacity)}else{if(b.type==JXG.OBJECT_TYPE_POLYGON){this.setObjectFillColor(b,b.visProp.fillColor,b.visProp.fillOpacity);for(a=0;a<b.borders.length;a++){this.setObjectStrokeColor(b.borders[a],b.borders[a].visProp.strokeColor,b.visProp.strokeOpacity)}}else{this.setObjectStrokeColor(b,b.visProp.strokeColor,b.visProp.strokeOpacity);this.setObjectFillColor(b,b.visProp.fillColor,b.visProp.fillOpacity)}}this.setObjectStrokeWidth(b,b.visProp.strokeWidth)}};JXG.AbstractRenderer.prototype.remove=function(a){};JXG.AbstractRenderer.prototype.suspendRedraw=function(){};JXG.AbstractRenderer.prototype.unsuspendRedraw=function(){};JXG.AbstractRenderer.prototype.drawZoomBar=function(g){var k,c,f,e,b,l,h,a,d;k=this.container.ownerDocument;c=k.createElement("div");c.className="JXGtext";c.style.color="#aaaaaa";c.style.backgroundColor="#f5f5f5";c.style.padding="2px";c.style.position="absolute";c.style.fontSize="10px";c.style.cursor="pointer";c.style.zIndex="100";this.container.appendChild(c);c.style.right="5px";c.style.bottom="5px";f=k.createElement("span");c.appendChild(f);f.innerHTML="&nbsp;&ndash;&nbsp;";JXG.addEvent(f,"click",g.zoomOut,g);e=k.createElement("span");c.appendChild(e);e.innerHTML="&nbsp;o&nbsp;";JXG.addEvent(e,"click",g.zoom100,g);b=k.createElement("span");c.appendChild(b);b.innerHTML="&nbsp;+&nbsp;";JXG.addEvent(b,"click",g.zoomIn,g);l=k.createElement("span");c.appendChild(l);l.innerHTML="&nbsp;&larr;&nbsp;";JXG.addEvent(l,"click",g.clickLeftArrow,g);h=k.createElement("span");c.appendChild(h);h.innerHTML="&nbsp;&uarr;&nbsp;";JXG.addEvent(h,"click",g.clickUpArrow,g);a=k.createElement("span");c.appendChild(a);a.innerHTML="&nbsp;&darr;&nbsp;";JXG.addEvent(a,"click",g.clickDownArrow,g);d=k.createElement("span");c.appendChild(d);d.innerHTML="&nbsp;&rarr;&nbsp;";JXG.addEvent(d,"click",g.clickRightArrow,g)};JXG.AbstractRenderer.prototype.getElementById=function(a){return document.getElementById(this.container.id+"_"+a)};JXG.AbstractRenderer.prototype.findSplit=function(w,h,g){var n=0,l=h,m,e,x,v,u,c,s,b,q,r,a;if(g-h<2){return[-1,0]}x=w[h].scrCoords;v=w[g].scrCoords;if(isNaN(x[1]+x[2]+v[1]+v[2])){return[NaN,g]}for(e=h+1;e<g;e++){u=w[e].scrCoords;c=u[1]-x[1];s=u[2]-x[2];b=v[1]-x[1];q=v[2]-x[2];r=b*b+q*q;if(r>=JXG.Math.eps){a=(c*b+s*q)/r;m=c*c+s*s-a*(c*b+s*q)}else{a=0;m=c*c+s*s}if(a<0){m=c*c+s*s}else{if(a>1){c=u[1]-v[1];s=u[2]-v[2];m=c*c+s*s}}if(m>n){n=m;l=e}}return[Math.sqrt(n),l]};JXG.AbstractRenderer.prototype.RDP=function(f,e,d,b,c){var a=this.findSplit(f,e,d);if(a[0]>b){this.RDP(f,e,a[1],b,c);this.RDP(f,a[1],d,b,c)}else{c.push(f[d])}};JXG.AbstractRenderer.prototype.RamenDouglasPeuker=function(f,b){var d=[],e,c,a;a=f.length;e=0;while(e<a&&isNaN(f[e].scrCoords[1]+f[e].scrCoords[2])){e++}c=a-1;while(c>e&&isNaN(f[c].scrCoords[1]+f[c].scrCoords[2])){c--}if(e>c||e==a){return[]}d[0]=f[e];this.RDP(f,e,c,b,d);return d};JXG.AbstractRenderer.prototype.setShadow=function(a){};JXG.AbstractRenderer.prototype.updatePathStringPoint=function(c,a,b){};JXG.AbstractRenderer.prototype.eval=function(a){if(typeof a=="function"){return a()}else{return a}};JXG.FileReader=new function(){this.parseFileContent=function(a,b,d){this.request=false;var c;try{this.request=new XMLHttpRequest();if(d.toLowerCase()=="raw"){this.request.overrideMimeType("text/plain; charset=iso-8859-1")}else{this.request.overrideMimeType("text/xml; charset=iso-8859-1")}}catch(c){try{this.request=new ActiveXObject("Msxml2.XMLHTTP")}catch(c){try{this.request=new ActiveXObject("Microsoft.XMLHTTP")}catch(c){this.request=false}}}if(!this.request){alert("AJAX not activated!");return}this.request.open("GET",a,true);if(d.toLowerCase()=="raw"){this.cbp=function(){var e=this.request;if(e.readyState==4){b(e.responseText)}}}else{this.cbp=function(){var e=this.request;if(e.readyState==4){var f="";if(typeof e.responseStream!="undefined"&&e.responseText.slice(0,2)=="PK"){f=(new JXG.Util.Unzip(JXG.Util.Base64.decodeAsArray(BinFileReader(this.request)))).unzip();f=f[0][0]}else{f=e.responseText}this.parseString(f,b,d,false)}}}this.cb=JXG.bind(this.cbp,this);this.request.onreadystatechange=this.cb;try{this.request.send(null)}catch(c){throw new Error("JSXGraph: problems opening "+a+" !")}};this.cleanWhitespace=function(a){var b=a.firstChild;while(b!=null){if(b.nodeType==3&&!/\S/.test(b.nodeValue)){a.removeChild(b)}else{if(b.nodeType==1){this.cleanWhitespace(b)}}b=b.nextSibling}};this.stringToXMLTree=function(b){if(typeof DOMParser=="undefined"){DOMParser=function(){};DOMParser.prototype.parseFromString=function(f,g){if(typeof ActiveXObject!="undefined"){var e=new ActiveXObject("MSXML.DomDocument");e.loadXML(f);return e}}}var c=new DOMParser();var a=c.parseFromString(b,"text/xml");this.cleanWhitespace(a);return a};this.parseString=function(e,c,f,b){var a,d;if(f.toLowerCase()=="cdy"){if(b){e=JXG.Util.Base64.decode(e)}e=JXG.CinderellaReader.readCinderella(e,c);c.xmlString=e;c.afterLoad();return}if(f.toLowerCase()=="graph"){e=JXG.GraphReader.readGraph(e,c);c.afterLoad();return}if(f.toLowerCase()=="geonext"){e=JXG.GeonextReader.prepareString(e)}if(f.toLowerCase()=="geogebra"){e=JXG.GeogebraReader.prepareString(e,b)}if(f.toLowerCase()=="intergeo"){if(b){e=JXG.Util.Base64.decode(e)}e=JXG.IntergeoReader.prepareString(e)}c.xmlString=e;a=this.stringToXMLTree(e);this.readElements(a,c,f)};this.readElements=function(a,b,c){if(c.toLowerCase()=="geonext"){b.suspendUpdate();if(a.getElementsByTagName("GEONEXT").length!=0){JXG.GeonextReader.readGeonext(a,b)}b.unsuspendUpdate()}else{if(a.getElementsByTagName("geogebra").length!=0){JXG.GeogebraReader.readGeogebra(a,b)}else{if(c.toLowerCase()=="intergeo"){JXG.IntergeoReader.readIntergeo(a,b)}}}b.afterLoad()}};if(/msie/i.test(navigator.userAgent)&&!/opera/i.test(navigator.userAgent)){document.write('<script type="text/vbscript">\nFunction Base64Encode(inData)\n Const Base64 = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"\n Dim cOut, sOut, I\n For I = 1 To LenB(inData) Step 3\n Dim nGroup, pOut, sGroup\n nGroup = &H10000 * AscB(MidB(inData, I, 1)) + _\n &H100 * MyASC(MidB(inData, I + 1, 1)) + MyASC(MidB(inData, I + 2, 1))\n nGroup = Oct(nGroup)\n nGroup = String(8 - Len(nGroup), "0") & nGroup\n pOut = Mid(Base64, CLng("&o" & Mid(nGroup, 1, 2)) + 1, 1) + _\n Mid(Base64, CLng("&o" & Mid(nGroup, 3, 2)) + 1, 1) + _\n Mid(Base64, CLng("&o" & Mid(nGroup, 5, 2)) + 1, 1) + _\n Mid(Base64, CLng("&o" & Mid(nGroup, 7, 2)) + 1, 1)\n sOut = sOut + pOut\n Next\n Select Case LenB(inData) Mod 3\n Case 1: \'8 bit final\n sOut = Left(sOut, Len(sOut) - 2) + "=="\n Case 2: \'16 bit final\n sOut = Left(sOut, Len(sOut) - 1) + "="\n End Select\n Base64Encode = sOut\nEnd Function\n\nFunction MyASC(OneChar)\n If OneChar = "" Then MyASC = 0 Else MyASC = AscB(OneChar)\nEnd Function\n\nFunction BinFileReader(xhr)\n Dim byteString\n Dim b64String\n Dim i\n byteString = xhr.responseBody\n ReDim byteArray(LenB(byteString))\n For i = 1 To LenB(byteString)\n byteArray(i-1) = AscB(MidB(byteString, i, 1))\n Next\n b64String = Base64Encode(byteString)\n BinFileReader = b64String\nEnd Function\n<\/script>\n')}JXG.GeonextParser={};JXG.GeonextParser.replacePow=function(d){var h,m,k,g,l,e,a,b,f,q,n;f=d.indexOf("^");while(f>=0){b=d.slice(0,f);if(b.charAt(b.length-1)==")"){h=1;m=b.length-2;while(m>=0&&h>0){k=b.charAt(m);if(k==")"){h++}else{if(k=="("){h--}}m--}if(h==0){g="";e=b.substring(0,m+1);a=m;while(a>=0&&e.substr(a,1).match(/(\w+)/)){g=RegExp.$1+g;a--}g+=b.substring(m+1,b.length);g=g.replace(/([\(\)\+\*\%\^\-\/\]\[])/g,"\\$1")}}else{g="[\\w\\.]+"}q=d.slice(f+1);if(q.match(/^([\w\.]*\()/)){h=1;m=RegExp.$1.length;while(m<q.length&&h>0){k=q.charAt(m);if(k==")"){h--}else{if(k=="("){h++}}m++}if(h==0){l=q.substring(0,m);l=l.replace(/([\(\)\+\*\%\^\-\/\[\]])/g,"\\$1")}}else{l="[\\w\\.]+"}n=new RegExp("("+g+")\\^("+l+")");d=d.replace(n,"JXG.Math.pow($1,$2)");f=d.indexOf("^")}return d};JXG.GeonextParser.replaceIf=function(b){var u="",d,r,f=null,a=null,k=null,e,q,g,l,h,m,n;e=b.indexOf("If(");if(e<0){return b}b=b.replace(/""/g,"0");while(e>=0){d=b.slice(0,e);r=b.slice(e+3);g=1;q=0;l=-1;h=-1;while(q<r.length&&g>0){m=r.charAt(q);if(m==")"){g--}else{if(m=="("){g++}else{if(m==","&&g==1){if(l<0){l=q}else{h=q}}}}q++}n=r.slice(0,q-1);r=r.slice(q);if(l<0){return""}if(h<0){return""}f=n.slice(0,l);a=n.slice(l+1,h);k=n.slice(h+1);f=this.replaceIf(f);a=this.replaceIf(a);k=this.replaceIf(k);u+=d+"(("+f+")?("+a+"):("+k+"))";b=r;f=null;a=null;e=b.indexOf("If(")}u+=r;return u};JXG.GeonextParser.replaceSub=function(c){if(c.indexOf){}else{return c}var b=c.indexOf("_{"),a;while(b>=0){c=c.substr(0,b)+c.substr(b).replace(/_\{/,"<sub>");a=c.substr(b).indexOf("}");if(a>=0){c=c.substr(0,a)+c.substr(a).replace(/\}/,"</sub>")}b=c.indexOf("_{")}b=c.indexOf("_");while(b>=0){c=c.substr(0,b)+c.substr(b).replace(/_(.?)/,"<sub>$1</sub>");b=c.indexOf("_")}return c};JXG.GeonextParser.replaceSup=function(c){if(c.indexOf){}else{return c}var b=c.indexOf("^{"),a;while(b>=0){c=c.substr(0,b)+c.substr(b).replace(/\^\{/,"<sup>");a=c.substr(b).indexOf("}");if(a>=0){c=c.substr(0,a)+c.substr(a).replace(/\}/,"</sup>")}b=c.indexOf("^{")}b=c.indexOf("^");while(b>=0){c=c.substr(0,b)+c.substr(b).replace(/\^(.?)/,"<sup>$1</sup>");b=c.indexOf("^")}return c};JXG.GeonextParser.replaceNameById=function(d,f){var h=0,a,g,e,c,b=["X","Y","L","V"];for(c=0;c<b.length;c++){h=d.indexOf(b[c]+"(");while(h>=0){if(h>=0){a=d.indexOf(")",h+2);if(a>=0){g=d.slice(h+2,a);g=g.replace(/\\(['"])?/g,"$1");e=f.elementsByName[g];d=d.slice(0,h+2)+e.id+d.slice(a)}}a=d.indexOf(")",h+2);h=d.indexOf(b[c]+"(",a)}}h=d.indexOf("Dist(");while(h>=0){if(h>=0){a=d.indexOf(",",h+5);if(a>=0){g=d.slice(h+5,a);g=g.replace(/\\(['"])?/g,"$1");e=f.elementsByName[g];d=d.slice(0,h+5)+e.id+d.slice(a)}}a=d.indexOf(",",h+5);h=d.indexOf(",",a);a=d.indexOf(")",h+1);if(a>=0){g=d.slice(h+1,a);g=g.replace(/\\(['"])?/g,"$1");e=f.elementsByName[g];d=d.slice(0,h+1)+e.id+d.slice(a)}a=d.indexOf(")",h+1);h=d.indexOf("Dist(",a)}b=["Deg","Rad"];for(c=0;c<b.length;c++){h=d.indexOf(b[c]+"(");while(h>=0){if(h>=0){a=d.indexOf(",",h+4);if(a>=0){g=d.slice(h+4,a);g=g.replace(/\\(['"])?/g,"$1");e=f.elementsByName[g];d=d.slice(0,h+4)+e.id+d.slice(a)}}a=d.indexOf(",",h+4);h=d.indexOf(",",a);a=d.indexOf(",",h+1);if(a>=0){g=d.slice(h+1,a);g=g.replace(/\\(['"])?/g,"$1");e=f.elementsByName[g];d=d.slice(0,h+1)+e.id+d.slice(a)}a=d.indexOf(",",h+1);h=d.indexOf(",",a);a=d.indexOf(")",h+1);if(a>=0){g=d.slice(h+1,a);g=g.replace(/\\(['"])?/g,"$1");e=f.elementsByName[g];d=d.slice(0,h+1)+e.id+d.slice(a)}a=d.indexOf(")",h+1);h=d.indexOf(b[c]+"(",a)}}return d};JXG.GeonextParser.replaceIdByObj=function(a){var b=/(X|Y|L)\(([\w_]+)\)/g;a=a.replace(b,'this.board.objects["$2"].$1()');b=/(V)\(([\w_]+)\)/g;a=a.replace(b,'this.board.objects["$2"].Value()');b=/(Dist)\(([\w_]+),([\w_]+)\)/g;a=a.replace(b,'this.board.objects["$2"].Dist(this.board.objects["$3"])');b=/(Deg)\(([\w_]+),([ \w\[\w_]+),([\w_]+)\)/g;a=a.replace(b,'JXG.Math.Geometry.trueAngle(this.board.objects["$2"],this.board.objects["$3"],this.board.objects["$4"])');b=/Rad\(([\w_]+),([\w_]+),([\w_]+)\)/g;a=a.replace(b,'JXG.Math.Geometry.rad(this.board.objects["$1"],this.board.objects["$2"],this.board.objects["$3"])');return a};JXG.GeonextParser.geonext2JS=function(b,d){var e,c,a,g=["Abs","ACos","ASin","ATan","Ceil","Cos","Exp","Floor","Log","Max","Min","Random","Round","Sin","Sqrt","Tan","Trunc"],f=["Math.abs","Math.acos","Math.asin","Math.atan","Math.ceil","Math.cos","Math.exp","Math.floor","Math.log","Math.max","Math.min","Math.random","this.board.round","Math.sin","Math.sqrt","Math.tan","Math.ceil"];b=b.replace(/&lt;/g,"<");b=b.replace(/&gt;/g,">");b=b.replace(/&amp;/g,"&");c=b;c=this.replaceNameById(c,d);c=this.replaceIf(c);c=this.replacePow(c);c=this.replaceIdByObj(c);for(a=0;a<g.length;a++){e=new RegExp(g[a],"ig");c=c.replace(e,f[a])}c=c.replace(/True/g,"true");c=c.replace(/False/g,"false");c=c.replace(/fasle/g,"false");c=c.replace(/Pi/g,"Math.PI");return c};JXG.GeonextParser.findDependencies=function(e,b,d){if(typeof d=="undefined"){d=e.board}var f=d.elementsByName,c,g,a;for(c in f){if(c!=e.name){if(f[c].type==JXG.OBJECT_TYPE_TEXT){if(!f[c].isLabel){a=c.replace(/\[/g,"\\[");a=a.replace(/\]/g,"\\]");g=new RegExp("\\(([\\w\\[\\]'_ ]+,)*("+a+")(,[\\w\\[\\]'_ ]+)*\\)","g");if(b.search(g)>=0){f[c].addChild(e)}}}else{a=c.replace(/\[/g,"\\[");a=a.replace(/\]/g,"\\]");g=new RegExp("\\(([\\w\\[\\]'_ ]+,)*("+a+")(,[\\w\\[\\]'_ ]+)*\\)","g");if(b.search(g)>=0){f[c].addChild(e)}}}}};JXG.Board=function(a,f,b,m,l,k,h,g,c,d,e){this.BOARD_MODE_NONE=0;this.BOARD_MODE_DRAG=1;this.BOARD_MODE_CONSTRUCT=16;this.BOARD_MODE_MOVE_ORIGIN=2;this.BOARD_QUALITY_LOW=1;this.BOARD_QUALITY_HIGH=2;this.CONSTRUCTION_TYPE_POINT=1129599060;this.CONSTRUCTION_TYPE_CIRCLE=1129595724;this.CONSTRUCTION_TYPE_LINE=1129598030;this.CONSTRUCTION_TYPE_GLIDER=1129596740;this.CONSTRUCTION_TYPE_MIDPOINT=1129598288;this.CONSTRUCTION_TYPE_PERPENDICULAR=1129599044;this.CONSTRUCTION_TYPE_PARALLEL=1129599052;this.CONSTRUCTION_TYPE_INTERSECTION=1129597267;this.container=a;this.containerObj=document.getElementById(this.container);if(this.containerObj==null){throw new Error("\nJSXGraph: HTML container element '"+(a)+"' not found.")}this.renderer=f;this.options=JXG.deepCopy(JXG.Options);this.dimension=2;this.origin={};this.origin.usrCoords=[1,0,0];this.origin.scrCoords=[1,m[0],m[1]];this.zoomX=l;this.zoomY=k;this.unitX=h;this.unitY=g;this.stretchX=this.zoomX*this.unitX;this.stretchY=this.zoomY*this.unitY;this.canvasWidth=c;this.canvasHeight=d;this.fontSize=this.options.text.fontSize;if((b!="")&&(b!=null)&&(typeof document.getElementById(b)!="undefined")){this.id=b}else{this.id=this.generateId()}this.hooks=[];this.cbHook=-1;this.dependentBoards=[];this.objects={};this.animationObjects={};this.highlightedObjects={};this.numObjects=0;this.elementsByName={};this.mode=this.BOARD_MODE_NONE;this.updateQuality=this.BOARD_QUALITY_HIGH;this.isSuspendedRedraw=false;this.snapToGrid=this.options.grid.snapToGrid;this.gridX=this.options.grid.gridX;this.gridY=this.options.grid.gridY;this.gridColor=this.options.grid.gridColor;this.gridOpacity=this.options.grid.gridOpacity;this.gridDash=this.options.grid.gridDash;this.snapSizeX=this.options.grid.snapSizeX;this.snapSizeY=this.options.grid.snapSizeY;this.calculateSnapSizes();this.hasGrid=this.options.grid.hasGrid;this.drag_dx=0;this.drag_dy=0;this.mousePosAbs=[0,0];this.mousePosRel=[0,0];this.drag_obj=[];this.xmlString="";if((e!=null&&e)||(e==null&&this.options.showCopyright)){this.renderer.displayCopyright(JXG.JSXGraph.licenseText,this.fontSize)}this.needsFullUpdate=false;this.reducedUpdate=false;this.geonextCompatibilityMode=false;if(this.options.text.useASCIIMathML){if(typeof translateASCIIMath!="undefined"){init()}else{this.options.text.useASCIIMathML=false}}JXG.addEvent(document,"mousedown",this.mouseDownListener,this);JXG.addEvent(this.containerObj,"mousemove",this.mouseMoveListener,this);JXG.addEvent(this.containerObj,"touchstart",this.touchStartListener,this);JXG.addEvent(this.containerObj,"touchmove",this.touchMoveListener,this);JXG.addEvent(this.containerObj,"touchend",this.touchEndListener,this)};JXG.Board.prototype.generateName=function(c){if(c.type==JXG.OBJECT_TYPE_TICKS){return""}var h;if(c.elementClass==JXG.OBJECT_CLASS_POINT){h=["","A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S","T","U","V","W","X","Y","Z"]}else{h=["","a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z"]}var e=3;var b="";var l="";var k="";if(c.elementClass==JXG.OBJECT_CLASS_POINT||c.elementClass==JXG.OBJECT_CLASS_LINE){}else{if(c.type==JXG.OBJECT_TYPE_POLYGON){b="P_{";k="}"}else{if(c.type==JXG.OBJECT_TYPE_CIRCLE){b="k_{";k="}"}else{if(c.type==JXG.OBJECT_TYPE_ANGLE){b="W_{";k="}"}else{b="s_{";k="}"}}}}var m=[];var a="";var g="";var f=0;var d=0;for(f=0;f<e;f++){m[f]=0}while(m[e-1]<h.length){for(m[0]=1;m[0]<h.length;m[0]++){a=b;for(f=e;f>0;f--){a+=h[m[f-1]]}if(this.elementsByName[a+k]==null){return a+k}}m[0]=h.length;for(f=1;f<e;f++){if(m[f-1]==h.length){m[f-1]=1;m[f]++}}}return""};JXG.Board.prototype.generateId=function(){var a=1;while(JXG.JSXGraph.boards["gxtBoard"+a]!=null){a=Math.round(Math.random()*33)}return("gxtBoard"+a)};JXG.Board.prototype.setId=function(d,c){var b=this.numObjects,a=d.id;this.numObjects++;if((a=="")||(a==null)){a=this.id+c+b}d.id=a;this.objects[a]=d;if(d.hasLabel){d.label.content.id=a+"Label";this.addText(d.label.content)}return a};JXG.Board.prototype.getRelativeMouseCoordinates=function(a){var c=this.containerObj,b=JXG.getOffset(c),d;d=parseInt(JXG.getStyle(c,"borderLeftWidth"));if(isNaN(d)){d=0}b[0]+=d;d=parseInt(JXG.getStyle(c,"borderTopWidth"));if(isNaN(d)){d=0}b[1]+=d;d=parseInt(JXG.getStyle(c,"paddingLeft"));if(isNaN(d)){d=0}b[0]+=d;d=parseInt(JXG.getStyle(c,"paddingTop"));if(isNaN(d)){d=0}b[1]+=d;return b};JXG.Board.prototype.clickLeftArrow=function(a){this.origin.scrCoords[1]+=this.canvasWidth*0.1;this.moveOrigin();return this};JXG.Board.prototype.clickRightArrow=function(a){this.origin.scrCoords[1]-=this.canvasWidth*0.1;this.moveOrigin();return this};JXG.Board.prototype.clickUpArrow=function(a){this.origin.scrCoords[2]+=this.canvasHeight*0.1;this.moveOrigin();return this};JXG.Board.prototype.clickDownArrow=function(a){this.origin.scrCoords[2]-=this.canvasHeight*0.1;this.moveOrigin();return this};JXG.Board.prototype.touchStartListener=function(b){b.preventDefault();var d=document.createEvent("MouseEvents"),c,a=false;this.drag_obj=[];if((b.targetTouches.length==2)&&(JXG.Math.Geometry.distance([b.targetTouches[0].screenX,b.targetTouches[0].screenY],[b.targetTouches[1].screenX,b.targetTouches[1].screenY])<80)){b.targetTouches.length=1;a=true}this.options.precision.hasPoint=this.options.precision.touch;for(c=0;c<b.targetTouches.length;c++){d.initMouseEvent("mousedown",true,false,this.containerObj,0,b.targetTouches[c].screenX,b.targetTouches[c].screenY,b.targetTouches[c].clientX,b.targetTouches[c].clientY,false,false,a,false,0,null);this.mouseDownListener(d)}};JXG.Board.prototype.touchMoveListener=function(a){a.preventDefault();var d=document.createEvent("MouseEvents"),c,b;for(c=0;c<a.targetTouches.length;c++){b={pageX:a.targetTouches[c].pageX,pageY:a.targetTouches[c].pageY,clientX:a.targetTouches[c].clientX,clientY:a.targetTouches[c].clientY};this.mouseMoveListener(b,c)}};JXG.Board.prototype.touchEndListener=function(a){var c=document.createEvent("MouseEvents"),b;for(b=0;b<a.targetTouches.length;b++){c.initMouseEvent("mouseup",true,false,this.containerObj,0,0,0,0,0,false,false,false,false,0,null);this.mouseUpListener(c)}this.options.precision.hasPoint=this.options.precision.mouse};JXG.Board.prototype.mouseUpListener=function(a){this.updateQuality=this.BOARD_QUALITY_HIGH;JXG.removeEvent(document,"mouseup",this.mouseUpListener,this);this.mode=this.BOARD_MODE_NONE;if(this.mode==this.BOARD_MODE_MOVE_ORIGIN){this.moveOrigin()}else{this.update()}this.drag_obj=[];this.updateHooks("mouseup")};JXG.Board.prototype.mouseDownListener=function(f){var d,g,e,a,c,b;e=this.getRelativeMouseCoordinates(f);a=JXG.getPosition(f);c=a[0]-e[0];b=a[1]-e[1];this.mousePosAbs=a;this.mousePosRel=[c,b];if(f.shiftKey){this.drag_dx=c-this.origin.scrCoords[1];this.drag_dy=b-this.origin.scrCoords[2];this.mode=this.BOARD_MODE_MOVE_ORIGIN;JXG.addEvent(document,"mouseup",this.mouseUpListener,this);return}if(this.mode==this.BOARD_MODE_CONSTRUCT){return}this.mode=this.BOARD_MODE_DRAG;if(this.mode==this.BOARD_MODE_DRAG){for(d in this.objects){g=this.objects[d];if((g.hasPoint!=undefined)&&((g.type==JXG.OBJECT_TYPE_POINT)||(g.type==JXG.OBJECT_TYPE_GLIDER))&&(g.visProp.visible)&&(!g.fixed)&&(!g.frozen)&&(g.hasPoint(c,b))){if((g.type==JXG.OBJECT_TYPE_POINT)||(g.type==JXG.OBJECT_TYPE_GLIDER)){this.drag_obj.push(this.objects[d]);if(this.options.takeFirst){break}}}}}if(this.drag_obj.length==0){this.mode=this.BOARD_MODE_NONE;return}this.updateHooks("mousedown");this.dragObjCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[c,b],this);JXG.addEvent(document,"mouseup",this.mouseUpListener,this)};JXG.Board.prototype.mouseMoveListener=function(h,c){var b,e,l,a,f,m,k,d=false;if(typeof c=="undefined"){c=0;d=true}l=this.getRelativeMouseCoordinates(h);a=JXG.getPosition(h);m=a[0]-l[0];k=a[1]-l[1];this.mousePosAbs=a;this.mousePosRel=[m,k];this.updateQuality=this.BOARD_QUALITY_LOW;this.dehighlightAll(m,k);if(this.mode!=this.BOARD_MODE_DRAG){this.renderer.hide(this.infobox)}if(this.mode==this.BOARD_MODE_MOVE_ORIGIN){this.origin.scrCoords[1]=m-this.drag_dx;this.origin.scrCoords[2]=k-this.drag_dy;this.moveOrigin()}else{if(this.mode==this.BOARD_MODE_DRAG){f=new JXG.Coords(JXG.COORDS_BY_SCREEN,this.getScrCoordsOfMouse(m,k),this);if(this.drag_obj[c].type==JXG.OBJECT_TYPE_POINT||this.drag_obj[c].type==JXG.OBJECT_TYPE_LINE||this.drag_obj[c].type==JXG.OBJECT_TYPE_CIRCLE||this.drag_obj[c].elementClass==JXG.OBJECT_CLASS_CURVE){this.drag_obj[c].setPositionDirectly(JXG.COORDS_BY_USER,f.usrCoords[1],f.usrCoords[2]);this.update(this.drag_obj[c])}else{if(this.drag_obj[c].type==JXG.OBJECT_TYPE_GLIDER){var g=this.drag_obj[c].coords;this.drag_obj[c].setPositionDirectly(JXG.COORDS_BY_USER,f.usrCoords[1],f.usrCoords[2]);if(this.drag_obj[c].slideObject.type==JXG.OBJECT_TYPE_CIRCLE){this.drag_obj[c].coords=JXG.Math.Geometry.projectPointToCircle(this.drag_obj[c],this.drag_obj[c].slideObject,this)}else{if(this.drag_obj[c].slideObject.type==JXG.OBJECT_TYPE_LINE){this.drag_obj[c].coords=JXG.Math.Geometry.projectPointToLine(this.drag_obj[c],this.drag_obj[c].slideObject,this)}}if(this.drag_obj[c].group.length!=0){this.drag_obj[c].group[this.drag_obj[c].group.length-1].dX=this.drag_obj[c].coords.scrCoords[1]-g.scrCoords[1];this.drag_obj[c].group[this.drag_obj[c].group.length-1].dY=this.drag_obj[c].coords.scrCoords[2]-g.scrCoords[2];this.drag_obj[c].group[this.drag_obj[c].group.length-1].update(this)}else{this.update(this.drag_obj[c])}}}this.updateInfobox(this.drag_obj[c])}else{for(b in this.objects){e=this.objects[b];if(e.hasPoint!=undefined&&e.visProp.visible&&e.hasPoint(m,k)){this.updateInfobox(e);if(this.highlightedObjects[b]==null){e.highlight();this.highlightedObjects[b]=e}}}}}this.updateQuality=this.BOARD_QUALITY_HIGH};JXG.Board.prototype.updateInfobox=function(b){var a,e,c,d;if(!b.showInfobox){return this}if(b.elementClass==JXG.OBJECT_CLASS_POINT){c=b.coords.usrCoords[1]*1;d=b.coords.usrCoords[2]*1;this.infobox.setCoords(c+this.infobox.distanceX/(this.stretchX),d+this.infobox.distanceY/(this.stretchY));if(typeof(b.infoboxText)!="string"){a=Math.abs(c);if(a>0.1){a=c.toFixed(2)}else{if(a>=0.01){a=c.toFixed(4)}else{if(a>=0.0001){a=c.toFixed(6)}else{a=c}}}e=Math.abs(d);if(e>0.1){e=d.toFixed(2)}else{if(e>=0.01){e=d.toFixed(4)}else{if(e>=0.0001){e=d.toFixed(6)}else{e=d}}}this.highlightInfobox(a,e,b)}else{this.highlightCustomInfobox(b.infoboxText,b)}this.renderer.show(this.infobox);this.renderer.updateText(this.infobox)}return this};JXG.Board.prototype.highlightCustomInfobox=function(b,a){this.infobox.setText('<span style="color:#bbbbbb;">'+b+"</span>");return this};JXG.Board.prototype.highlightInfobox=function(a,c,b){this.highlightCustomInfobox("("+a+", "+c+")");return this};JXG.Board.prototype.dehighlightAll=function(a,d){var b,c;for(b in this.highlightedObjects){c=this.highlightedObjects[b];if((c.hasPoint==undefined)||(!c.hasPoint(a,d))||(!c.visProp.visible)){c.noHighlight();delete (this.highlightedObjects[b])}}return this};JXG.Board.prototype.getScrCoordsOfMouse=function(a,c){if(this.snapToGrid){var b=new JXG.Coords(JXG.COORDS_BY_SCREEN,[a,c],this);b.setCoordinates(JXG.COORDS_BY_USER,[Math.round((b.usrCoords[1])*this.snapSizeX)/this.snapSizeX,Math.round((b.usrCoords[2])*this.snapSizeY)/this.snapSizeY]);return[b.scrCoords[1],b.scrCoords[2]]}else{return[a,c]}};JXG.Board.prototype.getUsrCoordsOfMouse=function(e){var c=this.getRelativeMouseCoordinates(e);var b=JXG.getPosition(e);var a=b[0]-c[0];var f=b[1]-c[1];var d=new JXG.Coords(JXG.COORDS_BY_SCREEN,[a,f],this);if(this.snapToGrid){d.setCoordinates(JXG.COORDS_BY_USER,[Math.round((d.usrCoords[1])*this.snapSizeX)/this.snapSizeX,Math.round((d.usrCoords[2])*this.snapSizeY)/this.snapSizeY])}return[d.usrCoords[1],d.usrCoords[2]]};JXG.Board.prototype.getAllUnderMouse=function(b){var a=this.getAllObjectsUnderMouse(b);a.push(this.getUsrCoordsOfMouse(b));return a};JXG.Board.prototype.getAllObjectsUnderMouse=function(g){var f=this.getRelativeMouseCoordinates(g);var a=JXG.getPosition(g);var c=a[0]-f[0];var b=a[1]-f[1];var d=[];for(var e in this.objects){if(this.objects[e].visProp.visible&&this.objects[e].hasPoint(c,b)){d.push(this.objects[e])}}return d};JXG.Board.prototype.setBoardMode=function(a){this.mode=a;return this};JXG.Board.prototype.moveOrigin=function(){var b,a;for(a in this.objects){b=this.objects[a];if(!b.frozen&&(b.elementClass==JXG.OBJECT_CLASS_POINT||b.elementClass==JXG.OBJECT_CLASS_CURVE||b.type==JXG.OBJECT_TYPE_AXIS||b.type==JXG.OBJECT_TYPE_TEXT)){if(b.elementClass!=JXG.OBJECT_CLASS_CURVE&&b.type!=JXG.OBJECT_TYPE_AXIS){b.coords.usr2screen()}}}this.clearTraces();this.fullUpdate();if(this.hasGrid){this.renderer.removeGrid(this);this.renderer.drawGrid(this)}return this};JXG.Board.prototype.finalizeAdding=function(a){if(a.hasLabel){this.renderer.drawText(a.label.content)}if(!a.visProp.visible){this.renderer.hide(a)}if(a.hasLabel&&!a.label.content.visProp.visible){this.renderer.hide(a.label.content)}};JXG.Board.prototype.addPoint=function(a){var b=this.setId(a,"P");this.renderer.drawPoint(a);this.finalizeAdding(a);return b};JXG.Board.prototype.addLine=function(a){var b=this.setId(a,"L");this.renderer.drawLine(a);this.finalizeAdding(a);return b};JXG.Board.prototype.addCircle=function(a){var b=this.setId(a,"C");this.renderer.drawCircle(a);this.finalizeAdding(a);return b};JXG.Board.prototype.addPolygon=function(a){var b=this.setId(a,"Py");this.renderer.drawPolygon(a);this.finalizeAdding(a);return b};JXG.Board.prototype.addCurve=function(a){var b=this.setId(a,"G");this.renderer.drawCurve(a);this.finalizeAdding(a);return b};JXG.Board.prototype.addChart=function(a){return this.setId(a,"Chart")};JXG.Board.prototype.addArrow=function(c){var b=this.numObjects,a;this.numObjects++;a=c.id;if((a=="")||(a==null)){a=this.id+"A"+b}this.objects[a]=c;c.id=a;this.renderer.drawArrow(c);return a};JXG.Board.prototype.addIntersection=function(c){var b=this.numObjects;this.numObjects++;var a=c.id;if((a=="")||(a==null)){a=this.id+"I"+b}this.objects[a]=c;c.id=a;c.intersect1.addChild(c);c.intersect2.addChild(c);return a};JXG.Board.prototype.addText=function(c){var b=this.numObjects;this.numObjects++;var a=c.id;if((a=="")||(a==null)){a=this.id+"T"+b}this.objects[a]=c;c.id=a;if(!c.isLabel){this.renderer.drawText(c);if(!c.visProp.visible){this.renderer.hide(c)}}return a};JXG.Board.prototype.addConditions=function(l){var k=null;var b="var el,x,y,c;\n";var h=l.indexOf("<data>");var g=l.indexOf("</data>");if(h<0){return}while(h>=0){var f=l.slice(h+6,g);var e=f.indexOf("=");var d=f.slice(0,e);var q=f.slice(e+1);e=d.indexOf(".");var a=d.slice(0,e);var c=this.elementsByName[JXG.unescapeHTML(a)];var n=d.slice(e+1).replace(/\s+/g,"").toLowerCase();q=JXG.GeonextParser.geonext2JS(q,this);q=q.replace(/this\.board\./g,"this.");if(typeof this.elementsByName[a]=="undefined"){alert("debug conditions: |"+a+"| undefined")}b+='el = this.objects["'+c.id+'"];\n';switch(n){case"x":b+="var y=el.coords.usrCoords[2];\n";b+="el.setPositionDirectly(JXG.COORDS_BY_USER,"+(q)+",y);\n";b+="el.update();\n";break;case"y":b+="var x=el.coords.usrCoords[1];\n";b+="el.coords=new JXG.Coords(JXG.COORDS_BY_USER,[x,"+(q)+"],this);\n";break;case"visible":b+="var c="+(q)+";\n";b+="if (c) {el.showElement();} else {el.hideElement();}\n";break;case"position":b+="el.position = "+(q)+";\n";b+="el.update();\n";break;case"stroke":b+="el.strokeColor = "+(q)+";\n";break;case"style":b+="el.setStyle("+(q)+");\n";break;case"strokewidth":b+="el.strokeWidth = "+(q)+";\n";break;case"fill":b+="var f="+(q)+";\n";b+="el.setProperty({fillColor:f})\n";break;case"label":break;default:alert("property '"+n+"' in conditions not yet implemented:"+q);break}l=l.slice(g+7);h=l.indexOf("<data>");g=l.indexOf("</data>")}b+="this.prepareUpdate();\n";b+="this.updateElements();\n";b+="return true;\n";this.updateConditions=new Function(b);this.updateConditions()};JXG.Board.prototype.updateConditions=function(){return false};JXG.Board.prototype.addImage=function(c){var b=this.numObjects;this.numObjects++;var a=c.id;if((a=="")||(a==null)){a=this.id+"Im"+b}this.objects[a]=c;this.elementsByName[c.name]=c;c.id=a;this.renderer.drawImage(c);if(!c.visProp.visible){this.renderer.hide(c)}return a};JXG.Board.prototype.calculateSnapSizes=function(){var c=new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this),b=new JXG.Coords(JXG.COORDS_BY_USER,[1/this.gridX,1/this.gridY],this),a=c.scrCoords[1]-b.scrCoords[1],d=c.scrCoords[2]-b.scrCoords[2];this.snapSizeX=this.gridX;while(Math.abs(a)>25){this.snapSizeX*=2;a/=2}this.snapSizeY=this.gridY;while(Math.abs(d)>25){this.snapSizeY*=2;d/=2}return this};JXG.Board.prototype.applyZoom=function(){var b,a;for(a in this.objects){b=this.objects[a];if(!b.frozen&&(b.elementClass==JXG.OBJECT_CLASS_POINT||b.elementClass==JXG.OBJECT_CLASS_CURVE||b.type==JXG.OBJECT_TYPE_AXIS||b.type==JXG.OBJECT_TYPE_TEXT)){if(b.elementClass!=JXG.OBJECT_CLASS_CURVE&&b.type!=JXG.OBJECT_TYPE_AXIS){b.coords.usr2screen()}}}this.calculateSnapSizes();this.clearTraces();this.fullUpdate();if(this.hasGrid){this.renderer.removeGrid(this);this.renderer.drawGrid(this)}return this};JXG.Board.prototype.zoomIn=function(){var b,a;this.zoomX*=this.options.zoom.factor;this.zoomY*=this.options.zoom.factor;b=this.origin.scrCoords[1]*this.options.zoom.factor;a=this.origin.scrCoords[2]*this.options.zoom.factor;this.origin=new JXG.Coords(JXG.COORDS_BY_SCREEN,[b,a],this);this.stretchX=this.zoomX*this.unitX;this.stretchY=this.zoomY*this.unitY;this.applyZoom();return this};JXG.Board.prototype.zoomOut=function(){var b,a;this.zoomX/=this.options.zoom.factor;this.zoomY/=this.options.zoom.factor;b=this.origin.scrCoords[1]/this.options.zoom.factor;a=this.origin.scrCoords[2]/this.options.zoom.factor;this.origin=new JXG.Coords(JXG.COORDS_BY_SCREEN,[b,a],this);this.stretchX=this.zoomX*this.unitX;this.stretchY=this.zoomY*this.unitY;this.applyZoom();return this};JXG.Board.prototype.zoom100=function(){var d,b,c,a;c=this.zoomX;a=this.zoomY;this.zoomX=1;this.zoomY=1;d=this.origin.scrCoords[1]/c;b=this.origin.scrCoords[2]/a;this.origin=new JXG.Coords(JXG.COORDS_BY_SCREEN,[d,b],this);this.stretchX=this.zoomX*this.unitX;this.stretchY=this.zoomY*this.unitY;this.applyZoom();return this};JXG.Board.prototype.zoomAllPoints=function(){var m,h,d,g,b,f,k,s,r,q,n,l,e,c,a,u;m=this.zoomX/this.zoomY;h=0;d=0;g=0;b=0;for(f in this.objects){if((this.objects[f].elementClass==JXG.OBJECT_CLASS_POINT)&&this.objects[f].visProp.visible){if(this.objects[f].coords.usrCoords[1]<h){h=this.objects[f].coords.usrCoords[1]}else{if(this.objects[f].coords.usrCoords[1]>d){d=this.objects[f].coords.usrCoords[1]}}if(this.objects[f].coords.usrCoords[2]>b){b=this.objects[f].coords.usrCoords[2]}else{if(this.objects[f].coords.usrCoords[2]<g){g=this.objects[f].coords.usrCoords[2]}}}}k=50;s=k/(this.unitX*this.zoomX);r=k/(this.unitY*this.zoomY);q=d-h+2*s;n=b-g+2*r;l=Math.min(this.canvasWidth/(this.unitX*q),this.canvasHeight/(this.unitY*n));c=l;e=l*m;a=-(h-s)*this.unitX*e;u=(b+r)*this.unitY*c;this.origin=new JXG.Coords(JXG.COORDS_BY_SCREEN,[a,u],this);this.zoomX=e;this.zoomY=c;this.stretchX=this.zoomX*this.unitX;this.stretchY=this.zoomY*this.unitY;this.applyZoom();return this};JXG.Board.prototype.removeObject=function(a){var c,b;if(JXG.isArray(a)){for(b=0;b<a.length;b++){this.removeObject(a[b])}}a=JXG.getReference(this,a);if(a==undefined){return this}try{for(c in a.childElements){a.childElements[c].board.removeObject(a.childElements[c])}for(c in this.objects){if(typeof this.objects[c].childElements!="undefined"){delete (this.objects[c].childElements[a.id])}}delete (this.objects[a.id]);delete (this.elementsByName[a.name]);if(a.remove!=undefined){a.remove()}}catch(d){}return this};JXG.Board.prototype.initGeonextBoard=function(){var e,d,c,b,a;e=new JXG.Point(this,[0,0],this.id+"gOOe0","Ursprung",false);e.fixed=true;d=new JXG.Point(this,[1,0],this.id+"gXOe0","Punkt_1_0",false);d.fixed=true;c=new JXG.Point(this,[0,1],this.id+"gYOe0","Punkt_0_1",false);c.fixed=true;b=new JXG.Line(this,this.id+"gOOe0",this.id+"gXOe0",this.id+"gXLe0","X-Achse",false);b.hideElement();a=new JXG.Line(this,this.id+"gOOe0",this.id+"gYOe0",this.id+"gYLe0","Y-Achse",false);a.hideElement();return this};JXG.Board.prototype.initInfobox=function(){this.infobox=new JXG.Text(this,"0,0","",[0,0],this.id+"__infobox",null,null,false,"html");this.infobox.distanceX=-20;this.infobox.distanceY=25;this.renderer.hide(this.infobox);return this};JXG.Board.prototype.resizeContainer=function(a,b){this.canvasWidth=1*a;this.canvasHeight=1*b;this.containerObj.style.width=(this.canvasWidth)+"px";this.containerObj.style.height=(this.canvasHeight)+"px";return this};JXG.Board.prototype.showDependencies=function(){var d,b,g,e,a;b="<p>\n";for(d in this.objects){a=0;for(g in this.objects[d].childElements){a++}if(a>=0){b+="<b>"+this.objects[d].id+":</b> "}for(g in this.objects[d].childElements){b+=this.objects[d].childElements[g].id+"("+this.objects[d].childElements[g].name+"), "}b+="<p>\n"}b+="</p>\n";e=window.open();e.document.open();e.document.write(b);e.document.close();return this};JXG.Board.prototype.showXML=function(){var a=window.open("");a.document.open();a.document.write("<pre>"+JXG.escapeHTML(this.xmlString)+"</pre>");a.document.close();return this};JXG.Board.prototype.prepareUpdate=function(b){var a;for(a in this.objects){this.objects[a].needsUpdate=true}return this};JXG.Board.prototype.updateElements=function(b){var a,d,c=true;b=JXG.getReference(this,b);if(b==null){c=false}for(a in this.objects){d=this.objects[a];if(b!=null&&d.id!=b.id){c=false}if(!(c||this.needsFullUpdate||d.needsRegularUpdate)){continue}if(b==null||d.id!=b.id){d.update(true)}else{d.update(false)}}return this};JXG.Board.prototype.updateRenderer=function(b){var a,c;b=JXG.getReference(this,b);for(a in this.objects){c=this.objects[a];if(!this.needsFullUpdate&&!c.needsRegularUpdate){continue}if(b==null||c.id!=b.id){c.updateRenderer()}else{c.updateRenderer()}}return this};JXG.Board.prototype.addHook=function(b,a){if(typeof a=="undefined"){a="update"}this.hooks.push({fn:b,mode:a});if(a=="update"){b(this)}return(this.hooks.length-1)};JXG.Board.prototype.removeHook=function(a){this.hooks[a]=null;return this};JXG.Board.prototype.updateHooks=function(a){var b;if(typeof a=="undefined"){a="update"}for(b=0;b<this.hooks.length;b++){if((this.hooks[b]!=null)&&(this.hooks[b].mode==a)){this.hooks[b].fn(this)}}return this};JXG.Board.prototype.addChild=function(a){this.dependentBoards.push(a);this.update();return this};JXG.Board.prototype.removeChild=function(b){var a;for(a=this.dependentBoards.length-1;a>=0;a--){if(this.dependentBoards[a]==b){this.dependentBoards.splice(a,1)}}return this};JXG.Board.prototype.update=function(e){var d,c,f,a;if(this.isSuspendedUpdate){return this}this.prepareUpdate(e).updateElements(e).updateConditions();this.renderer.suspendRedraw();this.updateRenderer(e);this.renderer.unsuspendRedraw();this.updateHooks();c=this.dependentBoards.length;for(d=0;d<c;d++){f=this.dependentBoards[d].id;a=JXG.JSXGraph.boards[f];if(a!=this){a.updateQuality=this.updateQuality;a.prepareUpdate(e).updateElements(e).updateConditions();a.renderer.suspendRedraw();a.updateRenderer(e);a.renderer.unsuspendRedraw();a.updateHooks()}}return this};JXG.Board.prototype.fullUpdate=function(){this.needsFullUpdate=true;this.update();this.needsFullUpdate=false;return this};JXG.Board.prototype.createElement=function(b,c,a){var f,d,e;if(b!="turtle"&&(c==null||c.length==0)){return null}if(c==null){c=[]}b=b.toLowerCase();if(a==null){a={}}for(d=0;d<c.length;d++){c[d]=JXG.getReference(this,c[d])}if(JXG.JSXGraph.elements[b]!=null){if(typeof JXG.JSXGraph.elements[b]=="function"){f=JXG.JSXGraph.elements[b](this,c,a)}else{f=JXG.JSXGraph.elements[b].creator(this,c,a)}}else{throw new Error("JSXGraph: JXG.createElement: Unknown element type given: "+b)}if(typeof f=="undefined"){return f}if(JXG.isArray(a)){a=a[0]}if(f.multipleElements){for(e in f){if(typeof f[e].setProperty!="undefined"){f[e].setProperty(a)}}}else{if(typeof f.setProperty!="undefined"){f.setProperty(a)}}this.update(f);return f};JXG.Board.prototype.create=JXG.Board.prototype.createElement;JXG.Board.prototype.clearTraces=function(){var a;for(a in this.objects){if(this.objects[a].traced){this.objects[a].clearTrace()}}return this};JXG.Board.prototype.beforeLoad=function(){};JXG.Board.prototype.afterLoad=function(){};JXG.Board.prototype.suspendUpdate=function(){this.isSuspendedUpdate=true;return this};JXG.Board.prototype.unsuspendUpdate=function(){this.isSuspendedUpdate=false;this.update();return this};JXG.Board.prototype.setBoundingBox=function(g,d){if(!JXG.isArray(g)){return}var e,c,b,a,f;f=JXG.getDimensions(this.container);this.canvasWidth=parseInt(f.width);this.canvasHeight=parseInt(f.height);c=this.canvasWidth;e=this.canvasHeight;if(d){this.unitX=c/(g[2]-g[0]);this.unitY=e/(-g[3]+g[1]);if(this.unitX<this.unitY){this.unitY=this.unitX}else{this.unitX=this.unitY}}else{this.unitX=c/(g[2]-g[0]);this.unitY=e/(-g[3]+g[1])}b=-this.unitX*g[0]*this.zoomX;a=this.unitY*g[1]*this.zoomY;this.origin=new JXG.Coords(JXG.COORDS_BY_SCREEN,[b,a],this);this.stretchX=this.zoomX*this.unitX;this.stretchY=this.zoomY*this.unitY;this.moveOrigin();return this};JXG.Board.prototype.animate=function(){var d=0,a,h,g,b,f,k,e=null;for(a in this.animationObjects){if(this.animationObjects[a]==null){continue}d++;h=this.animationObjects[a];if(h.animationPath){g=h.animationPath.pop();if(typeof g=="undefined"){delete (h.animationPath)}else{h.setPositionDirectly(JXG.COORDS_BY_USER,g[0],g[1]);h.prepareUpdate().update().updateRenderer();e=h}}if(h.animationData){k=0;for(b in h.animationData){f=h.animationData[b].pop();if(typeof f=="undefined"){delete (h.animationData[f])}else{k++;h.setProperty(b+":"+f)}}if(k==0){delete (h.animationData)}}if(typeof h.animationData=="undefined"&&typeof h.animationPath=="undefined"){this.animationObjects[a]=null;delete (this.animationObjects[a])}}if(d==0){window.clearInterval(this.animationIntervalCode);delete (this.animationIntervalCode)}else{this.update(e)}};JXG.Board.prototype.simulateColorblindness=function(a){var b,c;if(this.cbHook!=-1){this.removeHook(this.cbHook);this.cbHook=-1}if((typeof a!="undefined")&&(a!="none")){this.cbHook=this.addHook(function(){for(b in brd.objects){c=brd.objects[b];brd.renderer.setObjectFillColor(c,JXG.rgb2cb(c.visProp.fillColor,a),c.visProp.opacity);brd.renderer.setObjectStrokeColor(c,JXG.rgb2cb(c.visProp.strokeColor,a),c.visProp.opacity)}},"update")}};JXG.Board.prototype.construct=function(a,v,E,z,e){var m,A,h,q,y,n={},r,c,u,d,b,D,g,x,w,C,B,s,f;if(typeof(v)=="undefined"){v="normal"}else{B=[]}n.lines=[];n.circles=[];n.points=[];n.intersections=[];n.angles=[];n.macros=[];n.functions=[];n.texts=[];n.polygons=[];if(a.search(/\{/)!=-1){D=a.match(/\{/);D=D.length;w=0;for(y=0;y<D;y++){x=a.slice(w).search(/\{/);f=a.slice(x);f=f.slice(0,f.search(/\}/)+1);f=f.replace(/;/g,"?");a=a.slice(0,x)+f+a.slice(x+f.length);w=x+1}}m=a.split(";");for(A=0;A<m.length;A++){m[A]=m[A].replace(/^\s+/,"").replace(/\s+$/,"");if(m[A].search(/\{/)!=-1){m[A]=m[A].replace(/\?/g,";")}if(m[A].search(/Macro/)!=-1){this.addMacro(m[A])}else{if(m[A].length>0){if(m[A].search(/=/)!=-1){r=m[A].split("=");m[A]=r[1].replace(/^\s+/,"");r=r[0].replace(/\s+$/,"")}else{r=""}attributes={};s=true;while(s){if(m[A].search(/(.*)draft$/)!=-1){attributes.draft=true;m[A]=RegExp.$1;m[A]=m[A].replace(/\s+$/,"")}if(m[A].search(/(.*)invisible$/)!=-1){attributes.visible=false;m[A]=RegExp.$1;m[A]=m[A].replace(/\s+$/,"")}if(m[A].search(/(.*)nolabel$/)!=-1){attributes.withLabel=false;m[A]=RegExp.$1;m[A]=m[A].replace(/\s+$/,"")}if(m[A].search(/nolabel|invisible|draft/)==-1){s=false}}g=true;if(this.definedMacros){for(y=0;y<this.definedMacros.macros.length;y++){C=new RegExp("^"+this.definedMacros.macros[y][0]+"\\s*\\(");if(m[A].search(C)!=-1){g=false;m[A].match(/\((.*)\)/);D=RegExp.$1;D=D.split(",");for(x=0;x<D.length;x++){D[x].match(/\s*(\S*)\s*/);D[x]=RegExp.$1}n[r]=this.construct(this.definedMacros.macros[y][2],"macro",this.definedMacros.macros[y][1],D,r);n.macros.push(n[r]);break}}}if(g){if(m[A].search(/^[\[\]].*[\[\]]$/)!=-1){m[A].match(/([\[\]])(.*)([\[\]])/);attributes.straightFirst=(RegExp.$1!="[");attributes.straightLast=(RegExp.$3=="[");c=(RegExp.$2).replace(/^\s+/,"").replace(/\s+$/,"");if(c.search(/ /)!=-1){c.match(/(\S*) +(\S*)/);c=[];c[0]=RegExp.$1;c[1]=RegExp.$2}if(r!=""){if(attributes.withLabel==undefined){attributes.withLabel=true}attributes.name=r;if(v=="macro"){B.push(r)}}if(v=="macro"){if(e!=""){for(y=0;y<B.length;y++){if(c[0]==B[y]){c[0]=e+"."+c[0]}if(c[1]==B[y]){c[1]=e+"."+c[1]}}}for(y=0;y<E.length;y++){if(c[0]==E[y]){c=[z[y],c[1]]}if(c[1]==E[y]){c=[c[0],z[y]]}}if(e!=""){attributes.id=e+"."+r}}if(typeof c=="string"){c=[JXG.getReference(this,c.charAt(0)),JXG.getReference(this,c.charAt(1))]}else{c=[JXG.getReference(this,c[0]),JXG.getReference(this,c[1])]}n.lines.push(this.createElement("line",c,attributes));if(r!=""){n[r]=n.lines[n.lines.length-1]}}else{if(m[A].search(/k\s*\(.*/)!=-1){m[A].match(/k\s*\(\s*(\S.*\S|\S)\s*,\s*(\S.*\S|\S)\s*\)/);c=[];c[0]=RegExp.$1;c[1]=RegExp.$2;for(y=0;y<=1;y++){if(c[y].search(/[\[\]]/)!=-1){c[y].match(/^[\[\]]\s*(\S.*\S)\s*[\[\]]$/);c[y]=RegExp.$1;if(c[y].search(/ /)!=-1){c[y].match(/(\S*) +(\S*)/);c[y]=[];c[y][0]=RegExp.$1;c[y][1]=RegExp.$2}if(v=="macro"){if(e!=""){for(x=0;x<B.length;x++){if(c[y][0]==B[x]){c[y][0]=e+"."+c[y][0]}if(c[y][1]==B[x]){c[y][1]=e+"."+c[y][1]}}}for(x=0;x<E.length;x++){if(c[y][0]==E[x]){c[y]=[z[x],c[y][1]]}if(c[y][1]==E[x]){c[y]=[c[y][0],z[x]]}}}if(typeof c[y]=="string"){c[y]=(function(l,k){return function(){return JXG.getReference(k,l.charAt(0)).Dist(JXG.getReference(k,l.charAt(1)))}})(c[y],this)}else{c[y]=(function(l,k){return function(){return JXG.getReference(k,l[0]).Dist(JXG.getReference(k,l[1]))}})(c[y],this)}}else{if(c[y].search(/[0-9\.\s]+/)!=-1){c[y]=1*c[y]}else{if(v=="macro"){if(e!=""){for(x=0;x<B.length;x++){if(c[y]==B[x]){c[y]=e+"."+B[x]}}}for(x=0;x<E.length;x++){if(c[y]==E[x]){c[y]=z[x]}}}c[y]=JXG.getReference(this,c[y])}}}if(r!=""){if(attributes.withLabel==undefined){attributes.withLabel=true}attributes.name=r;if(v=="macro"){if(e!=""){attributes.id=e+"."+r}B.push(r)}}n.circles.push(this.createElement("circle",c,attributes));if(r!=""){n[r]=n.circles[n.circles.length-1]}}else{if(m[A].search(/^[A-Z]+.*\(\s*[0-9\.\-]+\s*[,\|]\s*[0-9\.\-]+\s*\)/)!=-1&&m[A].search(/Macro\((.*)\)/)==-1){m[A].match(/^([A-Z]+\S*)\s*\(\s*(.*)\s*[,\|]\s*(.*)\s*\)$/);r=RegExp.$1;attributes.name=r;if(v=="macro"){if(e!=""){attributes.id=e+"."+r}B.push(r)}n.points.push(this.createElement("point",[1*RegExp.$2,1*RegExp.$3],attributes));n[r]=n.points[n.points.length-1]}else{if(m[A].search(/^[A-Z]+.*\(.+(([,\|]\s*[0-9\.\-]+\s*){2})?/)!=-1&&m[A].search(/Macro\((.*)\)/)==-1){m[A].match(/([A-Z]+.*)\((.*)\)/);r=RegExp.$1;c=RegExp.$2;r=r.replace(/^\s+/,"").replace(/\s+$/,"");c=c.replace(/^\s+/,"").replace(/\s+$/,"");if(c.search(/[,\|]/)!=-1){c.match(/(\S*)\s*[,\|]\s*([0-9\.]+)\s*[,\|]\s*([0-9\.]+)\s*/);c=[];c[0]=RegExp.$1;c[1]=1*RegExp.$2;c[2]=1*RegExp.$3}else{u=c;c=[];c[0]=u;c[1]=0;c[2]=0}attributes.name=r;if(v=="macro"){if(e!=""){for(x=0;x<B.length;x++){if(c[0]==B[x]){c[0]=e+"."+B[x]}}}for(x=0;x<E.length;x++){if(c[0]==E[x]){c[0]=z[x]}}if(e!=""){attributes.id=e+"."+r}B.push(r)}n.points.push(this.createElement("glider",[c[1],c[2],JXG.getReference(this,c[0])],attributes));n[r]=n.points[n.points.length-1]}else{if(m[A].search(/&/)!=-1){m[A].match(/(.*)&(.*)/);c=[];c[0]=RegExp.$1;c[1]=RegExp.$2;c[0]=c[0].replace(/\s+$/,"");c[1]=c[1].replace(/^\s+/,"");if(v=="macro"){for(y=0;y<=1;y++){if(e!=""){for(x=0;x<B.length;x++){if(c[y]==B[x]){c[y]=e+"."+B[x]}}}for(x=0;x<E.length;x++){if(c[y]==E[x]){c[y]=z[x]}}}}c[0]=JXG.getReference(this,c[0]);c[1]=JXG.getReference(this,c[1]);if((c[0].elementClass==JXG.OBJECT_CLASS_LINE||c[0].elementClass==JXG.OBJECT_CLASS_CURVE)&&(c[1].elementClass==JXG.OBJECT_CLASS_LINE||c[1].elementClass==JXG.OBJECT_CLASS_CURVE)){if(r!=""){attributes.name=r;if(v=="macro"){if(e!=""){attributes.id=e+"."+r}B.push(r)}}u=this.createElement("intersection",[c[0],c[1],0],attributes);n.intersections.push(u);if(r!=""){n[attributes.name]=u}}else{if(r!=""){attributes.name=r+"_1";if(v=="macro"){if(e!=""){attributes.id=e+"."+r+"_1"}B.push(r+"_1")}}u=this.createElement("intersection",[c[0],c[1],0],attributes);n.intersections.push(u);if(r!=""){n[attributes.name]=u}if(r!=""){attributes.name=r+"_2";if(v=="macro"){if(e!=""){attributes.id=e+"."+r+"_2"}B.push(r+"_2")}}u=this.createElement("intersection",[c[0],c[1],1],attributes);n.intersections.push(u);if(r!=""){n[attributes.name]=u}}}else{if(m[A].search(/\|[\|_]\s*\(/)!=-1){m[A].match(/\|([\|_])\s*\(\s*(\S*)\s*,\s*(\S*)\s*\)/);d=RegExp.$1;if(d=="|"){d="parallel"}else{d="normal"}c=[];c[0]=RegExp.$2;c[1]=RegExp.$3;if(v=="macro"){for(y=0;y<=1;y++){if(e!=""){for(x=0;x<B.length;x++){if(c[y]==B[x]){c[y]=e+"."+B[x]}}}for(x=0;x<E.length;x++){if(c[y]==E[x]){c[y]=z[x]}}}}if(r!=""){attributes.name=r;if(attributes.withLabel==undefined){attributes.withLabel=true}if(v=="macro"){if(e!=""){attributes.id=e+"."+r}B.push(r)}}n.lines.push(this.createElement(d,[JXG.getReference(this,c[0]),JXG.getReference(this,c[1])],attributes));if(r!=""){n[r]=n.lines[n.lines.length-1]}}else{if(m[A].search(/^</)!=-1){m[A].match(/<\s*\(\s*(\S*)\s*,\s*(\S*)\s*,\s*(\S*)\s*\)/);c=[];c[0]=RegExp.$1;c[1]=RegExp.$2;c[2]=RegExp.$3;if(v=="macro"){for(y=0;y<=2;y++){if(e!=""){for(x=0;x<B.length;x++){if(c[y]==B[x]){c[y]=e+"."+B[x]}}}for(x=0;x<E.length;x++){if(c[y]==E[x]){c[y]=z[x]}}}}if(r==""){n.lines.push(this.createElement("angle",[JXG.getReference(this,c[0]),JXG.getReference(this,c[1]),JXG.getReference(this,c[2])],attributes))}else{b=["alpha","beta","gamma","delta","epsilon","zeta","eta","theta","iota","kappa","lambda","mu","nu","xi","omicron","pi","rho","sigmaf","sigma","tau","upsilon","phi","chi","psi","omega"];d="";for(y=0;y<b.length;y++){if(r==b[y]){attributes.text="&"+r+";";attributes.name="&"+r+";";d="greek";break}else{if(y==b.length-1){attributes.text=r;attributes.name=r}}}if(attributes.withLabel==undefined){attributes.withLabel=true}if(v=="macro"){if(e!=""){attributes.id=e+"."+r}B.push(r)}n.angles.push(this.createElement("angle",[JXG.getReference(this,c[0]),JXG.getReference(this,c[1]),JXG.getReference(this,c[2])],attributes));n[r]=n.angles[n.angles.length-1]}}else{if(m[A].search(/([0-9]+)\/([0-9]+)\(\s*(\S*)\s*,\s*(\S*)\s*\)/)!=-1){c=[];c[0]=1*(RegExp.$1)/(1*(RegExp.$2));c[1]=RegExp.$3;c[2]=RegExp.$4;if(v=="macro"){for(y=1;y<=2;y++){if(e!=""){for(x=0;x<B.length;x++){if(c[y]==B[x]){c[y]=e+"."+B[x]}}}for(x=0;x<E.length;x++){if(c[y]==E[x]){c[y]=z[x]}}}}c[1]=JXG.getReference(this,RegExp.$3);c[2]=JXG.getReference(this,RegExp.$4);u=[];u[0]=(function(l,k){return function(){return(1-l[0])*l[1].coords.usrCoords[1]+l[0]*l[2].coords.usrCoords[1]}})(c,this);u[1]=(function(l,k){return function(){return(1-l[0])*l[1].coords.usrCoords[2]+l[0]*l[2].coords.usrCoords[2]}})(c,this);if(r!=""){attributes.name=r;if(v=="macro"){if(e!=""){attributes.id=e+"."+r}B.push(r)}}n.points.push(this.createElement("point",[u[0],u[1]],attributes));if(r!=""){n[r]=n.points[n.points.length-1]}}else{if(m[A].search(/(\S*)\s*:\s*(.*)/)!=-1){r=RegExp.$1;D=JXG.GeonextParser.geonext2JS(RegExp.$2,this);c=[new Function("x","var y = "+D+"; return y;")];attributes.name=r;n.functions.push(this.create("functiongraph",c,attributes));n[r]=n.functions[n.functions.length-1]}else{if(m[A].search(/#(.*)\(\s*([0-9])\s*[,|]\s*([0-9])\s*\)/)!=-1){c=[];c[0]=RegExp.$1;c[1]=1*RegExp.$2;c[2]=1*RegExp.$3;c[0]=c[0].replace(/^\s+/,"").replace(/\s+$/,"");n.texts.push(this.createElement("text",[c[1],c[2],c[0]],attributes))}else{if(m[A].search(/(\S*)\s*\[(.*)\]/)!=-1){attributes.name=RegExp.$1;if(attributes.withLabel==undefined){attributes.withLabel=true}c=RegExp.$2;c=c.split(",");for(y=0;y<c.length;y++){c[y]=c[y].replace(/^\s+/,"").replace(/\s+$/,"");if(v=="macro"){if(e!=""){for(x=0;x<B.length;x++){if(c[y]==B[x]){c[y]=e+"."+B[x]}}}for(x=0;x<E.length;x++){if(c[y]==E[x]){c[y]=z[x]}}}c[y]=JXG.getReference(this,c[y])}n.polygons.push(this.createElement("polygon",c,attributes));n[attributes.name]=n.polygons[n.polygons.length-1]}}}}}}}}}}}}}}}return n};JXG.Board.prototype.addMacro=function(c){var e,a,b="",d;c.match(/(.*)\{(.*)\}/);e=RegExp.$1;a=RegExp.$2;if(e.search(/=/)!=-1){e.match(/\s*(\S*)\s*=.*/);b=RegExp.$1;e=(e.split("="))[1]}e.match(/Macro\((.*)\)/);e=RegExp.$1;e=e.split(",");for(d=0;d<e.length;d++){e[d].match(/\s*(\S*)\s*/);e[d]=RegExp.$1}if(this.definedMacros==null){this.definedMacros={};this.definedMacros.macros=[]}this.definedMacros.macros.push([b,e,a]);if(b!=""){this.definedMacros.defName=this.definedMacros.macros[this.definedMacros.macros.length-1]}};JXG.Options={showCopyright:true,showNavigation:true,takeSizeFromFile:false,renderer:"svg",grid:{hasGrid:false,gridX:2,gridY:2,gridColor:"#C0C0C0",gridOpacity:"0.5",gridDash:true,snapToGrid:false,snapSizeX:2,snapSizeY:2},zoom:{factor:1.25},elements:{strokeColor:"#0000ff",highlightStrokeColor:"#C3D9FF",fillColor:"none",highlightFillColor:"none",strokeOpacity:1,highlightStrokeOpacity:1,fillOpacity:1,highlightFillOpacity:1,strokeWidth:"2px",withLabel:false,draft:{draft:false,color:"#565656",opacity:0.8,strokeWidth:"1px"}},point:{withLabel:true,style:5,face:"o",size:3,fillColor:"#ff0000",highlightFillColor:"#EEEEEE",strokeWidth:"2px",strokeColor:"#ff0000",highlightStrokeColor:"#C3D9FF",zoom:false},line:{firstArrow:false,lastArrow:false,straightFirst:true,straightLast:true,fillColor:"#000000",highlightFillColor:"none",strokeColor:"#0000ff",highlightStrokeColor:"#888888",ticks:{drawLabels:true,drawZero:false,insertTicks:false,minTicksDistance:50,maxTicksDistance:300,minorHeight:4,majorHeight:10,minorTicks:4,defaultDistance:1},labelOffsets:[10,10]},axis:{strokeColor:"#666666",highlightStrokeColor:"#888888"},circle:{fillColor:"none",highlightFillColor:"none",strokeColor:"#0000ff",highlightStrokeColor:"#C3D9FF"},conic:{fillColor:"none",highlightFillColor:"none",strokeColor:"#0000ff",highlightStrokeColor:"#C3D9FF"},angle:{withLabel:true,radius:1,fillColor:"#FF7F00",highlightFillColor:"#FF7F00",strokeColor:"#FF7F00",textColor:"#0000FF",fillOpacity:0.3,highlightFillOpacity:0.3},arc:{firstArrow:false,lastArrow:false,fillColor:"none",highlightFillColor:"none",strokeColor:"#0000ff",highlightStrokeColor:"#C3D9FF"},polygon:{fillColor:"#00FF00",highlightFillColor:"#00FF00",fillOpacity:0.3,highlightFillOpacity:0.3},sector:{fillColor:"#00FF00",highlightFillColor:"#00FF00",fillOpacity:0.3,highlightFillOpacity:0.3},text:{fontSize:12,strokeColor:"#000000",useASCIIMathML:false,defaultDisplay:"html"},curve:{strokeWidth:"1px",strokeColor:"#0000ff",RDPsmoothing:false,numberPointsHigh:1600,numberPointsLow:400,doAdvancedPlot:true},precision:{touch:30,mouse:4,epsilon:0.0001,hasPoint:4},layer:{numlayers:20,text:9,point:9,arc:8,line:7,circle:6,curve:5,polygon:4,sector:3,angle:3,grid:1,image:0}};JXG.useStandardOptions=function(d){var e=JXG.Options,c=d.hasGrid,b,a;d.hasGrid=e.grid.hasGrid;d.gridX=e.grid.gridX;d.gridY=e.grid.gridY;d.gridColor=e.grid.gridColor;d.gridOpacity=e.grid.gridOpacity;d.gridDash=e.grid.gridDash;d.snapToGrid=e.grid.snapToGrid;d.snapSizeX=e.grid.SnapSizeX;d.snapSizeY=e.grid.SnapSizeY;d.takeSizeFromFile=e.takeSizeFromFile;for(b in d.objects){p=d.objects[b];if(p.elementClass==JXG.OBJECT_CLASS_POINT){p.visProp.fillColor=e.point.fillColor;p.visProp.highlightFillColor=e.point.highlightFillColor;p.visProp.strokeColor=e.point.strokeColor;p.visProp.highlightStrokeColor=e.point.highlightStrokeColor}else{if(p.elementClass==JXG.OBJECT_CLASS_LINE){p.visProp.fillColor=e.line.fillColor;p.visProp.highlightFillColor=e.line.highlightFillColor;p.visProp.strokeColor=e.line.strokeColor;p.visProp.highlightStrokeColor=e.line.highlightStrokeColor;for(a in p.ticks){a.majorTicks=e.line.ticks.majorTicks;a.minTicksDistance=e.line.ticks.minTicksDistance;a.minorHeight=e.line.ticks.minorHeight;a.majorHeight=e.line.ticks.majorHeight}}else{if(p.elementClass==JXG.OBJECT_CLASS_CIRCLE){p.visProp.fillColor=e.circle.fillColor;p.visProp.highlightFillColor=e.circle.highlightFillColor;p.visProp.strokeColor=e.circle.strokeColor;p.visProp.highlightStrokeColor=e.circle.highlightStrokeColor}else{if(p.type==JXG.OBJECT_TYPE_ANGLE){p.visProp.fillColor=e.angle.fillColor;p.visProp.highlightFillColor=e.angle.highlightFillColor;p.visProp.strokeColor=e.angle.strokeColor}else{if(p.type==JXG.OBJECT_TYPE_ARC){p.visProp.fillColor=e.arc.fillColor;p.visProp.highlightFillColor=e.arc.highlightFillColor;p.visProp.strokeColor=e.arc.strokeColor;p.visProp.highlightStrokeColor=e.arc.highlightStrokeColor}else{if(p.type==JXG.OBJECT_TYPE_POLYGON){p.visProp.fillColor=e.polygon.fillColor;p.visProp.highlightFillColor=e.polygon.highlightFillColor;p.visProp.fillOpacity=e.polygon.fillOpacity;p.visProp.highlightFillOpacity=e.polygon.highlightFillOpacity}else{if(p.type==JXG.OBJECT_TYPE_CONIC){p.visProp.fillColor=e.conic.fillColor;p.visProp.highlightFillColor=e.conic.highlightFillColor;p.visProp.strokeColor=e.conic.strokeColor;p.visProp.highlightStrokeColor=e.conic.highlightStrokeColor}else{if(p.type==JXG.OBJECT_TYPE_CURVE){p.visProp.strokeColor=e.curve.strokeColor}}}}}}}}}for(b in d.objects){p=d.objects[b];if(p.type==JXG.OBJECT_TYPE_SECTOR){p.arc.visProp.fillColor=e.sector.fillColor;p.arc.visProp.highlightFillColor=e.sector.highlightFillColor;p.arc.visProp.fillOpacity=e.sector.fillOpacity;p.arc.visProp.highlightFillOpacity=e.sector.highlightFillOpacity}}d.fullUpdate();if(c&&d.hasGrid){d.renderer.removeGrid(d);d.renderer.drawGrid(d)}else{if(c&&!d.hasGrid){d.renderer.removeGrid(d)}else{if(!c&&d.hasGrid){d.renderer.drawGrid(d)}}}};JXG.useBlackWhiteOptions=function(a){o=JXG.Options;o.point.fillColor=JXG.rgb2bw(o.point.fillColor);o.point.highlightFillColor=JXG.rgb2bw(o.point.highlightFillColor);o.point.strokeColor=JXG.rgb2bw(o.point.strokeColor);o.point.highlightStrokeColor=JXG.rgb2bw(o.point.highlightStrokeColor);o.line.fillColor=JXG.rgb2bw(o.line.fillColor);o.line.highlightFillColor=JXG.rgb2bw(o.line.highlightFillColor);o.line.strokeColor=JXG.rgb2bw(o.line.strokeColor);o.line.highlightStrokeColor=JXG.rgb2bw(o.line.highlightStrokeColor);o.circle.fillColor=JXG.rgb2bw(o.circle.fillColor);o.circle.highlightFillColor=JXG.rgb2bw(o.circle.highlightFillColor);o.circle.strokeColor=JXG.rgb2bw(o.circle.strokeColor);o.circle.highlightStrokeColor=JXG.rgb2bw(o.circle.highlightStrokeColor);o.arc.fillColor=JXG.rgb2bw(o.arc.fillColor);o.arc.highlightFillColor=JXG.rgb2bw(o.arc.highlightFillColor);o.arc.strokeColor=JXG.rgb2bw(o.arc.strokeColor);o.arc.highlightStrokeColor=JXG.rgb2bw(o.arc.highlightStrokeColor);o.polygon.fillColor=JXG.rgb2bw(o.polygon.fillColor);o.polygon.highlightFillColor=JXG.rgb2bw(o.polygon.highlightFillColor);o.sector.fillColor=JXG.rgb2bw(o.sector.fillColor);o.sector.highlightFillColor=JXG.rgb2bw(o.sector.highlightFillColor);o.curve.strokeColor=JXG.rgb2bw(o.curve.strokeColor);o.grid.gridColor=JXG.rgb2bw(o.grid.gridColor);JXG.useStandardOptions(a)};JXG.rgb2bw=function(c){if(c=="none"){return c}var b,e="0123456789ABCDEF",d,a;a=JXG.rgbParser(c);b=0.3*a[0]+0.59*a[1]+0.11*a[2];d=e.charAt((b>>4)&15)+e.charAt(b&15);c="#"+d+""+d+""+d;return c};JXG.simulateColorBlindness=function(b,a){o=JXG.Options;o.point.fillColor=JXG.rgb2cb(o.point.fillColor,a);o.point.highlightFillColor=JXG.rgb2cb(o.point.highlightFillColor,a);o.point.strokeColor=JXG.rgb2cb(o.point.strokeColor,a);o.point.highlightStrokeColor=JXG.rgb2cb(o.point.highlightStrokeColor,a);o.line.fillColor=JXG.rgb2cb(o.line.fillColor,a);o.line.highlightFillColor=JXG.rgb2cb(o.line.highlightFillColor,a);o.line.strokeColor=JXG.rgb2cb(o.line.strokeColor,a);o.line.highlightStrokeColor=JXG.rgb2cb(o.line.highlightStrokeColor,a);o.circle.fillColor=JXG.rgb2cb(o.circle.fillColor,a);o.circle.highlightFillColor=JXG.rgb2cb(o.circle.highlightFillColor,a);o.circle.strokeColor=JXG.rgb2cb(o.circle.strokeColor,a);o.circle.highlightStrokeColor=JXG.rgb2cb(o.circle.highlightStrokeColor,a);o.arc.fillColor=JXG.rgb2cb(o.arc.fillColor,a);o.arc.highlightFillColor=JXG.rgb2cb(o.arc.highlightFillColor,a);o.arc.strokeColor=JXG.rgb2cb(o.arc.strokeColor,a);o.arc.highlightStrokeColor=JXG.rgb2cb(o.arc.highlightStrokeColor,a);o.polygon.fillColor=JXG.rgb2cb(o.polygon.fillColor,a);o.polygon.highlightFillColor=JXG.rgb2cb(o.polygon.highlightFillColor,a);o.sector.fillColor=JXG.rgb2cb(o.sector.fillColor,a);o.sector.highlightFillColor=JXG.rgb2cb(o.sector.highlightFillColor,a);o.curve.strokeColor=JXG.rgb2cb(o.curve.strokeColor,a);o.grid.gridColor=JXG.rgb2cb(o.grid.gridColor,a);JXG.useStandardOptions(b)};JXG.rgb2cb=function(f,n){if(f=="none"){return f}var r,e,d,w,q,k,c,v,h,b,u,g;q=JXG.rgb2LMS(f);e=q.l;d=q.m;w=q.s;n=n.toLowerCase();switch(n){case"protanopia":c=-0.06150039994295001;v=0.08277001656812001;h=-0.013200141220000003;b=0.05858939668799999;u=-0.07934519995360001;g=0.013289415272000003;inflection=0.6903216543277437;k=w/d;if(k<inflection){e=-(v*d+h*w)/c}else{e=-(u*d+g*w)/b}break;case"tritanopia":c=-0.00058973116217;v=0.007690316482;h=-0.01011703519052;b=0.025495080838999994;u=-0.0422740347;g=0.017005316784;inflection=0.8349489908460004;k=d/e;if(k<inflection){w=-(c*e+v*d)/h}else{w=-(b*e+u*d)/g}break;default:c=-0.06150039994295001;v=0.08277001656812001;h=-0.013200141220000003;b=0.05858939668799999;u=-0.07934519995360001;g=0.013289415272000003;inflection=0.5763833686400911;k=w/e;if(k<inflection){d=-(c*e+h*w)/v}else{d=-(b*e+g*w)/u}break}r=JXG.LMS2rgb(e,d,w);var a="0123456789ABCDEF";k=a.charAt((r.r>>4)&15)+a.charAt(r.r&15);f="#"+k;k=a.charAt((r.g>>4)&15)+a.charAt(r.g&15);f+=k;k=a.charAt((r.b>>4)&15)+a.charAt(r.b&15);f+=k;return f};JXG.loadOptionsFromFile=function(b,c,a){this.cbp=function(d){this.parseString(d,c,a)};this.cb=JXG.bind(this.cbp,this);JXG.FileReader.parseFileContent(b,this.cb,"raw")};JXG.parseOptionsString=function(text,applyTo,board){var newOptions="";if(text!=""){newOptions=eval("("+text+")")}else{return}var maxDepth=10;var applyOption=function(base,option,depth){if(depth==10){return}depth++;for(var key in option){if((JXG.isNumber(option[key]))||(JXG.isArray(option[key]))||(JXG.isString(option[key]))||(option[key]==true)||(option[key]==false)){base[key]=option[key]}else{applyOption(base[key],option[key],depth)}}};applyOption(this,newOptions,0);if(applyTo&&typeof board!="undefined"){JXG.useStandardOptions(board)}};JXG.JSXGraph=new function(){var e,b,d,a;this.licenseText="JSXGraph v0.82rc4 Copyright (C) see http://jsxgraph.org";this.rendererType="";this.boards={};this.elements={};if((typeof forceRenderer=="undefined")||(forceRenderer==null)||(forceRenderer=="")){e=navigator.appVersion.match(/MSIE (\d\.\d)/);b=(navigator.userAgent.toLowerCase().indexOf("opera")!=-1);if((!e)||(b)){JXG.Options.renderer="svg"}else{JXG.Options.renderer="vml";function c(f){document.body.scrollLeft;document.body.scrollTop}document.onmousemove=c}}else{JXG.Options.renderer=forceRenderer}a=JXG.rendererFiles[JXG.Options.renderer].split(",");for(d=0;d<a.length;d++){(function(f){JXG.require(JXG.requirePath+f+".js")})(a[d])}this.initBoard=function(l,g){var r,C,B,v,s,y,k,f,A,z,x,u,q,m,n;f=JXG.getDimensions(l);if(typeof g=="undefined"){g={}}if(typeof g.boundingbox!="undefined"){A=g.boundingbox;y=parseInt(f.width);k=parseInt(f.height);if(g.keepaspectratio){v=y/(A[2]-A[0]);s=k/(-A[3]+A[1]);if(v<s){s=v}else{v=s}}else{v=y/(A[2]-A[0]);s=k/(-A[3]+A[1])}C=-v*A[0];B=s*A[1]}else{C=((typeof g.originX)=="undefined"?150:g.originX);B=((typeof g.originY)=="undefined"?150:g.originY);v=((typeof g.unitX)=="undefined"?50:g.unitX);s=((typeof g.unitY)=="undefined"?50:g.unitY)}z=((typeof g.zoom)=="undefined"?1:g.zoom);x=z*((typeof g.zoomX)=="undefined"?1:g.zoomX);u=z*((typeof g.zoomY)=="undefined"?1:g.zoomY);q=((typeof g.showCopyright)=="undefined"?JXG.Options.showCopyright:g.showCopyright);if(JXG.Options.renderer=="svg"){r=new JXG.SVGRenderer(document.getElementById(l))}else{if(JXG.Options.renderer=="vml"){r=new JXG.VMLRenderer(document.getElementById(l))}else{r=new JXG.SilverlightRenderer(document.getElementById(l),f.width,f.height)}}n=new JXG.Board(l,r,"",[C,B],1,1,v,s,f.width,f.height,q);this.boards[n.id]=n;n.initInfobox();if((typeof g.axis!="undefined")&&g.axis){n.defaultAxes={};n.defaultAxes.x=n.create("axis",[[0,0],[1,0]],{});n.defaultAxes.y=n.create("axis",[[0,0],[0,1]],{})}if((typeof g.grid!="undefined")&&g.grid){n.renderer.drawGrid(n)}if(typeof g.shownavigation!="undefined"){g.showNavigation=g.shownavigation}m=((typeof g.showNavigation)=="undefined"?n.options.showNavigation:g.showNavigation);if(m){n.renderer.drawZoomBar(n)}return n};this.loadBoardFromFile=function(k,f,m){var l,g,h;if(JXG.Options.renderer=="svg"){l=new JXG.SVGRenderer(document.getElementById(k))}else{l=new JXG.VMLRenderer(document.getElementById(k))}h=JXG.getDimensions(k);g=new JXG.Board(k,l,"",[150,150],1,1,50,50,h.width,h.height);g.initInfobox();g.beforeLoad();JXG.FileReader.parseFileContent(f,g,m);if(g.options.showNavigation){g.renderer.drawZoomBar(g)}this.boards[g.id]=g;return g};this.loadBoardFromString=function(k,f,m){var l,h,g;if(JXG.Options.renderer=="svg"){l=new JXG.SVGRenderer(document.getElementById(k))}else{l=new JXG.VMLRenderer(document.getElementById(k))}h=JXG.getDimensions(k);g=new JXG.Board(k,l,"",[150,150],1,1,50,50,h.width,h.height);g.initInfobox();g.beforeLoad();JXG.FileReader.parseString(f,g,m,true);if(g.options.showNavigation){g.renderer.drawZoomBar(g)}this.boards[g.id]=g;return g};this.freeBoard=function(g){var f;if(typeof(g)=="string"){g=this.boards[g]}JXG.removeEvent(document,"mousedown",g.mouseDownListener,g);JXG.removeEvent(document,"mouseup",g.mouseUpListener,g);JXG.removeEvent(g.containerObj,"mousemove",g.mouseMoveListener,g);for(f in g.objects){g.removeObject(g.objects[f])}g.containerObj.innerHTML="";for(f in g.objects){delete (g.objects[f])}delete (g.renderer);delete (g.algebra);delete (this.boards[g.id])};this.registerElement=function(f,g){f=f.toLowerCase();this.elements[f]=g;if(JXG.Board.prototype["_"+f]){throw new Error("JSXGraph: Can't create wrapper method in JXG.Board because member '_"+f+"' already exists'")}JXG.Board.prototype["_"+f]=function(k,h){return this.create(f,k,h)}};this.unregisterElement=function(f){delete (this.elements[f.toLowerCase()]);delete (JXG.Board.prototype["_"+f.toLowerCase()])}};JXG.getReference=function(b,a){if(typeof(a)=="string"){if(b.objects[a]!=null){a=b.objects[a]}else{if(b.elementsByName[a]!=null){a=b.elementsByName[a]}}}return a};JXG.getRef=JXG.getReference;JXG.isString=function(a){return typeof a=="string"};JXG.isNumber=function(a){return typeof a=="number"};JXG.isFunction=function(a){return typeof a=="function"};JXG.isArray=function(a){return a!=null&&typeof a=="object"&&"splice" in a&&"join" in a};JXG.isPoint=function(a){if(typeof a=="object"){return(a.elementClass==JXG.OBJECT_CLASS_POINT)}return false};JXG.str2Bool=function(a){if(a==undefined||a==null){return true}if(typeof a=="boolean"){return a}if(a.toLowerCase()!="true"){return false}else{return true}};JXG._board=function(b,a){return JXG.JSXGraph.initBoard(b,a)};JXG.createEvalFunction=function(b,e,g){var c=[],a,d;for(a=0;a<g;a++){if(typeof e[a]=="string"){d=JXG.GeonextParser.geonext2JS(e[a],b);d=d.replace(/this\.board\./g,"board.");c[a]=new Function("","return "+(d)+";")}}return function(h){var f=e[h];if(typeof f=="string"){return c[h]()}else{if(typeof f=="function"){return f()}else{if(typeof f=="number"){return f}}}return 0}};JXG.createFunction=function(b,c,d,e){var a;if((e==null||e==true)&&JXG.isString(b)){a=JXG.GeonextParser.geonext2JS(b,c);return new Function(d,"return "+a+";")}else{if(JXG.isFunction(b)){return b}else{if(JXG.isNumber(b)){return function(){return b}}else{if(JXG.isString(b)){return function(){return b}}}}}return null};JXG.readOption=function(a,c,b){var d=a.elements[b];if(typeof a[c][b]!="undefined"){d=a[c][b]}return d};JXG.checkAttributes=function(c,b){var a;if(c==null){c={}}for(a in b){if(c[a]==null||typeof c[a]=="undefined"){c[a]=b[a]}}return c};JXG.getDimensions=function(f){var e,h,c,k,g,b,a,d;e=document.getElementById(f);if(e==null){throw new Error("\nJSXGraph: HTML container element '"+(f)+"' not found.")}h=e.style.display;if(h!="none"&&h!=null){return{width:e.offsetWidth,height:e.offsetHeight}}c=e.style;k=c.visibility;g=c.position;b=c.display;c.visibility="hidden";c.position="absolute";c.display="block";a=e.clientWidth;d=e.clientHeight;c.display=b;c.position=g;c.visibility=k;return{width:a,height:d}};JXG.addEvent=function(d,c,b,a){a["x_internal"+c]=function(){return b.apply(a,arguments)};if(typeof d.addEventListener!="undefined"){d.addEventListener(c,a["x_internal"+c],false)}else{d.attachEvent("on"+c,a["x_internal"+c])}};JXG.removeEvent=function(f,c,b,a){try{if(typeof f.addEventListener!="undefined"){f.removeEventListener(c,a["x_internal"+c],false)}else{f.detachEvent("on"+c,a["x_internal"+c])}}catch(d){}};JXG.bind=function(b,a){return function(){return b.apply(a,arguments)}};JXG.getPosition=function(b){var a=0,c=0,b;if(!b){b=window.event}if(b.pageX||b.pageY){a=b.pageX;c=b.pageY}else{if(b.clientX||b.clientY){a=b.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;c=b.clientY+document.body.scrollTop+document.documentElement.scrollTop}}return[a,c]};JXG.getOffset=function(c){var d=c,a=d.offsetLeft,b=d.offsetTop;while(d=d.offsetParent){a+=d.offsetLeft;b+=d.offsetTop;if(d.offsetParent){a+=d.clientLeft;b+=d.clientTop}}return[a,b]};JXG.getStyle=function(b,a){return b.style[a]};JXG.keys=function(a){var b=[],c;for(c in a){b.push(c)}return b};JXG.escapeHTML=function(a){return a.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;")};JXG.unescapeHTML=function(a){return a.replace(/<\/?[^>]+>/gi,"").replace(/&amp;/g,"&").replace(/&lt;/g,"<").replace(/&gt;/g,">")};JXG.clone=function(b){var a={};a.prototype=b;return a};JXG.deepCopy=function(d){var f,b,e,a;if(typeof d!=="object"||d==null){return d}if(this.isArray(d)){f=[];for(b=0;b<d.length;b++){e=d[b];if(typeof e=="object"){if(this.isArray(e)){f[b]=[];for(a=0;a<e.length;a++){if(typeof e[a]!="object"){f[b].push(e[a])}else{f[b].push(this.deepCopy(e[a]))}}}else{f[b]=this.deepCopy(e)}}else{f[b]=e}}}else{f={};for(b in d){e=d[b];if(typeof e=="object"){if(this.isArray(e)){f[b]=[];for(a=0;a<e.length;a++){if(typeof e[a]!="object"){f[b].push(e[a])}else{f[b].push(this.deepCopy(e[a]))}}}else{f[b]=this.deepCopy(e)}}else{f[b]=e}}}return f};JXG.cloneAndCopy=function(d,c){var a={},b;a.prototype=d;for(b in c){a[b]=c[b]}return a};JXG.toJSON=function(c){switch(typeof c){case"object":if(c){var b=[];if(c instanceof Array){for(var a=0;a<c.length;a++){b.push(JXG.toJSON(c[a]))}return"["+b.join(",")+"]"}else{for(var d in c){b.push('"'+d+'":'+JXG.toJSON(c[d]))}return"{"+b.join(",")+"}"}}else{return"null"}case"string":return'"'+c.replace(/(["'])/g,"\\$1")+'"';case"number":case"boolean":return new String(c)}};JXG.capitalize=function(a){return a.charAt(0).toUpperCase()+a.substring(1).toLowerCase()};JXG.timedChunk=function(b,d,c,e){var a=b.concat();setTimeout(function(){var f=+new Date();do{d.call(c,a.shift())}while(a.length>0&&(+new Date()-f<300));if(a.length>0){setTimeout(arguments.callee,1)}else{e(b)}},1)};JXG.trimNumber=function(a){a=a.replace(/^0+/,"");a=a.replace(/0+$/,"");if(a[a.length-1]=="."||a[a.length-1]==","){a=a.slice(0,-1)}if(a[0]=="."||a[0]==","){a="0"+a}return a};JXG.trim=function(a){a=a.replace(/^w+/,"");a=a.replace(/w+$/,"");return a};JXG.debug=function(a){if(typeof console!="undefined"&&console.log){if(typeof a==="string"){a=a.replace(/<\S[^><]*>/g,"")}console.log(a)}else{if(document.getElementById("debug")){document.getElementById("debug").innerHTML+=a+"<br/>"}}};JXG.addEvent(window,"load",function(b){var a=document.getElementsByTagName("script"),c,e,d;for(c=0;c<a.length;c++){if(a[c].getAttribute("type","none")=="text/jessiescript"){e=document.createElement("div");e.setAttribute("id","jessiescript_autgen_jxg_"+c);e.setAttribute("style","width:500px; height:500px; float:left");e.setAttribute("class","jxgbox");document.body.insertBefore(e,a[c]);d=JXG.JSXGraph.initBoard("jessiescript_autgen_jxg_"+c,{boundingbox:[-5,5,5,-5],keepaspectratio:true});d.construct(a[c].innerHTML)}}},window);JXG.OBJECT_TYPE_ARC=1330921795;JXG.OBJECT_TYPE_ARROW=1330921815;JXG.OBJECT_TYPE_AXIS=1330921816;JXG.OBJECT_TYPE_TICKS=1330926680;JXG.OBJECT_TYPE_CIRCLE=1330922316;JXG.OBJECT_TYPE_CONIC=1330922319;JXG.OBJECT_TYPE_CURVE=1330923344;JXG.OBJECT_TYPE_GLIDER=1330923340;JXG.OBJECT_TYPE_IMAGE=1330926157;JXG.OBJECT_TYPE_LINE=1330924622;JXG.OBJECT_TYPE_POINT=1330925652;JXG.OBJECT_TYPE_SLIDER=1330926404;JXG.OBJECT_TYPE_CAS=1330922320;JXG.OBJECT_TYPE_POLYGON=1330925657;JXG.OBJECT_TYPE_SECTOR=1330926403;JXG.OBJECT_TYPE_TEXT=1330926661;JXG.OBJECT_TYPE_ANGLE=1330921799;JXG.OBJECT_TYPE_INTERSECTION=1330926158;JXG.OBJECT_TYPE_TURTLE=5198933;JXG.OBJECT_TYPE_VECTOR=1330927188;JXG.OBJECT_CLASS_POINT=1;JXG.OBJECT_CLASS_LINE=2;JXG.OBJECT_CLASS_CIRCLE=3;JXG.OBJECT_CLASS_CURVE=4;JXG.OBJECT_CLASS_AREA=5;JXG.OBJECT_CLASS_OTHER=6;JXG.GeometryElement=function(){this.board=null;this.id="";this.needsUpdate=true;this.name="";this.visProp={};JXG.clearVisPropOld(this);this.isReal=true;this.visProp.dash=0;this.childElements={};this.hasLabel=false;this.layer=9;this.notExistingParents={};this.traced=false;this.fixed=false;this.frozen=false;this.traces={};this.numTraces=0;this.transformations=[];this.baseElement=null;this.descendants={};this.ancestors={};this.symbolic={};this.stdform=[1,0,0,0,1,1,0,0];this.quadraticform=[[1,0,0],[0,1,0],[0,0,1]];this.needsRegularUpdate=true};JXG.GeometryElement.prototype.init=function(b,c,a){if(typeof(b)=="string"){b=JXG.JSXGraph.boards[b]}this.board=b;this.id=c;if((a!=null)&&(typeof a!="undefined")){a=a}else{a=this.board.generateName(this)}this.board.elementsByName[a]=this;this.name=a;this.visProp.strokeColor=this.board.options.elements.strokeColor;this.visProp.highlightStrokeColor=this.board.options.elements.highlightStrokeColor;this.visProp.fillColor=this.board.options.elements.fillColor;this.visProp.highlightFillColor=this.board.options.elements.highlightFillColor;this.visProp.strokeWidth=this.board.options.elements.strokeWidth;this.visProp.highlightStrokeWidth=this.visProp.strokeWidth;this.visProp.strokeOpacity=this.board.options.elements.strokeOpacity;this.visProp.highlightStrokeOpacity=this.board.options.elements.highlightStrokeOpacity;this.visProp.fillOpacity=this.board.options.elements.fillOpacity;this.visProp.highlightFillOpacity=this.board.options.elements.highlightFillOpacity;this.visProp.draft=this.board.options.elements.draft.draft;this.visProp.visible=true;this.visProp.shadow=false;this.visProp.gradient="none";this.visProp.gradientSecondColor="black";this.visProp.gradientAngle="270";this.visProp.gradientSecondOpacity=this.visProp.fillOpacity;this.visProp.gradientPositionX=0.5;this.visProp.gradientPositionY=0.5};JXG.GeometryElement.prototype.addChild=function(c){var b,a;this.childElements[c.id]=c;this.addDescendants(c);c.ancestors[this.id]=this;for(b in this.descendants){this.descendants[b].ancestors[this.id]=this;for(a in this.ancestors){this.descendants[b].ancestors[this.ancestors[a].id]=this.ancestors[a]}}for(b in this.ancestors){for(a in this.descendants){this.ancestors[b].descendants[this.descendants[a].id]=this.descendants[a]}}return this};JXG.GeometryElement.prototype.addDescendants=function(b){var a;this.descendants[b.id]=b;for(a in b.childElements){this.addDescendants(b.childElements[a])}return this};JXG.GeometryElement.prototype.generatePolynomial=function(){return[]};JXG.GeometryElement.prototype.animate=function(d,c){var a,b,f=35,g=Math.ceil(c/(f*1)),e,k=this;this.animationData={};var l=function(w,v,s){var u,r,q,n,m;u=JXG.rgb2hsv(w);r=JXG.rgb2hsv(v);q=(r[0]-u[0])/(1*g);n=(r[1]-u[1])/(1*g);m=(r[2]-u[2])/(1*g);k.animationData[s]=new Array(g);for(e=0;e<g;e++){k.animationData[s][g-e-1]=JXG.hsv2rgb(u[0]+(e+1)*q,u[1]+(e+1)*n,u[2]+(e+1)*m)}},h=function(r,m,q){r=parseFloat(r);m=parseFloat(m);if(isNaN(r)||isNaN(m)){return}var n=(m-r)/(1*g);k.animationData[q]=new Array(g);for(e=0;e<g;e++){k.animationData[q][g-e-1]=r+(e+1)*n}};for(a in d){b=a.toLowerCase();switch(b){case"strokecolor":l(this.visProp.strokeColor,d[a],"strokeColor");break;case"strokeopacity":h(this.visProp.strokeOpacity,d[a],"strokeOpacity");break;case"strokewidth":h(this.visProp.strokeWidth,d[a],"strokeWidth");break;case"fillcolor":l(this.visProp.fillColor,d[a],"fillColor");break;case"fillopacity":h(this.visProp.fillOpacity,d[a],"fillOpacity");break}}this.board.animationObjects[this.id]=this;if(typeof this.board.animationIntervalCode=="undefined"){this.board.animationIntervalCode=window.setInterval("JXG.JSXGraph.boards['"+this.board.id+"'].animate();",f)}return this};JXG.GeometryElement.prototype.update=function(){if(this.traced){this.cloneToBackground(true)}return this};JXG.GeometryElement.prototype.updateRenderer=function(){};JXG.GeometryElement.prototype.hideElement=function(){this.visProp.visible=false;this.board.renderer.hide(this);if(this.label!=null&&this.hasLabel){this.label.hiddenByParent=true;if(this.label.content.visProp.visible){this.board.renderer.hide(this.label.content)}}return this};JXG.GeometryElement.prototype.showElement=function(){this.visProp.visible=true;this.board.renderer.show(this);if(this.label!=null&&this.hasLabel&&this.label.hiddenByParent){this.label.hiddenByParent=false;if(this.label.content.visProp.visible){this.board.renderer.show(this.label.content)}}return this};JXG.GeometryElement.prototype.setProperty=function(){var f,e,c,b,d,g;for(f=0;f<arguments.length;f++){b=arguments[f];if(typeof b=="string"){g=b.split(":");g[0]=g[0].replace(/^\s+/,"").replace(/\s+$/,"");g[1]=g[1].replace(/^\s+/,"").replace(/\s+$/,"")}else{if(!JXG.isArray(b)){for(e in b){this.setProperty([e,b[e]])}return this}else{g=b}}if(g[1]==null){continue}switch(g[0].replace(/\s+/g).toLowerCase()){case"strokewidth":this.visProp.strokeWidth=g[1];this.visProp.highlightStrokeWidth=g[1];this.board.renderer.setObjectStrokeWidth(this,this.visProp.strokeWidth);break;case"strokecolor":c=g[1];if(c.length=="9"&&c.substr(0,1)=="#"){d=c.substr(7,2);c=c.substr(0,7)}else{d="FF"}this.visProp.strokeColor=c;this.visProp.strokeOpacity=parseInt(d.toUpperCase(),16)/255;this.board.renderer.setObjectStrokeColor(this,this.visProp.strokeColor,this.visProp.strokeOpacity);break;case"fillcolor":c=g[1];if(c.length=="9"&&c.substr(0,1)=="#"){d=c.substr(7,2);c=c.substr(0,7)}else{d="FF"}this.visProp.fillColor=c;this.visProp.fillOpacity=parseInt(d.toUpperCase(),16)/255;this.board.renderer.setObjectFillColor(this,this.visProp.fillColor,this.visProp.fillOpacity);break;case"highlightstrokewidth":this.visProp.highlightStrokeWidth=g[1];break;case"highlightstrokecolor":c=g[1];if(c.length=="9"&&c.substr(0,1)=="#"){d=c.substr(7,2);c=c.substr(0,7)}else{d="FF"}this.visProp.highlightStrokeColor=c;this.visProp.highlightStrokeOpacity=parseInt(d.toUpperCase(),16)/255;break;case"highlightfillcolor":c=g[1];if(c.length=="9"&&c.substr(0,1)=="#"){d=c.substr(7,2);c=c.substr(0,7)}else{d="FF"}this.visProp.highlightFillColor=c;this.visProp.highlightFillOpacity=parseInt(d.toUpperCase(),16)/255;break;case"fillopacity":this.visProp.fillOpacity=g[1];this.board.renderer.setObjectFillColor(this,this.visProp.fillColor,this.visProp.fillOpacity);break;case"strokeopacity":this.visProp.strokeOpacity=g[1];this.board.renderer.setObjectStrokeColor(this,this.visProp.strokeColor,this.visProp.strokeOpacity);break;case"highlightfillopacity":this.visProp.highlightFillOpacity=g[1];break;case"highlightstrokeopacity":this.visProp.highlightStrokeOpacity=g[1];break;case"labelcolor":c=g[1];if(c.length=="9"&&c.substr(0,1)=="#"){d=c.substr(7,2);c=c.substr(0,7)}else{d="FF"}if(d=="00"){if(this.label!=null&&this.hasLabel){this.label.content.hideElement()}}if(this.label!=null&&this.hasLabel){this.label.color=c;this.board.renderer.setObjectStrokeColor(this.label.content,c,d)}if(this.type==JXG.OBJECT_TYPE_TEXT){this.visProp.strokeColor=c;this.board.renderer.setObjectStrokeColor(this,this.visProp.strokeColor,1)}break;case"infoboxtext":if(typeof(g[1])=="string"){this.infoboxText=g[1]}else{this.infoboxText=false}break;case"showinfobox":if(g[1]=="false"||g[1]==false){this.showInfobox=false}else{if(g[1]=="true"||g[1]==true){this.showInfobox=true}}break;case"visible":if(g[1]=="false"||g[1]==false){this.visProp.visible=false;this.hideElement()}else{if(g[1]=="true"||g[1]==true){this.visProp.visible=true;this.showElement()}}break;case"dash":this.setDash(g[1]);break;case"trace":if(g[1]=="false"||g[1]==false){this.traced=false}else{if(g[1]=="true"||g[1]==true){this.traced=true}}break;case"style":this.setStyle(1*g[1]);break;case"face":if(this.elementClass==JXG.OBJECT_CLASS_POINT){this.setFace(g[1])}break;case"size":if(this.elementClass==JXG.OBJECT_CLASS_POINT){this.visProp.size=1*g[1];this.board.renderer.updatePoint(this)}break;case"fixed":this.fixed=((g[1]=="false")||(g[1]==false))?false:true;break;case"frozen":this.frozen=((g[1]=="false")||(g[1]==false))?false:true;break;case"shadow":if(g[1]=="false"||g[1]==false){this.visProp.shadow=false}else{if(g[1]=="true"||g[1]==true){this.visProp.shadow=true}}this.board.renderer.setShadow(this);break;case"gradient":this.visProp.gradient=g[1];this.board.renderer.setGradient(this);break;case"gradientsecondcolor":c=g[1];if(c.length=="9"&&c.substr(0,1)=="#"){d=c.substr(7,2);c=c.substr(0,7)}else{d="FF"}this.visProp.gradientSecondColor=c;this.visProp.gradientSecondOpacity=parseInt(d.toUpperCase(),16)/255;this.board.renderer.updateGradient(this);break;case"gradientsecondopacity":this.visProp.gradientSecondOpacity=g[1];this.board.renderer.updateGradient(this);break;case"draft":if(g[1]=="false"||g[1]==false){if(this.visProp.draft==true){this.visProp.draft=false;this.board.renderer.removeDraft(this)}}else{if(g[1]=="true"||g[1]==true){this.visProp.draft=true;this.board.renderer.setDraft(this)}}break;case"straightfirst":if(g[1]=="false"||g[1]==false){this.visProp.straightFirst=false}else{if(g[1]=="true"||g[1]==true){this.visProp.straightFirst=true}}this.setStraight(this.visProp.straightFirst,this.visProp.straightLast);break;case"straightlast":if(g[1]=="false"||g[1]==false){this.visProp.straightLast=false}else{if(g[1]=="true"||g[1]==true){this.visProp.straightLast=true}}this.setStraight(this.visProp.straightFirst,this.visProp.straightLast);break;case"firstarrow":if(g[1]=="false"||g[1]==false){this.visProp.firstArrow=false}else{if(g[1]=="true"||g[1]==true){this.visProp.firstArrow=true}}this.setArrow(this.visProp.firstArrow,this.visProp.lastArrow);break;case"lastarrow":if(g[1]=="false"||g[1]==false){this.visProp.lastArrow=false}else{if(g[1]=="true"||g[1]==true){this.visProp.lastArrow=true}}this.setArrow(this.visProp.firstArrow,this.visProp.lastArrow);break;case"curvetype":this.curveType=g[1];break;case"fontsize":this.visProp.fontSize=g[1];break;case"insertticks":if(this.type==JXG.OBJECT_TYPE_TICKS){var a=this.insertTicks;this.insertTicks=true;if(g[1]=="false"||g[1]==false){this.insertTicks=false}if(a!=this.insertTicks){this.calculateTicksCoordinates()}}break;case"drawlabels":if(this.type==JXG.OBJECT_TYPE_TICKS){var a=this.drawLabels;this.drawLabels=true;if(g[1]=="false"||g[1]==false){this.drawLabels=false}if(a!=this.drawLabels){this.calculateTicksCoordinates()}}break;case"drawzero":if(this.type==JXG.OBJECT_TYPE_TICKS){var a=this.drawZero;this.drawZero=true;if(g[1]=="false"||g[1]==false){this.drawZero=false}if(a!=this.drawZero){this.calculateTicksCoordinates()}}break;case"minorticks":if(this.type==JXG.OBJECT_TYPE_TICKS){var a=this.minorTicks;if((g[1]!=null)&&(g[1]>0)){this.minorTicks=g[1]}if(a!=this.minorTicks){this.calculateTicksCoordinates()}}break;case"majortickheight":if(this.type==JXG.OBJECT_TYPE_TICKS){var a=this.majorHeight;if((g[1]!=null)&&(g[1]>0)){this.majorHeight=g[1]}if(a!=this.majorHeight){this.calculateTicksCoordinates()}}break;case"minortickheight":if(this.type==JXG.OBJECT_TYPE_TICKS){var a=this.minorHeight;if((g[1]!=null)&&(g[1]>0)){this.minorHeight=g[1]}if(a!=this.minorHeight){this.calculateTicksCoordinates()}}break;case"snapwidth":if(this.type==JXG.OBJECT_TYPE_GLIDER){this.snapWidth=g[1]}break;case"withlabel":if(!g[1]){if(this.label!=null&&this.hasLabel){this.label.content.hideElement()}}else{if(this.label!=null&&this.hasLabel){if(this.visProp.visible){this.label.content.showElement()}}else{this.addLabelToElement();if(!this.visProp.visible){this.label.content.hideElement()}}}this.hasLabel=g[1]}}return this};JXG.GeometryElement.prototype.setDash=function(a){this.visProp.dash=a;this.board.renderer.setDashStyle(this,this.visProp);return this};JXG.GeometryElement.prototype.prepareUpdate=function(){this.needsUpdate=true;return this};JXG.GeometryElement.prototype.remove=function(){this.board.renderer.remove(this.board.renderer.getElementById(this.id));if(this.hasLabel){this.board.renderer.remove(this.board.renderer.getElementById(this.label.content.id))}return this};JXG.GeometryElement.prototype.getTextAnchor=function(){return new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board)};JXG.GeometryElement.prototype.getLabelAnchor=function(){return new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board)};JXG.GeometryElement.prototype.setStyle=function(a){return this};JXG.GeometryElement.prototype.setStraight=function(a,b){return this};JXG.GeometryElement.prototype.setArrow=function(b,a){this.visProp.firstArrow=b;this.visProp.lastArrow=a;this.prepareUpdate().update();return this};JXG.GeometryElement.prototype.createLabel=function(b,c){var a=false;if(typeof c=="undefined"||c==null){c=[10,10]}this.nameHTML=JXG.GeonextParser.replaceSup(JXG.GeonextParser.replaceSub(this.name));this.label={};if(typeof b=="undefined"||b==true){if(this.board.objects[this.id]==null){this.board.objects[this.id]=this;a=true}this.label.relativeCoords=c;this.label.content=new JXG.Text(this.board,this.nameHTML,this.id,[this.label.relativeCoords[0],-this.label.relativeCoords[1]],this.id+"Label","",null,true,this.board.options.text.defaultDisplay);if(a){delete (this.board.objects[this.id])}this.label.color="#000000";if(!this.visProp.visible){this.label.hiddenByParent=true;this.label.content.visProp.visible=false}this.hasLabel=true}return this};JXG.GeometryElement.prototype.addLabelToElement=function(){this.createLabel(true);this.label.content.id=this.id+"Label";this.board.addText(this.label.content);this.board.renderer.drawText(this.label.content);if(!this.label.content.visProp.visible){this.board.renderer.hide(this.label.content)}return this};JXG.GeometryElement.prototype.highlight=function(){this.board.renderer.highlight(this);return this};JXG.GeometryElement.prototype.noHighlight=function(){this.board.renderer.noHighlight(this);return this};JXG.GeometryElement.prototype.clearTrace=function(){var a;for(a in this.traces){this.board.renderer.remove(this.traces[a])}this.numTraces=0;return this};JXG.GeometryElement.prototype.cloneToBackground=function(a){return this};JXG.GeometryElement.prototype.normalize=function(){this.stdform=JXG.Math.normalize(this.stdform);return this};JXG.GeometryElement.prototype.toJSON=function(){var b='{"name":'+this.name;b+=', "id":'+this.id;var c=[];for(var a in this.visProp){if(this.visProp[a]!=null){c.push('"'+a+'":'+this.visProp[a])}}b+=', "visProp":{'+c.toString()+"}";b+="}";return b};JXG.GeometryElement.prototype.highlightStrokeColor=function(a){this.setProperty({highlightStrokeColor:a})};JXG.GeometryElement.prototype.strokeColor=function(a){this.setProperty({strokeColor:a})};JXG.GeometryElement.prototype.strokeWidth=function(a){this.setProperty({strokeWidth:a})};JXG.GeometryElement.prototype.fillColor=function(a){this.setProperty({fillColor:a})};JXG.GeometryElement.prototype.highlightFillColor=function(a){this.setProperty({highlightFillColor:a})};JXG.GeometryElement.prototype.labelColor=function(a){this.setProperty({labelColor:a})};JXG.GeometryElement.prototype.dash=function(a){this.setProperty({dash:a})};JXG.GeometryElement.prototype.visible=function(a){this.setProperty({visible:a})};JXG.GeometryElement.prototype.shadow=function(a){this.setProperty({shadow:a})};JXG.clearVisPropOld=function(a){a.visPropOld={};a.visPropOld.strokeColor="";a.visPropOld.strokeOpacity="";a.visPropOld.strokeWidth="";a.visPropOld.fillColor="";a.visPropOld.fillOpacity="";a.visPropOld.shadow=false;a.visPropOld.firstArrow=false;a.visPropOld.lastArrow=false};JXG.COORDS_BY_USER=1;JXG.COORDS_BY_SCREEN=2;JXG.Coords=function(c,b,a){this.board=a;this.usrCoords=[];this.scrCoords=[];if(c==JXG.COORDS_BY_USER){if(b.length<=2){this.usrCoords[0]=1;this.usrCoords[1]=b[0];this.usrCoords[2]=b[1]}else{this.usrCoords[0]=b[0];this.usrCoords[1]=b[1];this.usrCoords[2]=b[2];this.normalizeUsrCoords()}this.usr2screen()}else{this.scrCoords[0]=1;this.scrCoords[1]=b[0];this.scrCoords[2]=b[1];this.screen2usr()}};JXG.Coords.prototype.normalizeUsrCoords=function(){var a=0.000001;if(Math.abs(this.usrCoords[0])>a){this.usrCoords[1]/=this.usrCoords[0];this.usrCoords[2]/=this.usrCoords[0];this.usrCoords[0]=1}};JXG.Coords.prototype.usr2screen=function(e){var d=Math.round,a=this.board,c=this.usrCoords;oc=a.origin.scrCoords;if(e==null||e){this.scrCoords[0]=d(c[0]);this.scrCoords[1]=d(c[0]*oc[1]+c[1]*a.stretchX);this.scrCoords[2]=d(c[0]*oc[2]-c[2]*a.stretchY)}else{this.scrCoords[0]=c[0];this.scrCoords[1]=c[0]*oc[1]+c[1]*a.stretchX;this.scrCoords[2]=c[0]*oc[2]-c[2]*a.stretchY}};JXG.Coords.prototype.screen2usr=function(){var d=this.board.origin.scrCoords,c=this.scrCoords,a=this.board;this.usrCoords[0]=1;this.usrCoords[1]=(c[1]-d[1])/a.stretchX;this.usrCoords[2]=(d[2]-c[2])/a.stretchY};JXG.Coords.prototype.distance=function(b,e){var d=0,k,a=this.usrCoords,h=this.scrCoords,g;if(b==JXG.COORDS_BY_USER){k=e.usrCoords;g=a[0]-k[0];d=g*g;g=a[1]-k[1];d+=g*g;g=a[2]-k[2];d+=g*g}else{k=e.scrCoords;g=h[0]-k[0];d=g*g;g=h[1]-k[1];d+=g*g;g=h[2]-k[2];d+=g*g}return Math.sqrt(d)};JXG.Coords.prototype.setCoordinates=function(e,c,b){var a=this.usrCoords,d=this.scrCoords;if(e==JXG.COORDS_BY_USER){if(c.length==2){a[0]=1;a[1]=c[0];a[2]=c[1]}else{a[0]=c[0];a[1]=c[1];a[2]=c[2];this.normalizeUsrCoords()}this.usr2screen(b)}else{d[1]=c[0];d[2]=c[1];this.screen2usr()}};JXG.POINT_STYLE_X_SMALL=0;JXG.POINT_STYLE_X=1;JXG.POINT_STYLE_X_BIG=2;JXG.POINT_STYLE_CIRCLE_TINY=3;JXG.POINT_STYLE_CIRCLE_SMALL=4;JXG.POINT_STYLE_CIRCLE=5;JXG.POINT_STYLE_CIRCLE_BIG=6;JXG.POINT_STYLE_SQUARE_SMALL=7;JXG.POINT_STYLE_SQUARE=8;JXG.POINT_STYLE_SQUARE_BIG=9;JXG.POINT_STYLE_PLUS_SMALL=10;JXG.POINT_STYLE_PLUS=11;JXG.POINT_STYLE_PLUS_BIG=12;JXG.Point=function(e,f,g,b,a,d,c){this.constructor();this.type=JXG.OBJECT_TYPE_POINT;this.elementClass=JXG.OBJECT_CLASS_POINT;this.init(e,g,b);if(f==null){f=[0,0]}this.coords=new JXG.Coords(JXG.COORDS_BY_USER,f,this.board);this.initialCoords=new JXG.Coords(JXG.COORDS_BY_USER,f,this.board);if(c==null){c=e.options.layer.point}this.layer=c;this.showInfobox=true;this.label={};this.label.relativeCoords=[10,-10];this.nameHTML=JXG.GeonextParser.replaceSup(JXG.GeonextParser.replaceSub(this.name));if(typeof d=="undefined"||d==true){this.board.objects[this.id]=this;this.label.content=new JXG.Text(this.board,this.nameHTML,this.id,this.label.relativeCoords,this.id+"Label","",null,true,this.board.options.text.defaultDisplay);delete (this.board.objects[this.id]);this.label.color="#000000";if(!a){this.label.hiddenByParent=true;this.label.content.visProp.visible=false}this.hasLabel=true}else{this.showInfobox=false}this.fixed=false;this.position=null;this.onPolygon=false;this.visProp.style=this.board.options.point.style;this.visProp.face=this.board.options.point.face;this.visProp.size=this.board.options.point.size;this.visProp.fillColor=this.board.options.point.fillColor;this.visProp.highlightFillColor=this.board.options.point.highlightFillColor;this.visProp.strokeColor=this.board.options.point.strokeColor;this.visProp.highlightStrokeColor=this.board.options.point.highlightStrokeColor;this.visProp.strokeWidth=this.board.options.point.strokeWidth;this.visProp.visible=a;this.slideObject=null;this.group=[];this.id=this.board.addPoint(this)};JXG.Point.prototype=new JXG.GeometryElement();JXG.Point.prototype.hasPoint=function(b,d){var a=this.coords.scrCoords,c;c=this.visProp.size;if(c<this.board.options.precision.hasPoint){c=this.board.options.precision.hasPoint}return((Math.abs(a[1]-b)<c+2)&&(Math.abs(a[2]-d))<c+2)};JXG.Point.prototype.updateConstraint=function(){return this};JXG.Point.prototype.update=function(e){if(!this.needsUpdate){return}if(typeof e=="undefined"){e=false}if(this.traced){this.cloneToBackground(true)}if(this.type==JXG.OBJECT_TYPE_GLIDER){if(this.slideObject.type==JXG.OBJECT_TYPE_CIRCLE){if(e){this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.slideObject.midpoint.X()+Math.cos(this.position),this.slideObject.midpoint.Y()+Math.sin(this.position)]);this.coords=JXG.Math.Geometry.projectPointToCircle(this,this.slideObject,this.board)}else{this.coords=JXG.Math.Geometry.projectPointToCircle(this,this.slideObject,this.board);this.position=JXG.Math.Geometry.rad([this.slideObject.midpoint.X()+1,this.slideObject.midpoint.Y()],this.slideObject.midpoint,this)}}else{if(this.slideObject.type==JXG.OBJECT_TYPE_LINE){this.coords=JXG.Math.Geometry.projectPointToLine(this,this.slideObject,this.board);var d=this.slideObject.point1.coords;var h=this.slideObject.point2.coords;if(e){if(Math.abs(d.usrCoords[0])>=JXG.Math.eps&&Math.abs(h.usrCoords[0])>=JXG.Math.eps){this.coords.setCoordinates(JXG.COORDS_BY_USER,[d.usrCoords[1]+this.position*(h.usrCoords[1]-d.usrCoords[1]),d.usrCoords[2]+this.position*(h.usrCoords[2]-d.usrCoords[2])])}}else{var k=1;var q=d.distance(JXG.COORDS_BY_USER,this.coords);var b=d.distance(JXG.COORDS_BY_USER,h);var g=h.distance(JXG.COORDS_BY_USER,this.coords);if(((q>b)||(g>b))&&(q<g)){k=-1}this.position=k*q/b;if(this.snapWidth!=null&&Math.abs(this._smax-this._smin)>=JXG.Math.eps){if(this.position<0){this.position=0}if(this.position>1){this.position=1}var r=this.position*(this._smax-this._smin)+this._smin;r=Math.round(r/this.snapWidth)*this.snapWidth;this.position=(r-this._smin)/(this._smax-this._smin);this.update(true)}}var c=this.slideObject.point1.coords.scrCoords;var n=this.slideObject.point2.coords.scrCoords;var f;if(this.slideObject.getSlope()==0){f=1}else{f=2}var l=this.coords.scrCoords[f];if(!this.slideObject.visProp.straightFirst){if(c[f]<n[f]){if(l<c[f]){this.coords=this.slideObject.point1.coords;this.position=0}}else{if(c[f]>n[f]){if(l>c[f]){this.coords=this.slideObject.point1.coords;this.position=0}}}}if(!this.slideObject.visProp.straightLast){if(c[f]<n[f]){if(l>n[f]){this.coords=this.slideObject.point2.coords;this.position=1}}else{if(c[f]>n[f]){if(l<n[f]){this.coords=this.slideObject.point2.coords;this.position=1}}}}if(this.onPolygon){var s=this.slideObject.point1.coords;var m=this.slideObject.point2.coords;if(Math.abs(this.coords.scrCoords[1]-s.scrCoords[1])<this.board.options.precision.hasPoint&&Math.abs(this.coords.scrCoords[2]-s.scrCoords[2])<this.board.options.precision.hasPoint){var a=this.slideObject.parentPolygon;for(var f=0;f<a.borders.length;f++){if(this.slideObject==a.borders[f]){this.slideObject=a.borders[(f-1+a.borders.length)%a.borders.length];break}}}else{if(Math.abs(this.coords.scrCoords[1]-m.scrCoords[1])<this.board.options.precision.hasPoint&&Math.abs(this.coords.scrCoords[2]-m.scrCoords[2])<this.board.options.precision.hasPoint){var a=this.slideObject.parentPolygon;for(var f=0;f<a.borders.length;f++){if(this.slideObject==a.borders[f]){this.slideObject=a.borders[(f+1+a.borders.length)%a.borders.length];break}}}}}}else{if(this.slideObject.type==JXG.OBJECT_TYPE_TURTLE){this.updateConstraint();this.coords=JXG.Math.Geometry.projectPointToTurtle(this,this.slideObject,this.board)}else{if(this.slideObject.elementClass==JXG.OBJECT_CLASS_CURVE){this.updateConstraint();this.coords=JXG.Math.Geometry.projectPointToCurve(this,this.slideObject,this.board)}}}}}if(this.type==JXG.OBJECT_TYPE_CAS){this.updateConstraint()}this.updateTransform();this.needsUpdate=false;return this};JXG.Point.prototype.updateRenderer=function(){if(this.visProp.visible){var a=this.isReal;this.isReal=(isNaN(this.coords.usrCoords[1]+this.coords.usrCoords[2]))?false:true;this.isReal=(Math.abs(this.coords.usrCoords[0])>JXG.Math.eps)?this.isReal:false;if(this.isReal){if(a!=this.isReal){this.board.renderer.show(this);if(this.hasLabel&&this.label.content.visProp.visible){this.board.renderer.show(this.label.content)}}this.board.renderer.updatePoint(this)}else{if(a!=this.isReal){this.board.renderer.hide(this);if(this.hasLabel&&this.label.content.visProp.visible){this.board.renderer.hide(this.label.content)}}}}if(this.hasLabel&&this.label.content.visProp.visible&&this.isReal){this.label.content.update();this.board.renderer.updateText(this.label.content)}return this};JXG.Point.prototype.X=function(){return this.coords.usrCoords[1]};JXG.Point.prototype.Y=function(){return this.coords.usrCoords[2]};JXG.Point.prototype.Z=function(){return this.coords.usrCoords[0]};JXG.Point.prototype.XEval=function(){return this.coords.usrCoords[1]};JXG.Point.prototype.YEval=function(){return this.coords.usrCoords[2]};JXG.Point.prototype.ZEval=function(){return this.coords.usrCoords[0]};JXG.Point.prototype.Dist=function(b){var d,g=b.coords.usrCoords,a=this.coords.usrCoords,e;e=a[0]-g[0];d=e*e;e=a[1]-g[1];d+=e*e;e=a[2]-g[2];d+=e*e;return Math.sqrt(d)};JXG.Point.prototype.setPositionDirectly=function(a,g,e){var d,k,h,c,b,f=this.coords;this.coords=new JXG.Coords(a,[g,e],this.board);if(this.group.length!=0){k=this.coords.usrCoords[1]-f.usrCoords[1];h=this.coords.usrCoords[2]-f.usrCoords[2];for(d=0;d<this.group.length;d++){for(c in this.group[d].objects){b=this.group[d].objects[c];b.initialCoords=new JXG.Coords(JXG.COORDS_BY_USER,[b.initialCoords.usrCoords[1]+k,b.initialCoords.usrCoords[2]+h],this.board)}}this.group[this.group.length-1].dX=this.coords.scrCoords[1]-f.scrCoords[1];this.group[this.group.length-1].dY=this.coords.scrCoords[2]-f.scrCoords[2];this.group[this.group.length-1].update(this)}else{for(d=this.transformations.length-1;d>=0;d--){this.initialCoords=new JXG.Coords(a,JXG.Math.matVecMult(JXG.Math.Numerics.Inverse(this.transformations[d].matrix),[1,g,e]),this.board)}this.update()}return this};JXG.Point.prototype.setPositionByTransform=function(e,a,d){var c=this.coords;var b=this.board.create("transform",[a,d],{type:"translate"});if(this.transformations.length>0&&this.transformations[this.transformations.length-1].isNumericMatrix){this.transformations[this.transformations.length-1].melt(b)}else{this.addTransform(this,b)}if(this.group.length!=0){}else{this.update()}return this};JXG.Point.prototype.setPosition=function(c,a,b){this.setPositionDirectly(c,a,b);return this};JXG.Point.prototype.makeGlider=function(a){this.slideObject=JXG.getReference(this.board,a);this.type=JXG.OBJECT_TYPE_GLIDER;this.snapWidth=null;this.slideObject.addChild(this);if(this.slideObject.elementClass==JXG.OBJECT_CLASS_LINE){this.generatePolynomial=function(){return this.slideObject.generatePolynomial(this)}}else{if(this.slideObject.elementClass==JXG.OBJECT_CLASS_CIRCLE){this.generatePolynomial=function(){return this.slideObject.generatePolynomial(this)}}}this.needsUpdate=true;this.update();return this};JXG.Point.prototype.addConstraint=function(e){this.type=JXG.OBJECT_TYPE_CAS;var f=this.board.elementsByName;var g=[];var a;for(var d=0;d<e.length;d++){var b=e[d];if(typeof b=="string"){var c=JXG.GeonextParser.geonext2JS(b,this.board);g[d]=new Function("","return "+c+";")}else{if(typeof b=="function"){g[d]=b}else{if(typeof b=="number"){g[d]=function(h){return function(){return h}}(b)}else{if(typeof b=="object"&&typeof b.Value=="function"){g[d]=(function(h){return function(){return h.Value()}})(b)}}}}}if(e.length==1){this.updateConstraint=function(){var h=g[0]();if(JXG.isArray(h)){this.coords.setCoordinates(JXG.COORDS_BY_USER,h)}else{this.coords=h}}}else{if(e.length==2){this.XEval=g[0];this.YEval=g[1];a="this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.XEval(),this.YEval()]);";this.updateConstraint=new Function("",a)}else{this.ZEval=g[0];this.XEval=g[1];this.YEval=g[2];a="this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.ZEval(),this.XEval(),this.YEval()]);";this.updateConstraint=new Function("",a)}}if(!this.board.isSuspendedUpdate){this.update()}return this};JXG.Point.prototype.updateTransform=function(){if(this.transformations.length==0||this.baseElement==null){return}var b,a;if(this===this.baseElement){b=this.transformations[0].apply(this.baseElement,"self")}else{b=this.transformations[0].apply(this.baseElement)}this.coords.setCoordinates(JXG.COORDS_BY_USER,b);for(a=1;a<this.transformations.length;a++){this.coords.setCoordinates(JXG.COORDS_BY_USER,this.transformations[a].apply(this))}return this};JXG.Point.prototype.addTransform=function(d,b){var e,c,a;if(this.transformations.length==0){this.baseElement=d}if(JXG.isArray(b)){e=b}else{e=[b]}a=e.length;for(c=0;c<a;c++){this.transformations.push(e[c])}return this};JXG.Point.prototype.startAnimation=function(a,b){if((this.type==JXG.OBJECT_TYPE_GLIDER)&&(typeof this.intervalCode=="undefined")){this.intervalCode=window.setInterval("JXG.JSXGraph.boards['"+this.board.id+"'].objects['"+this.id+"']._anim("+a+", "+b+")",250);if(typeof this.intervalCount=="undefined"){this.intervalCount=0}}return this};JXG.Point.prototype.stopAnimation=function(){if(typeof this.intervalCode!="undefined"){window.clearInterval(this.intervalCode);delete (this.intervalCode)}return this};JXG.Point.prototype.moveTo=function(g,c){if(typeof c=="undefined"||c==0){this.setPosition(JXG.COORDS_BY_USER,g[0],g[1]);this.board.update(this);return this}var h=35,k=Math.ceil(c/(h*1)),l=new Array(k+1),b=this.coords.usrCoords[1],a=this.coords.usrCoords[2],e=(g[0]-b),d=(g[1]-a),f;if(Math.abs(e)<JXG.Math.eps&&Math.abs(d)<JXG.Math.eps){return this}for(f=k;f>=0;f--){l[k-f]=[b+e*Math.sin((f/(k*1))*Math.PI/2),a+d*Math.sin((f/(k*1))*Math.PI/2)]}this.animationPath=l;this.board.animationObjects[this.id]=this;if(typeof this.board.animationIntervalCode=="undefined"){this.board.animationIntervalCode=window.setInterval("JXG.JSXGraph.boards['"+this.board.id+"'].animate();",h)}return this};JXG.Point.prototype.visit=function(k,d,b){if(arguments.length==2){b=1}var l=35,m=Math.ceil(d/(l*1)),n=new Array(b*(m+1)),c=this.coords.usrCoords[1],a=this.coords.usrCoords[2],g=(k[0]-c),e=(k[1]-a),h,f;for(f=0;f<b;f++){for(h=m;h>=0;h--){n[f*(m+1)+m-h]=[c+g*Math.pow(Math.sin((h/(m*1))*Math.PI),2),a+e*Math.pow(Math.sin((h/(m*1))*Math.PI),2)]}}this.animationPath=n;this.board.animationObjects[this.id]=this;if(typeof this.board.animationIntervalCode=="undefined"){this.board.animationIntervalCode=window.setInterval("JXG.JSXGraph.boards['"+this.board.id+"'].animate();",l)}return this};JXG.Point.prototype._anim=function(m,f){var b,k,g,e,d,c,l=1,a,h;this.intervalCount++;if(this.intervalCount>f){this.intervalCount=0}if(this.slideObject.elementClass==JXG.OBJECT_CLASS_LINE){b=this.slideObject.point1.coords.distance(JXG.COORDS_BY_SCREEN,this.slideObject.point2.coords);k=this.slideObject.getSlope();if(k!="INF"){d=Math.atan(k);g=Math.round((this.intervalCount/f)*b*Math.cos(d));e=Math.round((this.intervalCount/f)*b*Math.sin(d))}else{g=0;e=Math.round((this.intervalCount/f)*b)}if(m<0){c=this.slideObject.point2;if(this.slideObject.point2.coords.scrCoords[1]-this.slideObject.point1.coords.scrCoords[1]>0){l=-1}else{if(this.slideObject.point2.coords.scrCoords[1]-this.slideObject.point1.coords.scrCoords[1]==0){if(this.slideObject.point2.coords.scrCoords[2]-this.slideObject.point1.coords.scrCoords[2]>0){l=-1}}}}else{c=this.slideObject.point1;if(this.slideObject.point1.coords.scrCoords[1]-this.slideObject.point2.coords.scrCoords[1]>0){l=-1}else{if(this.slideObject.point1.coords.scrCoords[1]-this.slideObject.point2.coords.scrCoords[1]==0){if(this.slideObject.point1.coords.scrCoords[2]-this.slideObject.point2.coords.scrCoords[2]>0){l=-1}}}}this.coords.setCoordinates(JXG.COORDS_BY_SCREEN,[c.coords.scrCoords[1]+l*g,c.coords.scrCoords[2]+l*e])}else{if(this.slideObject.elementClass==JXG.OBJECT_CLASS_CURVE){if(m>0){a=Math.round(this.intervalCount/f*this.board.canvasWidth)}else{a=Math.round((f-this.intervalCount)/f*this.board.canvasWidth)}this.coords.setCoordinates(JXG.COORDS_BY_SCREEN,[a,0]);this.coords=JXG.Math.Geometry.projectPointToCurve(this,this.slideObject,this.board)}else{if(this.slideObject.elementClass==JXG.OBJECT_CLASS_CIRCLE){if(m<0){d=this.intervalCount/f*2*Math.PI}else{d=(f-this.intervalCount)/f*2*Math.PI}h=this.slideObject.Radius();this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.slideObject.midpoint.coords.usrCoords[1]+h*Math.cos(d),this.slideObject.midpoint.coords.usrCoords[2]+h*Math.sin(d)])}}}this.board.update(this);return this};JXG.Point.prototype.setStyle=function(a){if(a==0||a==1||a==2){this.visProp.face="cross";if(a==0){this.visProp.size=2}else{if(a==1){this.visProp.size=3}else{this.visProp.size=4}}}else{if(a==3||a==4||a==5||a==6){this.visProp.face="circle";if(a==3){this.visProp.size=1}else{if(a==4){this.visProp.size=2}else{if(a==5){this.visProp.size=3}else{this.visProp.size=4}}}}else{if(a==7||a==8||a==9){this.visProp.face="square";if(a==7){this.visProp.size=2}else{if(a==8){this.visProp.size=3}else{this.visProp.size=4}}}else{if(a==10||a==11||a==12){this.visProp.face="plus";if(a==10){this.visProp.size=2}else{if(a==11){this.visProp.size=3}else{this.visProp.size=4}}}}}}this.board.renderer.changePointStyle(this);return this};JXG.Point.prototype.setFace=function(a){a=a.toLowerCase();if(a=="cross"||a=="x"||a=="plus"||a=="+"||a=="circle"||a=="o"||a=="square"||a=="[]"||a=="diamond"||a=="<>"||a=="triangleup"||a=="a"||a=="triangledown"||a=="v"||a=="triangleleft"||a=="<"||a=="triangleright"||a==">"){this.visProp.face=a}else{this.visProp.face="circle"}this.board.renderer.changePointStyle(this);return this};JXG.Point.prototype.remove=function(){if(this.hasLabel){this.board.renderer.remove(this.board.renderer.getElementById(this.label.content.id))}this.board.renderer.remove(this.board.renderer.getElementById(this.id))};JXG.Point.prototype.getTextAnchor=function(){return this.coords};JXG.Point.prototype.getLabelAnchor=function(){return this.coords};JXG.Point.prototype.face=function(a){this.setProperty({face:a})};JXG.Point.prototype.size=function(a){this.setProperty({size:a})};JXG.Point.prototype.cloneToBackground=function(a){var b={};b.id=this.id+"T"+this.numTraces;this.numTraces++;b.coords=this.coords;b.visProp=this.visProp;b.elementClass=JXG.OBJECT_CLASS_POINT;JXG.clearVisPropOld(b);this.board.renderer.drawPoint(b);this.traces[b.id]=document.getElementById(b.id);delete b;return this};JXG.createPoint=function(f,c,g){var e,b=false,d,a;g=JXG.checkAttributes(g,{withLabel:JXG.readOption(f.options,"point","withLabel"),layer:null});a=(typeof g.visible=="undefined")||JXG.str2Bool(g.visible);for(d=0;d<c.length;d++){if(typeof c[d]=="function"||typeof c[d]=="string"){b=true}}if(!b){if((JXG.isNumber(c[0]))&&(JXG.isNumber(c[1]))){e=new JXG.Point(f,c,g.id,g.name,a,g.withLabel,g.layer);if(g.slideObject!=null){e.makeGlider(g.slideObject)}else{e.baseElement=e}}else{if((typeof c[0]=="object")&&(typeof c[1]=="object")){e=new JXG.Point(f,[0,0],g.id,g.name,a,g.withLabel,g.layer);e.addTransform(c[0],c[1])}else{throw new Error("JSXGraph: Can't create point with parent types '"+(typeof c[0])+"' and '"+(typeof c[1])+"'.\nPossible parent types: [x,y], [z,x,y], [point,transformation]")}}}else{e=new JXG.Point(f,[0,0],g.id,g.name,a,g.withLabel,g.layer);e.addConstraint(c)}return e};JXG.createGlider=function(d,b,e){var c,a;e=JXG.checkAttributes(e,{withLabel:JXG.readOption(d.options,"point","withLabel"),layer:null});a=(typeof e.visible=="undefined")||JXG.str2Bool(e.visible);if(b.length==1){c=new JXG.Point(d,[0,0],e.id,e.name,a,e.withLabel)}else{c=d.create("point",b.slice(0,-1),e)}c.makeGlider(b[b.length-1]);return c};JXG.createIntersectionPoint=function(d,b,a){var c;if(b.length>=3){if(b.length==3){b.push(null)}c=d.create("point",[d.intersection(b[0],b[1],b[2],b[3])],a)}b[0].addChild(c);b[1].addChild(c);c.generatePolynomial=function(){var e=b[0].generatePolynomial(c);var f=b[1].generatePolynomial(c);if((e.length==0)||(f.length==0)){return[]}else{return[e[0],f[0]]}};return c};JXG.createOtherIntersectionPoint=function(d,b,a){var c;if(b.length!=3||!JXG.isPoint(b[2])||(b[0].elementClass!=JXG.OBJECT_CLASS_LINE&&b[0].elementClass!=JXG.OBJECT_CLASS_CIRCLE)||(b[1].elementClass!=JXG.OBJECT_CLASS_LINE&&b[1].elementClass!=JXG.OBJECT_CLASS_CIRCLE)){throw new Error("JSXGraph: Can't create 'other intersection point' with parent types '"+(typeof b[0])+"', '"+(typeof b[1])+"'and '"+(typeof b[2])+"'.\nPossible parent types: [circle|line,circle|line,point]")}else{c=d.create("point",[d.otherIntersection(b[0],b[1],b[2])],a)}b[0].addChild(c);b[1].addChild(c);c.generatePolynomial=function(){var e=b[0].generatePolynomial(c);var f=b[1].generatePolynomial(c);if((e.length==0)||(f.length==0)){return[]}else{return[e[0],f[0]]}};return c};JXG.JSXGraph.registerElement("point",JXG.createPoint);JXG.JSXGraph.registerElement("glider",JXG.createGlider);JXG.JSXGraph.registerElement("intersection",JXG.createIntersectionPoint);JXG.JSXGraph.registerElement("otherintersection",JXG.createOtherIntersectionPoint);JXG.Line=function(d,f,e,g,a,c,b){this.constructor();this.type=JXG.OBJECT_TYPE_LINE;this.elementClass=JXG.OBJECT_CLASS_LINE;this.init(d,g,a);if(b==null){b=d.options.layer.line}this.layer=b;this.point1=JXG.getReference(this.board,f);this.point2=JXG.getReference(this.board,e);this.image=null;this.imageTransformMatrix=[[1,0,0],[0,1,0],[0,0,1]];this.visProp.fillColor=this.board.options.line.fillColor;this.visProp.highlightFillColor=this.board.options.line.highlightFillColor;this.visProp.strokeColor=this.board.options.line.strokeColor;this.visProp.highlightStrokeColor=this.board.options.line.highlightStrokeColor;this.visProp.straightFirst=this.board.options.line.straightFirst;this.visProp.straightLast=this.board.options.line.straightLast;this.visProp.visible=true;this.visProp.firstArrow=this.board.options.line.firstArrow;this.visProp.lastArrow=this.board.options.line.lastArrow;this.ticks=[];this.defaultTicks=null;this.parentPolygon=null;this.labelOffsets=[].concat(this.board.options.line.labelOffsets);this.labelOffsets[0]=Math.abs(this.labelOffsets[0]);this.labelOffsets[1]=Math.abs(this.labelOffsets[1]);this.createLabel(c);this.id=this.board.addLine(this);this.point1.addChild(this);this.point2.addChild(this);this.needsUpdate=true;this.update()};JXG.Line.prototype=new JXG.GeometryElement;JXG.Line.prototype.hasPoint=function(k,g){var f=[],r,n=[1,k,g],l=[],u,d,h,b,m,q,e,a;f[0]=this.stdform[0]-this.stdform[1]*this.board.origin.scrCoords[1]/this.board.stretchX+this.stdform[2]*this.board.origin.scrCoords[2]/this.board.stretchY;f[1]=this.stdform[1]/this.board.stretchX;f[2]=this.stdform[2]/(-this.board.stretchY);var l=[0,f[1],f[2]];l=JXG.Math.crossProduct(l,n);l=JXG.Math.crossProduct(l,f);l[1]/=l[0];l[2]/=l[0];l[0]=1;r=(n[0]-l[0])*(n[0]-l[0])+(n[1]-l[1])*(n[1]-l[1])+(n[2]-l[2])*(n[2]-l[2]);if(isNaN(r)||r>this.board.options.precision.hasPoint*this.board.options.precision.hasPoint){return false}if(this.visProp.straightFirst&&this.visProp.straightLast){return true}else{b=this.point1.coords.scrCoords;m=this.point2.coords.scrCoords;a=(m[1]-b[1])*(m[1]-b[1])+(m[2]-b[2])*(m[2]-b[2]);q=(l[1]-b[1])*(l[1]-b[1])+(l[2]-b[2])*(l[2]-b[2]);e=(l[1]-m[1])*(l[1]-m[1])+(l[2]-m[2])*(l[2]-m[2]);if((q>a)||(e>a)){if(q<e){if(!this.visProp.straightFirst){return false}}else{if(!this.visProp.straightLast){return false}}}return true}};JXG.Line.prototype.update=function(){var a,b;if(this.constrained){if(typeof this.funps!="undefined"){b=this.funps();this.point1=b[0];this.point2=b[1]}else{this.point1=this.funp1();this.point2=this.funp2()}}if(this.needsUpdate){if(true||!this.board.geonextCompatibilityMode){this.updateStdform()}for(a=0;a<this.ticks.length;a++){if(typeof this.ticks[a]!="undefined"){this.ticks[a].calculateTicksCoordinates()}}}if(this.traced){this.cloneToBackground(true)}};JXG.Line.prototype.updateStdform=function(){var a=JXG.Math.crossProduct(this.point1.coords.usrCoords,this.point2.coords.usrCoords);this.stdform[0]=a[0];this.stdform[1]=a[1];this.stdform[2]=a[2];this.stdform[3]=0;this.normalize()};JXG.Line.prototype.updateRenderer=function(){var a;if(this.needsUpdate&&this.visProp.visible){a=this.isReal;this.isReal=(isNaN(this.point1.coords.usrCoords[1]+this.point1.coords.usrCoords[2]+this.point2.coords.usrCoords[1]+this.point2.coords.usrCoords[2]))?false:true;if(this.isReal){if(a!=this.isReal){this.board.renderer.show(this);if(this.hasLabel&&this.label.content.visProp.visible){this.board.renderer.show(this.label.content)}}this.board.renderer.updateLine(this)}else{if(a!=this.isReal){this.board.renderer.hide(this);if(this.hasLabel&&this.label.content.visProp.visible){this.board.renderer.hide(this.label.content)}}}this.needsUpdate=false}if(this.hasLabel&&this.label.content.visProp.visible&&this.isReal){this.label.content.update();this.board.renderer.updateText(this.label.content)}};JXG.Line.prototype.generatePolynomial=function(e){var d=this.point1.symbolic.x,c=this.point1.symbolic.y,g=this.point2.symbolic.x,f=this.point2.symbolic.y,b=e.symbolic.x,a=e.symbolic.y;return[["(",c,")*(",b,")-(",c,")*(",g,")+(",a,")*(",g,")-(",d,")*(",a,")+(",d,")*(",f,")-(",b,")*(",f,")"].join("")]};JXG.Line.prototype.getRise=function(){if(Math.abs(this.stdform[2])>=JXG.Math.eps){return -this.stdform[0]/this.stdform[2]}else{return Infinity}};JXG.Line.prototype.getSlope=function(){if(Math.abs(this.stdform[2])>=JXG.Math.eps){return -this.stdform[1]/this.stdform[2]}else{return Infinity}};JXG.Line.prototype.setStraight=function(a,b){this.visProp.straightFirst=a;this.visProp.straightLast=b;this.board.renderer.updateLine(this)};JXG.Line.prototype.getTextAnchor=function(){return new JXG.Coords(JXG.COORDS_BY_USER,[this.point1.X()+0.5*(this.point2.X()-this.point1.X()),this.point1.Y()+0.5*(this.point2.Y()-this.point1.Y())],this.board)};JXG.Line.prototype.setLabelRelativeCoords=function(a){if(typeof this.label.content!="undefined"){this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[a[0],-a[1]],this.board)}};JXG.Line.prototype.getLabelAnchor=function(){var e,c,b,d,a,f=this.labelOffsets[0],g=this.labelOffsets[1];if(!this.visProp.straightFirst&&!this.visProp.straightLast){this.setLabelRelativeCoords(this.labelOffsets);return new JXG.Coords(JXG.COORDS_BY_USER,[this.point2.X()-0.5*(this.point2.X()-this.point1.X()),this.point2.Y()-0.5*(this.point2.Y()-this.point1.Y())],this.board)}else{c=new JXG.Coords(JXG.COORDS_BY_USER,this.point1.coords.usrCoords,this.board);b=new JXG.Coords(JXG.COORDS_BY_USER,this.point2.coords.usrCoords,this.board);this.board.renderer.calcStraight(this,c,b);if(this.visProp.straightFirst){e=c}else{e=b}if(this.label.content!=null){d=[0,0];a=this.getSlope();if(e.scrCoords[2]==0){if(a==Infinity){d=[f,-g]}else{if(a>=0){d=[f,-g]}else{d=[-f,-g]}}}else{if(e.scrCoords[2]==this.board.canvasHeight){if(a==Infinity){d=[f,g]}else{if(a>=0){d=[-f,g]}else{d=[f,g]}}}}if(e.scrCoords[1]==0){if(a==Infinity){d=[f,g]}else{if(a>=0){d=[f,-g]}else{d=[f,g]}}}else{if(e.scrCoords[1]==this.board.canvasWidth){if(a==Infinity){d=[-f,g]}else{if(a>=0){d=[-f,g]}else{d=[-f,-g]}}}}this.setLabelRelativeCoords(d)}return e}};JXG.Line.prototype.cloneToBackground=function(b){var d={},c,a;d.id=this.id+"T"+this.numTraces;this.numTraces++;d.point1=this.point1;d.point2=this.point2;d.stdform=this.stdform;JXG.clearVisPropOld(d);d.board={};d.board.unitX=this.board.unitX;d.board.unitY=this.board.unitY;d.board.zoomX=this.board.zoomX;d.board.zoomY=this.board.zoomY;d.board.stretchX=this.board.stretchX;d.board.stretchY=this.board.stretchY;d.board.origin=this.board.origin;d.board.canvasHeight=this.board.canvasHeight;d.board.canvasWidth=this.board.canvasWidth;d.board.dimension=this.board.dimension;d.board.algebra=this.board.algebra;d.visProp=this.visProp;a=this.getSlope();c=this.getRise();d.getSlope=function(){return a};d.getRise=function(){return c};this.board.renderer.enhancedRendering=true;this.board.renderer.drawLine(d);this.board.renderer.enhancedRendering=false;this.traces[d.id]=this.board.renderer.getElementById(d.id);delete d};JXG.Line.prototype.addTransform=function(a){var c,b;if(JXG.isArray(a)){c=a}else{c=[a]}for(b=0;b<c.length;b++){this.point1.transformations.push(c[b]);this.point2.transformations.push(c[b])}};JXG.Line.prototype.setPosition=function(d,a,c){var b=this.board.create("transform",[a,c],{type:"translate"});if(this.point1.transformations.length>0&&this.point1.transformations[this.point1.transformations.length-1].isNumericMatrix){this.point1.transformations[this.point1.transformations.length-1].melt(b)}else{this.point1.addTransform(this.point1,b)}if(this.point2.transformations.length>0&&this.point2.transformations[this.point2.transformations.length-1].isNumericMatrix){this.point2.transformations[this.point2.transformations.length-1].melt(b)}else{this.point2.addTransform(this.point2,b)}};JXG.Line.prototype.X=function(k){var n=this.stdform[1],m=this.stdform[2],l=this.stdform[0],g,f,d,e,h;k*=Math.PI;g=n*Math.cos(k)+m*Math.sin(k);f=l;d=Math.sqrt(g*g+f*f);e=-f/d;h=g/d;if(Math.abs(h)<JXG.Math.eps){h=1}return e*Math.cos(k)/h};JXG.Line.prototype.Y=function(k){var n=this.stdform[1],m=this.stdform[2],l=this.stdform[0],g,f,d,e,h;k*=Math.PI;g=n*Math.cos(k)+m*Math.sin(k);f=l;d=Math.sqrt(g*g+f*f);e=-f/d;h=g/d;if(Math.abs(h)<JXG.Math.eps){h=1}return e*Math.sin(k)/h};JXG.Line.prototype.Z=function(h){var f=this.stdform[1],e=this.stdform[2],m=this.stdform[0],d,l,g,k;h*=Math.PI;d=f*Math.cos(h)+e*Math.sin(h);l=m;g=Math.sqrt(d*d+l*l);k=d/g;if(Math.abs(k)>=JXG.Math.eps){return 1}else{return 0}};JXG.Line.prototype.minX=function(){return 0};JXG.Line.prototype.maxX=function(){return 1};JXG.Line.prototype.addTicks=function(a){if(a.id==""||typeof a.id=="undefined"){a.id=this.id+"_ticks_"+(this.ticks.length+1)}this.board.renderer.drawTicks(a);this.ticks.push(a);this.ticks[this.ticks.length-1].updateRenderer();return a.id};JXG.Line.prototype.removeAllTicks=function(){var a;for(a=this.ticks.length;a>0;a--){this.board.renderer.remove(this.ticks[a-1].rendNode)}this.ticks=new Array()};JXG.Line.prototype.removeTicks=function(c){var b,a;if(this.defaultTicks!=null&&this.defaultTicks==c){this.defaultTicks=null}for(b=this.ticks.length;b>0;b--){if(this.ticks[b-1]==c){this.board.renderer.remove(this.ticks[b-1].rendNode);for(a=0;a<this.ticks[b-1].ticks.length;a++){if(this.ticks[b-1].labels[a]!=null){if(this.ticks[b-1].labels[a].show){this.board.renderer.remove(this.ticks[b-1].labels[a].rendNode)}}}delete (this.ticks[b-1])}}};JXG.createLine=function(g,k,f){var b,m,l,e,h=[];f=JXG.checkAttributes(f,{withLabel:JXG.readOption(g.options,"line","withLabel"),layer:null,labelOffsets:JXG.readOption(g.options,"line","labelOffsets")});var d=false;if(k.length==2){if(k[0].length>1){m=g.create("point",k[0],{visible:false,fixed:true})}else{if(k[0].elementClass==JXG.OBJECT_CLASS_POINT){m=JXG.getReference(g,k[0])}else{if((typeof k[0]=="function")&&(k[0]().elementClass==JXG.OBJECT_CLASS_POINT)){m=k[0]();d=true}else{throw new Error("JSXGraph: Can't create line with parent types '"+(typeof k[0])+"' and '"+(typeof k[1])+"'.\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]")}}}if(k[1].length>1){l=g.create("point",k[1],{visible:false,fixed:true})}else{if(k[1].elementClass==JXG.OBJECT_CLASS_POINT){l=JXG.getReference(g,k[1])}else{if((typeof k[1]=="function")&&(k[1]().elementClass==JXG.OBJECT_CLASS_POINT)){l=k[1]();d=true}else{throw new Error("JSXGraph: Can't create line with parent types '"+(typeof k[0])+"' and '"+(typeof k[1])+"'.\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]")}}}b=new JXG.Line(g,m.id,l.id,f.id,f.name,f.withLabel,f.layer);if(d){b.constrained=true;b.funp1=k[0];b.funp2=k[1]}}else{if(k.length==3){for(e=0;e<3;e++){if(typeof k[e]=="number"){h[e]=function(c){return function(){return c}}(k[e])}else{if(typeof k[e]=="function"){h[e]=k[e]}else{throw new Error("JSXGraph: Can't create line with parent types '"+(typeof k[0])+"' and '"+(typeof k[1])+"' and '"+(typeof k[2])+"'.\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]");return}}}m=g.create("point",[function(){return(0+h[2]()*h[2]()+h[1]()*h[1]())*0.5},function(){return(h[2]()-h[1]()*h[0]()+h[2]())*0.5},function(){return(-h[1]()-h[2]()*h[0]()-h[1]())*0.5}],{visible:false,name:" "});l=g.create("point",[function(){return h[2]()*h[2]()+h[1]()*h[1]()},function(){return -h[1]()*h[0]()+h[2]()},function(){return -h[2]()*h[0]()-h[1]()}],{visible:false,name:" "});b=new JXG.Line(g,m.id,l.id,f.id,f.name,f.withLabel)}else{if((k.length==1)&&(typeof k[0]=="function")&&(k[0]().length==2)&&(k[0]()[0].elementClass==JXG.OBJECT_CLASS_POINT)&&(k[0]()[1].elementClass==JXG.OBJECT_CLASS_POINT)){var a=k[0]();b=new JXG.Line(g,a[0].id,a[1].id,f.id,f.name,f.withLabel,f.layer);b.constrained=true;b.funps=k[0]}else{throw new Error("JSXGraph: Can't create line with parent types '"+(typeof k[0])+"' and '"+(typeof k[1])+"'.\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]")}}}b.labelOffsets=f.labelOffsets;return b};JXG.JSXGraph.registerElement("line",JXG.createLine);JXG.createSegment=function(c,a,d){var b;d=JXG.checkAttributes(d,{withLabel:JXG.readOption(c.options,"line","withLabel"),layer:null});d.straightFirst=false;d.straightLast=false;b=c.create("line",a,d);return b};JXG.JSXGraph.registerElement("segment",JXG.createSegment);JXG.createArrow=function(d,b,a){var c;a=JXG.checkAttributes(a,{withLabel:JXG.readOption(d.options,"line","withLabel"),layer:null});c=d.create("line",b,a);c.setStraight(false,false);c.setArrow(false,true);c.type=JXG.OBJECT_TYPE_VECTOR;return c};JXG.JSXGraph.registerElement("arrow",JXG.createArrow);JXG.createAxis=function(e,l,b){var h,g,m,f,c,a,d,k;if((JXG.isArray(l[0])||JXG.isPoint(l[0]))&&(JXG.isArray(l[1])||JXG.isPoint(l[1]))){if(JXG.isPoint(l[0])){h=l[0]}else{h=new JXG.Point(e,l[0],"","",false)}if(JXG.isPoint(l[1])){g=l[1]}else{g=new JXG.Point(e,l[1],"","",false)}h.fixed=true;g.fixed=true;b=JXG.checkAttributes(b,{lastArrow:true,straightFirst:true,straightLast:true,strokeWidth:1,withLabel:false,strokeColor:e.options.axis.strokeColor});b.highlightStrokeColor=b.highlightStrokeColor||b.strokeColor||e.options.axis.highlightStrokeColor;m=e.create("line",[h,g],b);m.needsRegularUpdate=false;b=JXG.checkAttributes(b,{minorTicks:4,insertTicks:true});if(b.ticksDistance!="undefined"&&b.ticksDistance!=null){f=b.ticksDistance}else{if(JXG.isArray(b.ticks)){f=b.ticks}else{c=new JXG.Coords(JXG.COORDS_BY_USER,[m.point1.coords.usrCoords.slice(1)],e);a=new JXG.Coords(JXG.COORDS_BY_USER,[m.point2.coords.usrCoords.slice(1)],e);e.renderer.calcStraight(m,c,a);d=c.distance(JXG.COORDS_BY_USER,a);f=1}}k=e.create("ticks",[m,f],b);k.needsRegularUpdate=false;m.defaultTicks=k}else{throw new Error("JSXGraph: Can't create point with parent types '"+(typeof l[0])+"' and '"+(typeof l[1])+"'.\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]")}return m};JXG.JSXGraph.registerElement("axis",JXG.createAxis);JXG.createTangent=function(m,q,e){var a,n,k,l,h,d,b,r,s,u;if(q.length==1){a=q[0];n=a.slideObject}else{if(q.length==2){if(JXG.isPoint(q[0])){a=q[0];n=q[1]}else{if(JXG.isPoint(q[1])){n=q[0];a=q[1]}else{throw new Error("JSXGraph: Can't create tangent with parent types '"+(typeof q[0])+"' and '"+(typeof q[1])+"'.\nPossible parent types: [glider], [point,line|curve|circle|conic]")}}}else{throw new Error("JSXGraph: Can't create tangent with parent types '"+(typeof q[0])+"' and '"+(typeof q[1])+"'.\nPossible parent types: [glider], [point,line|curve|circle|conic]")}}e=JXG.checkAttributes(e,{withLabel:JXG.readOption(m.options,"line","withLabel"),layer:null});if(n.elementClass==JXG.OBJECT_CLASS_LINE){u=m.create("line",[n.point1,n.point2],e)}else{if(n.elementClass==JXG.OBJECT_CLASS_CURVE&&!(n.type==JXG.OBJECT_TYPE_CONIC)){if(n.curveType!="plot"){k=n.X;l=n.Y;u=m.create("line",[function(){return -a.X()*m.D(l)(a.position)+a.Y()*m.D(k)(a.position)},function(){return m.D(l)(a.position)},function(){return -m.D(k)(a.position)}],e);a.addChild(u);u.glider=a}else{u=m.create("line",[function(){h=Math.floor(a.position);if(h==n.numberPoints-1){h--}if(h<0){return 1}return n.Y(h)*n.X(h+1)-n.X(h)*n.Y(h+1)},function(){h=Math.floor(a.position);if(h==n.numberPoints-1){h--}if(h<0){return 0}return n.Y(h+1)-n.Y(h)},function(){h=Math.floor(a.position);if(h==n.numberPoints-1){h--}if(h<0){return 0}return n.X(h)-n.X(h+1)}],e);a.addChild(u);u.glider=a}}else{if(n.type==JXG.OBJECT_TYPE_TURTLE){u=m.create("line",[function(){h=Math.floor(a.position);for(d=0;d<n.objects.length;d++){b=n.objects[d];if(b.type==JXG.OBJECT_TYPE_CURVE){if(h<b.numberPoints){break}h-=b.numberPoints}}if(h==b.numberPoints-1){h--}if(h<0){return 1}return b.Y(h)*b.X(h+1)-b.X(h)*b.Y(h+1)},function(){h=Math.floor(a.position);for(d=0;d<n.objects.length;d++){b=n.objects[d];if(b.type==JXG.OBJECT_TYPE_CURVE){if(h<b.numberPoints){break}h-=b.numberPoints}}if(h==b.numberPoints-1){h--}if(h<0){return 0}return b.Y(h+1)-b.Y(h)},function(){h=Math.floor(a.position);for(d=0;d<n.objects.length;d++){b=n.objects[d];if(b.type==JXG.OBJECT_TYPE_CURVE){if(h<b.numberPoints){break}h-=b.numberPoints}}if(h==b.numberPoints-1){h--}if(h<0){return 0}return b.X(h)-b.X(h+1)}],e);a.addChild(u);u.glider=a}else{if(n.elementClass==JXG.OBJECT_CLASS_CIRCLE||n.type==JXG.OBJECT_TYPE_CONIC){u=m.create("line",[function(){return JXG.Math.matVecMult(n.quadraticform,a.coords.usrCoords)[0]},function(){return JXG.Math.matVecMult(n.quadraticform,a.coords.usrCoords)[1]},function(){return JXG.Math.matVecMult(n.quadraticform,a.coords.usrCoords)[2]}],e);a.addChild(u);u.glider=a}}}}return u};JXG.JSXGraph.registerElement("tangent",JXG.createTangent);JXG.JSXGraph.registerElement("polar",JXG.createTangent);JXG.Group=function(e,h,a){var f,d,b,g,c;this.board=e;this.objects={};f=this.board.numObjects;this.board.numObjects++;if((h=="")||(h==null)||(typeof h=="undefined")){this.id=this.board.id+"Group"+f}else{this.id=h}this.type=JXG.OBJECT_TYPE_POINT;this.elementClass=JXG.OBJECT_CLASS_POINT;if((a=="")||(a==null)||(typeof a=="undefined")){this.name="group_"+this.board.generateName(this)}else{this.name=a}delete (this.type);if((arguments.length==4)&&(JXG.isArray(arguments[3]))){d=arguments[3]}else{d=[];for(b=3;b<arguments.length;b++){d.push(arguments[b])}}for(b=0;b<d.length;b++){g=JXG.getReference(this.board,d[b]);if((!g.fixed)&&((g.type==JXG.OBJECT_TYPE_POINT)||(g.type==JXG.OBJECT_TYPE_GLIDER))){if(g.group.length!=0){this.addGroup(g.group[g.group.length-1])}else{this.addPoint(g)}}}for(c in this.objects){this.objects[c].group.push(this)}this.dX=0;this.dY=0};JXG.Group.prototype.ungroup=function(){var a;for(a in this.objects){if(this.objects[a].group[this.objects[a].group.length-1]==this){this.objects[a].group.pop()}delete (this.objects[a])}};JXG.Group.prototype.update=function(a){var c=null,b;for(b in this.objects){c=this.objects[b];if(c.id!=a.id){c.coords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[c.coords.scrCoords[1]+this.dX,c.coords.scrCoords[2]+this.dY],c.board)}}for(b in this.objects){if(this.board.objects[b]!=undefined){this.objects[b].update(false)}else{delete (this.objects[b])}}};JXG.Group.prototype.addPoint=function(a){this.objects[a.id]=a};JXG.Group.prototype.addPoints=function(a){var b;for(b in a){this.objects[b.id]=b}};JXG.Group.prototype.addGroup=function(b){var a;for(a in b.objects){this.addPoint(b.objects[a])}};JXG.createGroup=function(c,b,a){return new JXG.Group(c,a.id,a.name,b)};JXG.JSXGraph.registerElement("group",JXG.createGroup);JXG.Circle=function(f,h,e,b,g,a,d,c){this.constructor();this.type=JXG.OBJECT_TYPE_CIRCLE;this.elementClass=JXG.OBJECT_CLASS_CIRCLE;this.init(f,g,a);if(c==null){c=f.options.layer.circle}this.layer=c;this.method=h;this.midpoint=JXG.getReference(this.board,e);this.midpoint.addChild(this);this.visProp.visible=true;this.visProp.fillColor=this.board.options.circle.fillColor;this.visProp.highlightFillColor=this.board.options.circle.highlightFillColor;this.visProp.strokeColor=this.board.options.circle.strokeColor;this.visProp.highlightStrokeColor=this.board.options.circle.highlightStrokeColor;this.point2=null;this.radius=0;this.line=null;this.circle=null;if(h=="twoPoints"){this.point2=JXG.getReference(f,b);this.point2.addChild(this);this.radius=this.Radius()}else{if(h=="pointRadius"){this.generateTerm(b);this.updateRadius()}else{if(h=="pointLine"){this.line=JXG.getReference(f,b);this.radius=this.line.point1.coords.distance(JXG.COORDS_BY_USER,this.line.point2.coords)}else{if(h=="pointCircle"){this.circle=JXG.getReference(f,b);this.radius=this.circle.Radius()}}}}if(d!=null){this.createLabel(d)}if(h=="twoPoints"){this.id=this.board.addCircle(this)}else{if(h=="pointRadius"){this.id=this.board.addCircle(this);this.notifyParents(b)}else{if(h=="pointLine"){this.line.addChild(this);this.id=this.board.addCircle(this)}else{if(h=="pointCircle"){this.circle.addChild(this);this.id=this.board.addCircle(this)}}}}};JXG.Circle.prototype=new JXG.GeometryElement;JXG.Circle.prototype.hasPoint=function(a,g){var b=this.board.options.precision.hasPoint/(this.board.stretchX),d=this.midpoint.coords.usrCoords,e=new JXG.Coords(JXG.COORDS_BY_SCREEN,[a,g],this.board),c=this.Radius();var f=Math.sqrt((d[1]-e.usrCoords[1])*(d[1]-e.usrCoords[1])+(d[2]-e.usrCoords[2])*(d[2]-e.usrCoords[2]));return(Math.abs(f-c)<b)};JXG.Circle.prototype.generatePolynomial=function(g){var e=this.midpoint.symbolic.x;var d=this.midpoint.symbolic.y;var c=g.symbolic.x;var b=g.symbolic.y;var a=this.generateRadiusSquared();if(a==""){return[]}var f="(("+c+")-("+e+"))^2 + (("+b+")-("+d+"))^2 - ("+a+")";return[f]};JXG.Circle.prototype.generateRadiusSquared=function(){var b="";if(this.method=="twoPoints"){var d=this.midpoint.symbolic.x;var c=this.midpoint.symbolic.y;var f=this.point2.symbolic.x;var e=this.point2.symbolic.y;b="("+f+"-"+d+")^2 + ("+e+"-"+c+")^2"}else{if(this.method=="pointRadius"){if(typeof(this.radius)=="number"){b=""+this.radius*this.radius}}else{if(this.method=="pointLine"){var f=this.line.point1.symbolic.x;var e=this.line.point1.symbolic.y;var a=this.line.point2.symbolic.x;var g=this.line.point2.symbolic.y;b="("+f+"-"+a+")^2 + ("+e+"-"+g+")^2"}else{if(this.method=="pointCircle"){b=this.circle.Radius()}}}}return b};JXG.Circle.prototype.update=function(){if(this.traced){this.cloneToBackground(true)}if(this.needsUpdate){if(this.method=="pointLine"){this.radius=this.line.point1.coords.distance(JXG.COORDS_BY_USER,this.line.point2.coords)}else{if(this.method=="pointCircle"){this.radius=this.circle.Radius()}else{if(this.method=="pointRadius"){this.radius=this.updateRadius()}}}if(!this.board.geonextCompatibilityMode){this.updateStdform();this.updateQuadraticform()}}};JXG.Circle.prototype.updateQuadraticform=function(){var a=this.midpoint,d=a.X(),c=a.Y(),b=this.Radius();this.quadraticform=[[d*d+c*c-b*b,-d,-c],[-d,1,0],[-c,0,1]]};JXG.Circle.prototype.updateStdform=function(){this.stdform[3]=0.5;this.stdform[4]=this.Radius();this.stdform[1]=-this.midpoint.coords.usrCoords[1];this.stdform[2]=-this.midpoint.coords.usrCoords[2];this.normalize()};JXG.Circle.prototype.updateRenderer=function(){if(this.needsUpdate&&this.visProp.visible){var a=this.isReal;this.isReal=(isNaN(this.midpoint.coords.usrCoords[1]+this.midpoint.coords.usrCoords[2]+this.Radius()))?false:true;if(this.isReal){if(a!=this.isReal){this.board.renderer.show(this);if(this.hasLabel&&this.label.content.visProp.visible){this.board.renderer.show(this.label.content)}}this.board.renderer.updateCircle(this)}else{if(a!=this.isReal){this.board.renderer.hide(this);if(this.hasLabel&&this.label.content.visProp.visible){this.board.renderer.hide(this.label.content)}}}this.needsUpdate=false}if(this.hasLabel&&this.label.content.visProp.visible&&this.isReal){this.label.content.update();this.board.renderer.updateText(this.label.content)}};JXG.Circle.prototype.generateTerm=function(b){if(typeof b=="string"){var c=this.board.elementsByName;var a=JXG.GeonextParser.geonext2JS(b+"",this.board);this.updateRadius=new Function("return "+a+";")}else{if(typeof b=="number"){this.updateRadius=function(){return b}}else{this.updateRadius=b}}};JXG.Circle.prototype.notifyParents=function(b){var a=null;var c=this.board.elementsByName;if(typeof b=="string"){JXG.GeonextParser.findDependencies(this,b+"",this.board)}};JXG.Circle.prototype.Radius=function(){if(this.method=="twoPoints"){return(Math.sqrt(Math.pow(this.midpoint.coords.usrCoords[1]-this.point2.coords.usrCoords[1],2)+Math.pow(this.midpoint.coords.usrCoords[2]-this.point2.coords.usrCoords[2],2)))}else{if(this.method=="pointLine"||this.method=="pointCircle"){return this.radius}else{if(this.method=="pointRadius"){return this.updateRadius()}}}};JXG.Circle.prototype.getRadius=function(){return this.Radius()};JXG.Circle.prototype.getTextAnchor=function(){return this.midpoint.coords};JXG.Circle.prototype.getLabelAnchor=function(){if(this.method=="twoPoints"){var b=this.midpoint.coords.usrCoords[1]-this.point2.coords.usrCoords[1];var a=this.midpoint.coords.usrCoords[2]-this.point2.coords.usrCoords[2];return new JXG.Coords(JXG.COORDS_BY_USER,[this.midpoint.coords.usrCoords[1]+b,this.midpoint.coords.usrCoords[2]+a],this.board)}else{if(this.method=="pointLine"||this.method=="pointCircle"||this.method=="pointRadius"){return new JXG.Coords(JXG.COORDS_BY_USER,[this.midpoint.coords.usrCoords[1]-this.Radius(),this.midpoint.coords.usrCoords[2]],this.board)}}};JXG.Circle.prototype.cloneToBackground=function(a){var c={};c.id=this.id+"T"+this.numTraces;this.numTraces++;c.midpoint={};c.midpoint.coords=this.midpoint.coords;var b=this.Radius();c.Radius=function(){return b};c.getRadius=function(){return b};c.board={};c.board.unitX=this.board.unitX;c.board.unitY=this.board.unitY;c.board.zoomX=this.board.zoomX;c.board.zoomY=this.board.zoomY;c.board.stretchX=this.board.stretchX;c.board.stretchY=this.board.stretchY;c.visProp=this.visProp;JXG.clearVisPropOld(c);this.board.renderer.drawCircle(c);this.traces[c.id]=this.board.renderer.getElementById(c.id);delete c};JXG.Circle.prototype.addTransform=function(a){var c;if(JXG.isArray(a)){c=a}else{c=[a]}for(var b=0;b<c.length;b++){this.midpoint.transformations.push(c[b]);if(this.method=="twoPoints"){this.point2.transformations.push(c[b])}}};JXG.Circle.prototype.setPosition=function(d,a,c){var b=this.board.create("transform",[a,c],{type:"translate"});this.addTransform(b)};JXG.Circle.prototype.X=function(a){a*=2*Math.PI;return this.Radius()*Math.cos(a)+this.midpoint.coords.usrCoords[1]};JXG.Circle.prototype.Y=function(a){a*=2*Math.PI;return this.Radius()*Math.sin(a)+this.midpoint.coords.usrCoords[2]};JXG.Circle.prototype.minX=function(){return 0};JXG.Circle.prototype.maxX=function(){return 1};JXG.Circle.prototype.Area=function(){var a=this.Radius();return a*a*Math.PI};JXG.createCircle=function(d,g,f){var c,e,b;f=JXG.checkAttributes(f,{withLabel:JXG.readOption(d.options,"circle","withLabel"),layer:null});e=[];for(b=0;b<g.length;b++){if(JXG.isPoint(g[b])){e[b]=g[b]}else{if(g[b].length>1){e[b]=d.create("point",g[b],{visible:false,fixed:true})}else{e[b]=g[b]}}}if(g.length==2&&JXG.isPoint(e[0])&&JXG.isPoint(e[1])){c=new JXG.Circle(d,"twoPoints",e[0],e[1],f.id,f.name,f.withLabel,f.layer)}else{if((JXG.isNumber(e[0])||JXG.isFunction(e[0])||JXG.isString(e[0]))&&JXG.isPoint(e[1])){c=new JXG.Circle(d,"pointRadius",e[1],e[0],f.id,f.name,f.withLabel,f.layer)}else{if((JXG.isNumber(e[1])||JXG.isFunction(e[1])||JXG.isString(e[1]))&&JXG.isPoint(e[0])){c=new JXG.Circle(d,"pointRadius",e[0],e[1],f.id,f.name,f.withLabel,f.layer)}else{if((e[0].type==JXG.OBJECT_TYPE_CIRCLE)&&JXG.isPoint(e[1])){c=new JXG.Circle(d,"pointCircle",e[1],e[0],f.id,f.name,f.withLabel,f.layer)}else{if((e[1].type==JXG.OBJECT_TYPE_CIRCLE)&&JXG.isPoint(e[0])){c=new JXG.Circle(d,"pointCircle",e[0],e[1],f.id,f.name,f.withLabel,f.layer)}else{if((e[0].type==JXG.OBJECT_TYPE_LINE)&&JXG.isPoint(e[1])){c=new JXG.Circle(d,"pointLine",e[1],e[0],f.id,f.name,f.withLabel,f.layer)}else{if((e[1].type==JXG.OBJECT_TYPE_LINE)&&JXG.isPoint(e[0])){c=new JXG.Circle(d,"pointLine",e[0],e[1],f.id,f.name,f.withLabel,f.layer)}else{if(g.length==3&&JXG.isPoint(e[0])&&JXG.isPoint(e[1])&&JXG.isPoint(e[2])){var a=JXG.createCircumcircle(d,e,f);a[0].setProperty({visible:false});return a[1]}else{throw new Error("JSXGraph: Can't create circle with parent types '"+(typeof g[0])+"' and '"+(typeof g[1])+"'.\nPossible parent types: [point,point], [point,number], [point,function], [point,circle], [point,point,point]")}}}}}}}}return c};JXG.JSXGraph.registerElement("circle",JXG.createCircle);JXG.createEllipse=function(h,l,g){var n=[],b,a,e,f;g=JXG.checkAttributes(g,{withLabel:JXG.readOption(h.options,"conic","withLabel"),layer:null});for(e=0;e<2;e++){if(l[e].length>1){n[e]=h.create("point",l[e],{visible:false,fixed:true})}else{if(JXG.isPoint(l[e])){n[e]=JXG.getReference(h,l[e])}else{if((typeof l[e]=="function")&&(l[e]().elementClass==JXG.OBJECT_CLASS_POINT)){n[e]=l[e]()}else{if(JXG.isString(l[e])){n[e]=JXG.getReference(h,l[e])}else{throw new Error("JSXGraph: Can't create Ellipse with parent types '"+(typeof l[0])+"' and '"+(typeof l[1])+"'.\nPossible parent types: [point,point,point], [point,point,number|function]")}}}}}if(JXG.isNumber(l[2])){a=JXG.createFunction(l[2],h)}else{if((typeof l[2]=="function")&&(JXG.isNumber(l[2]()))){a=l[2]}else{if(JXG.isPoint(l[2])){b=JXG.getReference(h,l[2])}else{if(l[2].length>1){b=h.create("point",l[2],{visible:false,fixed:true})}else{if((typeof l[2]=="function")&&(l[2]().elementClass==JXG.OBJECT_CLASS_POINT)){b=l[2]()}else{if(JXG.isString(l[2])){b=JXG.getReference(h,l[2])}else{throw new Error("JSXGraph: Can't create Ellipse with parent types '"+(typeof l[0])+"' and '"+(typeof l[1])+"' and '"+(typeof l[2])+"'.\nPossible parent types: [point,point,point], [point,point,number|function]")}}}}a=function(){return b.Dist(n[0])+b.Dist(n[1])}}}if(typeof l[4]=="undefined"){l[4]=1.0001*Math.PI}if(typeof l[3]=="undefined"){l[3]=-1.0001*Math.PI}g=JXG.checkAttributes(g,{curveType:"parameter"});var k=h.create("point",[function(){return(n[0].X()+n[1].X())*0.5},function(){return(n[0].Y()+n[1].Y())*0.5}],{visible:false,name:"",withLabel:false});var m=function(){var q=n[0].X(),z=n[0].Y(),w=n[1].X(),v=n[1].Y(),y,x,u;var s=(w-q>0)?1:-1;if(Math.abs(w-q)>1e-7){y=Math.atan2(v-z,w-q)+((s<0)?Math.PI:0)}else{y=((v-z>0)?0.5:-0.5)*Math.PI}x=Math.cos(y);u=Math.sin(y);var r=[[1,0,0],[k.X(),x,-u],[k.Y(),u,x]];return r};var c=h.create("curve",[function(q){return 0},function(q){return 0},l[3],l[4]],g);var d=function(u,r){var y=a()*0.5,q=y*y,s=n[1].Dist(n[0])*0.5,v=q-s*s,x=Math.sqrt(v),w=[[1,0,0],[0,1,0],[0,0,1]],A,z;if(!r){f=m();A=k.X();z=k.Y();w[0][0]=f[0][0];w[0][1]=0;w[0][2]=0;w[1][0]=A*(1-f[1][1])+z*f[1][2];w[1][1]=f[1][1];w[1][2]=f[2][1];w[2][0]=z*(1-f[1][1])-A*f[1][2];w[2][1]=f[1][2];w[2][2]=f[2][2];c.quadraticform=JXG.Math.matMatMult(JXG.Math.Matrix.transpose(w),JXG.Math.matMatMult([[-1+A*A/(y*y)+z*z/v,-A/q,-A/v],[-A/q,1/q,0],[-z/v,0,1/v]],w))}return JXG.Math.matVecMult(f,[1,y*Math.cos(u),x*Math.sin(u)])};c.X=function(q,r){return d(q,r)[1]};c.Y=function(q,r){return d(q,r)[2]};c.midpoint=k;c.type=JXG.OBJECT_TYPE_CONIC;return c};JXG.createHyperbola=function(h,l,g){var n=[],b,a,e,f;g=JXG.checkAttributes(g,{withLabel:JXG.readOption(h.options,"conic","withLabel"),layer:null});for(e=0;e<2;e++){if(l[e].length>1){n[e]=h.create("point",l[e],{visible:false,fixed:true})}else{if(JXG.isPoint(l[e])){n[e]=JXG.getReference(h,l[e])}else{if((typeof l[e]=="function")&&(l[e]().elementClass==JXG.OBJECT_CLASS_POINT)){n[e]=l[e]()}else{if(JXG.isString(l[e])){n[e]=JXG.getReference(h,l[e])}else{throw new Error("JSXGraph: Can't create Hyperbola with parent types '"+(typeof l[0])+"' and '"+(typeof l[1])+"'.\nPossible parent types: [point,point,point], [point,point,number|function]")}}}}}if(JXG.isNumber(l[2])){a=JXG.createFunction(l[2],h)}else{if((typeof l[2]=="function")&&(JXG.isNumber(l[2]()))){a=l[2]}else{if(JXG.isPoint(l[2])){b=JXG.getReference(h,l[2])}else{if(l[2].length>1){b=h.create("point",l[2],{visible:false,fixed:true})}else{if((typeof l[2]=="function")&&(l[2]().elementClass==JXG.OBJECT_CLASS_POINT)){b=l[2]()}else{if(JXG.isString(l[2])){b=JXG.getReference(h,l[2])}else{throw new Error("JSXGraph: Can't create Hyperbola with parent types '"+(typeof l[0])+"' and '"+(typeof l[1])+"' and '"+(typeof l[2])+"'.\nPossible parent types: [point,point,point], [point,point,number|function]")}}}}a=function(){return b.Dist(n[0])-b.Dist(n[1])}}}if(typeof l[4]=="undefined"){l[4]=1.0001*Math.PI}if(typeof l[3]=="undefined"){l[3]=-1.0001*Math.PI}g=JXG.checkAttributes(g,{curveType:"parameter"});var k=h.create("point",[function(){return(n[0].X()+n[1].X())*0.5},function(){return(n[0].Y()+n[1].Y())*0.5}],{visible:false,name:"",withLabel:false});var m=function(){var s=n[0].X(),r=n[0].Y(),x=n[1].X(),v=n[1].Y(),u;var w=(x-s>0)?1:-1;if(Math.abs(x-s)>1e-7){u=Math.atan2(v-r,x-s)+((w<0)?Math.PI:0)}else{u=((v-r>0)?0.5:-0.5)*Math.PI}var q=[[1,0,0],[k.X(),Math.cos(u),-Math.sin(u)],[k.Y(),Math.sin(u),Math.cos(u)]];return q};var c=h.create("curve",[function(q){return 0},function(q){return 0},l[3],l[4]],g);var d=function(u,r){var y=a()*0.5,q=y*y,s=n[1].Dist(n[0])*0.5,x=Math.sqrt(-y*y+s*s),v=x*x,w=[[1,0,0],[0,1,0],[0,0,1]],A,z;if(!r){f=m();A=k.X();z=k.Y();w[0][0]=f[0][0];w[0][1]=0;w[0][2]=0;w[1][0]=A*(1-f[1][1])+z*f[1][2];w[1][1]=f[1][1];w[1][2]=f[2][1];w[2][0]=z*(1-f[1][1])-A*f[1][2];w[2][1]=f[1][2];w[2][2]=f[2][2];c.quadraticform=JXG.Math.matMatMult(JXG.Math.Matrix.transpose(w),JXG.Math.matMatMult([[-1+A*A/q+z*z/v,-A/q,z/v],[-A/q,1/q,0],[z/v,0,-1/v]],w))}return JXG.Math.matVecMult(f,[1,y/Math.cos(u),x*Math.tan(u)])};c.X=function(q,r){return d(q,r)[1]};c.Y=function(q,r){return d(q,r)[2]};c.midpoint=k;c.type=JXG.OBJECT_TYPE_CONIC;return c};JXG.createParabola=function(g,k,f){var e=k[0],b=k[1],d;f=JXG.checkAttributes(f,{withLabel:JXG.readOption(g.options,"conic","withLabel"),layer:null});if(k[0].length>1){e=g.create("point",k[0],{visible:false,fixed:true})}else{if(JXG.isPoint(k[0])){e=JXG.getReference(g,k[0])}else{if((typeof k[0]=="function")&&(k[0]().elementClass==JXG.OBJECT_CLASS_POINT)){e=k[0]()}else{if(JXG.isString(k[0])){e=JXG.getReference(g,k[0])}else{throw new Error("JSXGraph: Can't create Parabola with parent types '"+(typeof k[0])+"' and '"+(typeof k[1])+"'.\nPossible parent types: [point,line]")}}}}if(typeof k[3]=="undefined"){k[3]=10}if(typeof k[2]=="undefined"){k[2]=-10}f=JXG.checkAttributes(f,{curveType:"parameter"});var h=g.create("point",[function(){var l=[0,b.stdform[1],b.stdform[2]];l=JXG.Math.crossProduct(l,e.coords.usrCoords);return JXG.Math.Geometry.meetLineLine(l,b.stdform,0,g).usrCoords}],{visible:false,name:"",withLabel:false});var m=function(){var q=Math.atan(b.getSlope()),n=(h.X()+e.X())*0.5,r=(h.Y()+e.Y())*0.5;q+=(e.Y()-h.Y()<0||(e.Y()==h.Y()&&e.X()>h.X()))?Math.PI:0;var l=[[1,0,0],[n*(1-Math.cos(q))+r*Math.sin(q),Math.cos(q),-Math.sin(q)],[r*(1-Math.cos(q))-n*Math.sin(q),Math.sin(q),Math.cos(q)]];return l};var a=g.create("curve",[function(l){return 0},function(l){return 0},k[2],k[3]],f);var c=function(r,s){var u=h.Dist(e)*0.5,q=[[1,0,0],[0,1,0],[0,0,1]],n=(h.X()+e.X())*0.5,l=(h.Y()+e.Y())*0.5;if(!s){d=m();q[0][0]=d[0][0];q[0][1]=0;q[0][2]=0;q[1][0]=n*(1-d[1][1])+l*d[1][2];q[1][1]=d[1][1];q[1][2]=d[2][1];q[2][0]=l*(1-d[1][1])-n*d[1][2];q[2][1]=d[1][2];q[2][2]=d[2][2];a.quadraticform=JXG.Math.matMatMult(JXG.Math.Matrix.transpose(q),JXG.Math.matMatMult([[-l*4*u-n*n,n,2*u],[n,-1,0],[2*u,0,0]],q))}return JXG.Math.matVecMult(d,[1,r+n,r*r/(u*4)+l])};a.X=function(l,n){return c(l,n)[1]};a.Y=function(l,n){return c(l,n)[2]};a.type=JXG.OBJECT_TYPE_CONIC;return a};JXG.createConic=function(e,x,q){var g=[[1,0,0],[0,1,0],[0,0,1]],C,A,z,y,f=[[1,0,0],[0,1,0],[0,0,1]],r,n,u=[],v,s,B,m=[];if(x.length==5){B=true}else{if(x.length==6){B=false}else{throw new Error("JSXGraph: Can't create generic Conic with "+parent.length+" parameters.")}}q=JXG.checkAttributes(q,{withLabel:JXG.readOption(e.options,"conic","withLabel"),layer:null});if(B){for(v=0;v<5;v++){if(x[v].length>1){u[v]=e.create("point",x[v],{visible:false,fixed:true})}else{if(JXG.isPoint(x[v])){u[v]=JXG.getReference(e,x[v])}else{if((typeof x[v]=="function")&&(x[v]().elementClass==JXG.OBJECT_CLASS_POINT)){u[v]=x[v]()}else{if(JXG.isString(x[v])){u[v]=JXG.getReference(e,x[v])}else{throw new Error("JSXGraph: Can't create Conic section with parent types '"+(typeof x[v])+"'.\nPossible parent types: [point,point,point,point,point], [a00,a11,a22,a01,a02,a12]")}}}}}}else{s=[[0,0,0],[0,0,0],[0,0,0]];s[0][0]=(JXG.isFunction(x[2]))?function(){return x[2]()}:function(){return x[2]};s[0][1]=(JXG.isFunction(x[4]))?function(){return x[4]()}:function(){return x[4]};s[0][2]=(JXG.isFunction(x[5]))?function(){return x[5]()}:function(){return x[5]};s[1][1]=(JXG.isFunction(x[0]))?function(){return x[0]()}:function(){return x[0]};s[1][2]=(JXG.isFunction(x[3]))?function(){return x[3]()}:function(){return x[3]};s[2][2]=(JXG.isFunction(x[1]))?function(){return x[1]()}:function(){return x[1]}}var h=function(a){var c,b;for(c=0;c<3;c++){for(b=c;b<3;b++){a[c][b]+=a[b][c]}}for(c=0;c<3;c++){for(b=0;b<c;b++){a[c][b]=a[b][c]}}return a};var l=function(b,a){var E,c,D=[[0,0,0],[0,0,0],[0,0,0]];for(E=0;E<3;E++){for(c=0;c<3;c++){D[E][c]=b[E]*a[c]}}return h(D)};var w=function(D,b,c){var G,H,a,I=[[0,0,0],[0,0,0],[0,0,0]],F,E;a=JXG.Math.matVecMult(b,c);G=JXG.Math.innerProduct(c,a);a=JXG.Math.matVecMult(D,c);H=JXG.Math.innerProduct(c,a);for(F=0;F<3;F++){for(E=0;E<3;E++){I[F][E]=G*D[F][E]-H*b[F][E]}}return I};var k=e.create("curve",[function(a){return 0},function(a){return 0},0,2*Math.PI],q);var d=function(E,F){var D,c,a,b;if(!F){if(B){for(D=0;D<5;D++){m[D]=u[D].coords.usrCoords}r=l(JXG.Math.crossProduct(m[0],m[1]),JXG.Math.crossProduct(m[2],m[3]));n=l(JXG.Math.crossProduct(m[0],m[2]),JXG.Math.crossProduct(m[1],m[3]));f=w(r,n,m[4])}else{for(D=0;D<3;D++){for(c=D;c<3;c++){f[D][c]=s[D][c]();if(c>D){f[c][D]=f[D][c]}}}}k.quadraticform=f;C=JXG.Math.Numerics.Jacobi(f);if(C[0][0][0]<0){C[0][0][0]*=(-1);C[0][1][1]*=(-1);C[0][2][2]*=(-1)}for(D=0;D<3;D++){a=0;for(c=0;c<3;c++){a+=C[1][c][D]*C[1][c][D]}a=Math.sqrt(a);for(c=0;c<3;c++){}}g=C[1];y=Math.sqrt(Math.abs(C[0][0][0]));A=Math.sqrt(Math.abs(C[0][1][1]));z=Math.sqrt(Math.abs(C[0][2][2]))}if(C[0][1][1]<0&&C[0][2][2]<0){b=JXG.Math.matVecMult(g,[1/y,Math.cos(E)/A,Math.sin(E)/z])}else{if(C[0][1][1]<0&&C[0][2][2]>0){b=JXG.Math.matVecMult(g,[Math.cos(E)/y,1/A,Math.sin(E)/z])}else{if(C[0][2][2]<0){b=JXG.Math.matVecMult(g,[Math.sin(E)/y,Math.cos(E)/A,1/z])}}}b[1]/=b[0];b[2]/=b[0];b[0]=1;return b};k.X=function(a,b){return d(a,b)[1]};k.Y=function(a,b){return d(a,b)[2]};k.midpoint=e.create("point",[function(){var a=k.quadraticform;return[a[1][1]*a[2][2]-a[1][2]*a[1][2],a[1][2]*a[0][2]-a[2][2]*a[0][1],a[0][1]*a[1][2]-a[1][1]*a[0][2]]}],{name:"",visible:false});k.type=JXG.OBJECT_TYPE_CONIC;return k};JXG.JSXGraph.registerElement("ellipse",JXG.createEllipse);JXG.JSXGraph.registerElement("hyperbola",JXG.createHyperbola);JXG.JSXGraph.registerElement("parabola",JXG.createParabola);JXG.JSXGraph.registerElement("conic",JXG.createConic);JXG.Polygon=function(m,n,q,c,b,d,a,g,k){this.constructor();this.type=JXG.OBJECT_TYPE_POLYGON;this.elementClass=JXG.OBJECT_CLASS_AREA;this.init(m,c,b);if(k==null){k=m.options.layer.polygon}this.layer=k;if((typeof d=="undefined")||(d==null)){d=true}if((typeof g=="undefined")||(g==null)){g=false}this.withLines=d;this.vertices=[];for(var f=0;f<n.length;f++){var h=JXG.getReference(this.board,n[f]);this.vertices[f]=h}if((typeof q=="undefined")||(q==null)){q=[];for(var f=0;f<n.length-1;f++){q[f]={}}}if(this.vertices[this.vertices.length-1]!=this.vertices[0]){this.vertices.push(this.vertices[0]);q.push({})}this.visProp.fillColor=this.board.options.polygon.fillColor;this.visProp.highlightFillColor=this.board.options.polygon.highlightFillColor;this.visProp.fillOpacity=this.board.options.polygon.fillOpacity;this.visProp.highlightFillOpacity=this.board.options.polygon.highlightFillOpacity;var e;this.borders=[];if(d){for(var f=0;f<this.vertices.length-1;f++){e=new JXG.Line(m,this.vertices[f],this.vertices[f+1],q[f].id,q[f].name,g,this.layer+1);e.setStraight(false,false);this.borders[f]=e;e.parentPolygon=this}}for(var f=0;f<this.vertices.length-1;f++){var h=JXG.getReference(this.board,this.vertices[f]);h.addChild(this)}this.createLabel(a,[0,0]);this.id=this.board.addPolygon(this)};JXG.Polygon.prototype=new JXG.GeometryElement;JXG.Polygon.prototype.hasPoint=function(a,b){return false};JXG.Polygon.prototype.updateRenderer=function(){if(this.needsUpdate){this.board.renderer.updatePolygon(this);this.needsUpdate=false}if(this.hasLabel&&this.label.content.visProp.visible){this.label.content.update();this.board.renderer.updateText(this.label.content)}};JXG.Polygon.prototype.getTextAnchor=function(){var e=0;var d=0;var c=0;var g=0;e=c=this.vertices[0].X();d=g=this.vertices[0].Y();for(var f=0;f<this.vertices.length;f++){if(this.vertices[f].X()<e){e=this.vertices[f].X()}if(this.vertices[f].X()>c){c=this.vertices[f].X()}if(this.vertices[f].Y()>d){d=this.vertices[f].Y()}if(this.vertices[f].Y()<g){g=this.vertices[f].Y()}}return new JXG.Coords(JXG.COORDS_BY_USER,[(e+c)*0.5,(d+g)*0.5],this.board)};JXG.Polygon.prototype.getLabelAnchor=function(){var e=0;var d=0;var c=0;var g=0;e=c=this.vertices[0].X();d=g=this.vertices[0].Y();for(var f=0;f<this.vertices.length;f++){if(this.vertices[f].X()<e){e=this.vertices[f].X()}if(this.vertices[f].X()>c){c=this.vertices[f].X()}if(this.vertices[f].Y()>d){d=this.vertices[f].Y()}if(this.vertices[f].Y()<g){g=this.vertices[f].Y()}}return new JXG.Coords(JXG.COORDS_BY_USER,[(e+c)*0.5,(d+g)*0.5],this.board)};JXG.Polygon.prototype.cloneToBackground=function(a){var b={};b.id=this.id+"T"+this.numTraces;this.numTraces++;b.vertices=this.vertices;b.visProp=this.visProp;JXG.clearVisPropOld(b);this.board.renderer.drawPolygon(b);this.traces[b.id]=$(b.id);delete b};JXG.createPolygon=function(d,a,e){var c,b;e=JXG.checkAttributes(e,{withLabel:JXG.readOption(d.options,"polygon","withLabel"),layer:null});for(b=0;b<a.length;b++){a[b]=JXG.getReference(d,a[b]);if(!JXG.isPoint(a[b])){throw new Error("JSXGraph: Can't create polygon with parent types other than 'point'.")}}c=new JXG.Polygon(d,a,e.borders,e.id,e.name,e.withLines,e.withLabel,e.lineLabels,e.layer);return c};JXG.JSXGraph.registerElement("polygon",JXG.createPolygon);JXG.Polygon.prototype.hideElement=function(){this.visProp.visible=false;this.board.renderer.hide(this);if(this.withLines){for(var a=0;a<this.borders.length;a++){this.borders[a].hideElement()}}if(this.hasLabel&&this.label!=null){this.label.hiddenByParent=true;if(this.label.content.visProp.visible){this.board.renderer.hide(this.label.content)}}};JXG.Polygon.prototype.showElement=function(){this.visProp.visible=true;this.board.renderer.show(this);if(this.withLines){for(var a=0;a<this.borders.length;a++){this.borders[a].showElement()}}};JXG.Polygon.prototype.Area=function(){var b=0,a;for(a=0;a<this.vertices.length-1;a++){b+=(this.vertices[a].X()*this.vertices[a+1].Y()-this.vertices[a+1].X()*this.vertices[a].Y())}b/=2;return Math.abs(b)};JXG.createRegularPolygon=function(k,q,h){var d,f,e,a=[],b,m,g,l;h=JXG.checkAttributes(h,{withLabel:JXG.readOption(k.options,"polygon","withLabel"),layer:null});if(JXG.isNumber(q[q.length-1])&&q.length!=3){throw new Error("JSXGraph: A regular polygon needs two point and a number as input.")}g=q.length;e=q[g-1];if((!JXG.isNumber(e)&&!JXG.isPoint(JXG.getReference(k,e)))||e<3){throw new Error("JSXGraph: The third parameter has to be number greater than 2 or a point.")}if(JXG.isPoint(JXG.getReference(k,e))){e=g;l=true}else{g--;l=false}for(f=0;f<g;f++){q[f]=JXG.getReference(k,q[f]);if(!JXG.isPoint(q[f])){throw new Error("JSXGraph: Can't create regular polygon if the first two parameters aren't points.")}}a[0]=q[0];a[1]=q[1];for(f=2;f<e;f++){b=k.create("transform",[Math.PI*(2-(e-2)/e),a[f-1]],{type:"rotate"});if(l){a[f]=q[f];a[f].addTransform(q[f-2],b)}else{a[f]=k.create("point",[a[f-2],b],{name:"",withLabel:false,fixed:true,face:"o",size:1})}}d=k.create("polygon",a,h);return d};JXG.JSXGraph.registerElement("regularpolygon",JXG.createRegularPolygon);JXG.Curve=function(e,b,f,a,d,c){this.constructor();this.points=[];this.type=JXG.OBJECT_TYPE_CURVE;this.elementClass=JXG.OBJECT_CLASS_CURVE;this.init(e,f,a);if(c==null){c=e.options.layer.curve}this.layer=c;this.doAdvancedPlot=this.board.options.curve.doAdvancedPlot;this.numberPointsHigh=this.board.options.curve.numberPointsHigh;this.numberPointsLow=this.board.options.curve.numberPointsLow;this.numberPoints=this.numberPointsHigh;this.visProp.strokeWidth=this.board.options.curve.strokeWidth;this.visProp.highlightStrokeWidth=this.visProp.strokeWidth;this.visProp.visible=true;this.dataX=null;this.dataY=null;this.curveType=null;if(b[0]!=null){this.varname=b[0]}else{this.varname="x"}this.xterm=b[1];this.yterm=b[2];this.generateTerm(this.varname,this.xterm,this.yterm,b[3],b[4]);this.updateCurve();this.createLabel(d);this.id=this.board.addCurve(this);if(typeof this.xterm=="string"){this.notifyParents(this.xterm)}if(typeof this.yterm=="string"){this.notifyParents(this.yterm)}};JXG.Curve.prototype=new JXG.GeometryElement;JXG.Curve.prototype.minX=function(){if(this.curveType=="polar"){return 0}else{var a=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board);return a.usrCoords[1]}};JXG.Curve.prototype.maxX=function(){var a;if(this.curveType=="polar"){return 2*Math.PI}else{a=new JXG.Coords(JXG.COORDS_BY_SCREEN,[this.board.canvasWidth,0],this.board);return a.usrCoords[1]}};JXG.Curve.prototype.hasPoint=function(r,q){var s,A=Infinity,I,k,C,B,v,u,w,b,J,z,m,G,h,F,f,l,n,E=this.numberPointsLow,H=(this.maxX()-this.minX())/E,a=this.board.options.precision.hasPoint/(this.board.unitX*this.board.zoomX),e,D,g=true;a=a*a;e=new JXG.Coords(JXG.COORDS_BY_SCREEN,[r,q],this.board);r=e.usrCoords[1];q=e.usrCoords[2];if(this.curveType=="parameter"||this.curveType=="polar"||this.curveType=="functiongraph"){D=this.transformations.length;for(C=0,s=this.minX();C<E;C++){v=this.X(s,g);u=this.Y(s,g);for(B=0;B<D;B++){k=this.transformations[B];k.update();I=JXG.Math.matVecMult(k.matrix,[1,v,u]);v=I[1];u=I[2]}A=(r-v)*(r-v)+(q-u)*(q-u);if(A<a){return true}s+=H}}else{if(this.curveType=="plot"){D=this.numberPoints;for(C=0;C<D-1;C++){w=this.X(C);b=this.X(C+1);J=this.Y(C);z=this.Y(C+1);F=b-w;f=z-J;G=r-w;h=q-J;n=F*F+f*f;if(n>=JXG.Math.eps){l=G*F+h*f;m=l/n;A=G*G+h*h-m*l}else{m=0;A=G*G+h*h}if(m>=0&&m<=1&&A<a){return true}}return false}}return(A<a)};JXG.Curve.prototype.allocatePoints=function(){var b,a;a=this.numberPoints;if(this.points.length<this.numberPoints){for(b=this.points.length;b<a;b++){this.points[b]=new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board)}}};JXG.Curve.prototype.update=function(){if(this.needsUpdate){this.updateCurve()}return this};JXG.Curve.prototype.updateRenderer=function(){if(this.needsUpdate){this.board.renderer.updateCurve(this);this.needsUpdate=false}if(this.hasLabel&&this.label.content.visProp.visible){this.label.content.update();this.board.renderer.updateText(this.label.content)}return this};JXG.Curve.prototype.updateDataArray=function(){return this};JXG.Curve.prototype.updateCurve=function(){var b,c,g,a,f,d,e=false;this.updateDataArray();c=this.minX();g=this.maxX();if(this.dataX!=null){this.numberPoints=this.dataX.length;b=this.numberPoints;this.allocatePoints();for(d=0;d<b;d++){a=d;if(this.dataY!=null){f=d}else{f=this.X(a)}this.points[d].setCoordinates(JXG.COORDS_BY_USER,[this.X(a,e),this.Y(f,e)],false);this.updateTransform(this.points[d]);e=true}}else{if(this.doAdvancedPlot){this.updateParametricCurve(c,g,b)}else{if(this.board.updateQuality==this.board.BOARD_QUALITY_HIGH){this.numberPoints=this.numberPointsHigh}else{this.numberPoints=this.numberPointsLow}b=this.numberPoints;this.allocatePoints();this.updateParametricCurveNaive(c,g,b)}}this.getLabelAnchor();return this};JXG.Curve.prototype.updateParametricCurveNaive=function(c,g,b){var e,d,f=false,a=(g-c)/b;for(e=0;e<b;e++){d=c+e*a;this.points[e].setCoordinates(JXG.COORDS_BY_USER,[this.X(d,f),this.Y(d,f)],false);this.updateTransform(this.points[e]);f=true}return this};JXG.Curve.prototype.updateParametricCurve=function(B,a,v){var s,k,h,c=false,u=new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board),g,f,z,b,l,D,C,n,e,r=[],d=[],A=[],w=[],m=false,q=0;if(this.board.updateQuality==this.board.BOARD_QUALITY_LOW){C=12;n=12;e=12}else{C=20;n=2;e=2}w[0]=a-B;for(s=1;s<C;s++){w[s]=w[s-1]*0.5}s=1;r[0]=1;d[0]=0;k=B;u.setCoordinates(JXG.COORDS_BY_USER,[this.X(k,c),this.Y(k,c)],false);c=true;z=u.scrCoords[1];b=u.scrCoords[2];h=k;k=a;u.setCoordinates(JXG.COORDS_BY_USER,[this.X(k,c),this.Y(k,c)],false);g=u.scrCoords[1];f=u.scrCoords[2];A[0]=[g,f];l=1;D=0;this.points=[];this.points[q++]=new JXG.Coords(JXG.COORDS_BY_SCREEN,[z,b],this.board);do{m=this.isDistOK(z,b,g,f,n,e)||this.isSegmentOutside(z,b,g,f);while(D<C&&(!m||D<3)&&!(!this.isSegmentDefined(z,b,g,f)&&D>8)){r[l]=s;d[l]=D;A[l]=[g,f];l++;s=2*s-1;D++;k=B+s*w[D];u.setCoordinates(JXG.COORDS_BY_USER,[this.X(k,c),this.Y(k,c)],false);g=u.scrCoords[1];f=u.scrCoords[2];m=this.isDistOK(z,b,g,f,n,e)||this.isSegmentOutside(z,b,g,f)}this.points[q]=new JXG.Coords(JXG.COORDS_BY_SCREEN,[g,f],this.board);this.updateTransform(this.points[q]);q++;z=g;b=f;h=k;l--;g=A[l][0];f=A[l][1];D=d[l]+1;s=r[l]*2}while(l!=0);this.numberPoints=this.points.length;return this};JXG.Curve.prototype.isSegmentOutside=function(b,d,a,c){if(d<0&&c<0){return true}else{if(d>this.board.canvasHeight&&c>this.board.canvasHeight){return true}else{if(b<0&&a<0){return true}else{if(b>this.board.canvasWidth&&a>this.board.canvasWidth){return true}}}}return false};JXG.Curve.prototype.isDistOK=function(d,f,c,e,b,a){if(isNaN(d+f+c+e)){return false}return(Math.abs(c-d)<a&&Math.abs(e-f)<a)};JXG.Curve.prototype.isSegmentDefined=function(b,d,a,c){if(isNaN(b+d)&&isNaN(a+c)){return false}return true};JXG.Curve.prototype.updateTransform=function(e){var d,f,b,a=this.transformations.length;if(a==0){return e}for(b=0;b<a;b++){d=this.transformations[b];d.update();f=JXG.Math.matVecMult(d.matrix,e.usrCoords);e.setCoordinates(JXG.COORDS_BY_USER,[f[1],f[2]])}return e};JXG.Curve.prototype.addTransform=function(b){var d,c,a;if(JXG.isArray(b)){d=b}else{d=[b]}a=d.length;for(c=0;c<a;c++){this.transformations.push(d[c])}return this};JXG.Curve.prototype.setPosition=function(d,a,c){var b=this.board.create("transform",[a,c],{type:"translate"});if(this.transformations.length>0&&this.transformations[this.transformations.length-1].isNumericMatrix){this.transformations[this.transformations.length-1].melt(b)}else{this.addTransform(b)}return this};JXG.Curve.prototype.generateTerm=function(b,f,c,a,g){var e,d;if(JXG.isArray(f)){this.dataX=f;this.X=function(h){return this.dataX[h]};this.curveType="plot";this.numberPoints=this.dataX.length}else{this.X=JXG.createFunction(f,this.board,b);if(JXG.isString(f)){this.curveType="functiongraph"}else{if(JXG.isFunction(f)||JXG.isNumber(f)){this.curveType="parameter"}}}if(JXG.isArray(c)){this.dataY=c;this.Y=function(h){if(JXG.isFunction(this.dataY[h])){return this.dataY[h]()}else{return this.dataY[h]}}}else{this.Y=JXG.createFunction(c,this.board,b)}if(JXG.isFunction(f)&&JXG.isArray(c)){e=JXG.createFunction(c[0],this.board,"");d=JXG.createFunction(c[1],this.board,"");this.X=function(h){return(f)(h)*Math.cos(h)+e()};this.Y=function(h){return(f)(h)*Math.sin(h)+d()};this.curveType="polar"}if(a!=null){this.minX=JXG.createFunction(a,this.board,"")}if(g!=null){this.maxX=JXG.createFunction(g,this.board,"")}};JXG.Curve.prototype.notifyParents=function(a){JXG.GeonextParser.findDependencies(this,a,this.board)};JXG.Curve.prototype.getLabelAnchor=function(){var a=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,this.board.canvasHeight*0.5],this.board);a=JXG.Math.Geometry.projectCoordsToCurve(a.usrCoords[1],a.usrCoords[2],0,this,this.board)[0];return a};JXG.createCurve=function(c,b,a){a=JXG.checkAttributes(a,{withLabel:JXG.readOption(c.options,"curve","withLabel"),layer:null});return new JXG.Curve(c,["x"].concat(b),a.id,a.name,a.withLabel,a.layer)};JXG.JSXGraph.registerElement("curve",JXG.createCurve);JXG.createFunctiongraph=function(d,b,a){var c=["x","x"].concat(b);a=JXG.checkAttributes(a,{withLabel:JXG.readOption(d.options,"curve","withLabel"),layer:null});a.curveType="functiongraph";return new JXG.Curve(d,c,a.id,a.name,a.withLabel,a.layer)};JXG.JSXGraph.registerElement("functiongraph",JXG.createFunctiongraph);JXG.createSpline=function(c,b,a){var d;a=JXG.checkAttributes(a,{withLabel:JXG.readOption(c.options,"curve","withLabel"),layer:null});d=function(){var g,e=[],h=[];var f=function(n,m){var l,k;if(!m){e=[];h=[];if(b.length==2&&JXG.isArray(b[0])&&JXG.isArray(b[1])&&b[0].length==b[1].length){for(l=0;l<b[0].length;l++){if(typeof b[0][l]=="function"){e.push(b[0][l]())}else{e.push(b[0][l])}if(typeof b[1][l]=="function"){h.push(b[1][l]())}else{h.push(b[1][l])}}}else{for(l=0;l<b.length;l++){if(JXG.isPoint(b[l])){e.push(b[l].X());h.push(b[l].Y())}else{if(JXG.isArray(b[l])&&b[l].length==2){for(l=0;l<b.length;l++){if(typeof b[l][0]=="function"){e.push(b[l][0]())}else{e.push(b[l][0])}if(typeof b[l][1]=="function"){h.push(b[l][1]())}else{h.push(b[l][1])}}}}}}g=JXG.Math.Numerics.splineDef(e,h)}return JXG.Math.Numerics.splineEval(n,e,h,g)};return f};return new JXG.Curve(c,["x","x",d()],a.id,a.name,a.withLabel,a.layer)};JXG.JSXGraph.registerElement("spline",JXG.createSpline);JXG.createRiemannsum=function(g,b,a){var l,e,h,d,k;a=JXG.checkAttributes(a,{withLabel:JXG.readOption(g.options,"curve","withLabel"),layer:null,fillOpacity:0.3,fillColor:"#ffff00",curveType:"plot"});h=b[0];l=JXG.createFunction(b[1],g,"");if(l==null){throw new Error("JSXGraph: JXG.createRiemannsum: argument '2' n has to be number or function.\nPossible parent types: [function,n:number|function,type,start:number|function,end:number|function]")}e=JXG.createFunction(b[2],g,"",false);if(e==null){throw new Error("JSXGraph: JXG.createRiemannsum: argument 3 'type' has to be string or function.\nPossible parent types: [function,n:number|function,type,start:number|function,end:number|function]")}d=["x",[0],[0]].concat(b.slice(3));k=new JXG.Curve(g,d,a.id,a.name,a.withLabel,a.layer);k.updateDataArray=function(){var c=JXG.Math.Numerics.riemann(h,l(),e(),this.minX(),this.maxX());this.dataX=c[0];this.dataY=c[1]};return k};JXG.JSXGraph.registerElement("riemannsum",JXG.createRiemannsum);JXG.createArc=function(f,c,a){var e,g,d,b;if(!(JXG.isPoint(c[0])&&JXG.isPoint(c[1])&&JXG.isPoint(c[2]))){throw new Error("JSXGraph: Can't create Arc with parent types '"+(typeof c[0])+"' and '"+(typeof c[1])+"' and '"+(typeof c[2])+"'.\nPossible parent types: [point,point,point]")}g={withLabel:JXG.readOption(f.options,"elements","withLabel"),layer:JXG.readOption(f.options,"layer","arc"),useDirection:false};g.strokeWidth=f.options.elements.strokeWidth;b=f.options.arc;for(d in b){g[d]=b[d]}a=JXG.checkAttributes(a,g);e=f.create("curve",[[0],[0]],a);e.type=JXG.OBJECT_TYPE_ARC;e.midpoint=JXG.getReference(f,c[0]);e.point2=JXG.getReference(f,c[1]);e.point3=JXG.getReference(f,c[2]);e.midpoint.addChild(e);e.point2.addChild(e);e.point3.addChild(e);e.useDirection=a.useDirection;e.updateDataArray=function(){var D=this.point2,z=this.midpoint,w=this.point3,I,m,K,F,h=JXG.Math.Geometry.rad(D,z,w),G,E=Math.ceil(h/Math.PI*90)+1,J=h/E,r=z.X(),q=z.Y(),s,l,k,u,H;if(this.useDirection){k=c[1].coords.usrCoords;u=c[3].coords.usrCoords;H=c[2].coords.usrCoords;l=(k[1]-H[1])*(k[2]-u[2])-(k[2]-H[2])*(k[1]-u[1]);if(l<0){this.point2=c[1];this.point3=c[2]}else{this.point2=c[2];this.point3=c[1]}}this.dataX=[D.X()];this.dataY=[D.Y()];for(I=J,G=1;G<=E;G++,I+=J){m=Math.cos(I);K=Math.sin(I);F=[[1,0,0],[r*(1-m)+q*K,m,-K],[q*(1-m)-r*K,K,m]];s=JXG.Math.matVecMult(F,D.coords.usrCoords);this.dataX.push(s[1]/s[0]);this.dataY.push(s[2]/s[0])}};e.Radius=function(){return this.point2.Dist(this.midpoint)};e.getRadius=function(){return this.Radius()};e.hasPoint=function(h,u){var l=this.board.options.precision.hasPoint/(this.board.stretchX),s=new JXG.Coords(JXG.COORDS_BY_SCREEN,[h,u],this.board),m=this.Radius(),q=this.midpoint.coords.distance(JXG.COORDS_BY_USER,s),k=(Math.abs(q-m)<l),n;if(k){n=JXG.Math.Geometry.rad(this.point2,this.midpoint,s.usrCoords.slice(1));if(n>JXG.Math.Geometry.rad(this.point2,this.midpoint,this.point3)){k=false}}return k};e.hasPointSector=function(h,s){var q=new JXG.Coords(JXG.COORDS_BY_SCREEN,[h,s],this.board),l=this.Radius(),n=this.midpoint.coords.distance(JXG.COORDS_BY_USER,q),k=(n<l),m;if(k){m=JXG.Math.Geometry.rad(this.point2,this.midpoint,q.usrCoords.slice(1));if(m>JXG.Math.Geometry.rad(this.point2,this.midpoint,this.point3)){k=false}}return k};e.getTextAnchor=function(){return this.midpoint.coords};e.getLabelAnchor=function(){var l=JXG.Math.Geometry.rad(this.point2,this.midpoint,this.point3),w=10/(this.board.stretchX),u=10/(this.board.stretchY),r=this.point2.coords.usrCoords,h=this.midpoint.coords.usrCoords,k=r[1]-h[1],v=r[2]-h[2],s,n,m,q;if(this.label.content!=null){this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board)}s=new JXG.Coords(JXG.COORDS_BY_USER,[h[1]+Math.cos(l*0.5)*k-Math.sin(l*0.5)*v,h[2]+Math.sin(l*0.5)*k+Math.cos(l*0.5)*v],this.board);n=s.usrCoords[1]-h[1];m=s.usrCoords[2]-h[2];q=Math.sqrt(n*n+m*m);n=n*(q+w)/q;m=m*(q+u)/q;return new JXG.Coords(JXG.COORDS_BY_USER,[h[1]+n,h[2]+m],this.board)};e.prepareUpdate().update();return e};JXG.JSXGraph.registerElement("arc",JXG.createArc);JXG.createSemicircle=function(d,b,a){var c,f,e="";a=JXG.checkAttributes(a,{});if(a.id!=null){e=a.id+"_mp"}if((JXG.isPoint(b[0]))&&(JXG.isPoint(b[1]))){f=d.create("midpoint",[b[0],b[1]],{id:e,withLabel:false,visible:false});c=d.create("arc",[f,b[1],b[0]],a)}else{throw new Error("JSXGraph: Can't create Semicircle with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"'.\nPossible parent types: [point,point]")}return c};JXG.JSXGraph.registerElement("semicircle",JXG.createSemicircle);JXG.createCircumcircleArc=function(d,b,a){var c,f,e;a=JXG.checkAttributes(a,{withLabel:JXG.readOption(d.options,"arc","withLabel"),layer:null});if(a.id!=null){e=a.id+"_mp"}if((JXG.isPoint(b[0]))&&(JXG.isPoint(b[1]))&&(JXG.isPoint(b[2]))){f=d.create("circumcirclemidpoint",[b[0],b[1],b[2]],{id:e,withLabel:false,visible:false});a.useDirection=true;c=d.create("arc",[f,b[0],b[2],b[1]],a)}else{throw new Error("JSXGraph: create Circumcircle Arc with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"' and '"+(typeof b[2])+"'.\nPossible parent types: [point,point,point]")}return c};JXG.JSXGraph.registerElement("circumcirclearc",JXG.createCircumcircleArc);JXG.createSector=function(f,c,a){var e,g,d,b;if(!(JXG.isPoint(c[0])&&JXG.isPoint(c[1])&&JXG.isPoint(c[2]))){throw new Error("JSXGraph: Can't create Sector with parent types '"+(typeof c[0])+"' and '"+(typeof c[1])+"' and '"+(typeof c[2])+"'.")}g={withLabel:JXG.readOption(f.options,"elements","withLabel"),layer:JXG.readOption(f.options,"layer","sector"),useDirection:false};g.strokeWidth=f.options.elements.strokeWidth;b=f.options.sector;for(d in b){g[d]=b[d]}a=JXG.checkAttributes(a,g);e=f.create("curve",[[0],[0]],a);e.type=JXG.OBJECT_TYPE_SECTOR;e.point1=JXG.getReference(f,c[0]);e.midpoint=e.point1;e.point2=JXG.getReference(f,c[1]);e.point3=JXG.getReference(f,c[2]);e.point1.addChild(e);e.point2.addChild(e);e.point3.addChild(e);e.useDirection=a.useDirection;e.updateDataArray=function(){var D=this.point2,z=this.point1,w=this.point3,I,m,K,F,h=JXG.Math.Geometry.rad(D,z,w),G,E=Math.ceil(h/Math.PI*90)+1,J=h/E,r=z.X(),q=z.Y(),s,l,k,u,H;if(this.useDirection){var l,k=c[1].coords.usrCoords,u=c[3].coords.usrCoords,H=c[2].coords.usrCoords;l=(k[1]-H[1])*(k[2]-u[2])-(k[2]-H[2])*(k[1]-u[1]);if(l<0){this.point2=c[1];this.point3=c[2]}else{this.point2=c[2];this.point3=c[1]}}this.dataX=[z.X(),D.X()];this.dataY=[z.Y(),D.Y()];for(I=J,G=1;G<=E;G++,I+=J){m=Math.cos(I);K=Math.sin(I);F=[[1,0,0],[r*(1-m)+q*K,m,-K],[q*(1-m)-r*K,K,m]];s=JXG.Math.matVecMult(F,D.coords.usrCoords);this.dataX.push(s[1]/s[0]);this.dataY.push(s[2]/s[0])}this.dataX.push(z.X());this.dataY.push(z.Y())};e.Radius=function(){return this.point2.Dist(this.point1)};e.getRadius=function(){return this.Radius()};e.hasPointSector=function(h,s){var q=new JXG.Coords(JXG.COORDS_BY_SCREEN,[h,s],this.board),l=this.Radius(),n=this.point1.coords.distance(JXG.COORDS_BY_USER,q),k=(n<l),m;if(k){m=JXG.Math.Geometry.rad(this.point2,this.point1,q.usrCoords.slice(1));if(m>JXG.Math.Geometry.rad(this.point2,this.point1,this.point3)){k=false}}return k};e.getTextAnchor=function(){return this.point1.coords};e.getLabelAnchor=function(){var l=JXG.Math.Geometry.rad(this.point2,this.point1,this.point3),w=10/(this.board.stretchX),u=10/(this.board.stretchY),r=this.point2.coords.usrCoords,h=this.point1.coords.usrCoords,k=r[1]-h[1],v=r[2]-h[2],s,n,m,q;if(this.label.content!=null){this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board)}s=new JXG.Coords(JXG.COORDS_BY_USER,[h[1]+Math.cos(l*0.5)*k-Math.sin(l*0.5)*v,h[2]+Math.sin(l*0.5)*k+Math.cos(l*0.5)*v],this.board);n=s.usrCoords[1]-h[1];m=s.usrCoords[2]-h[2];q=Math.sqrt(n*n+m*m);n=n*(q+w)/q;m=m*(q+u)/q;return new JXG.Coords(JXG.COORDS_BY_USER,[h[1]+n,h[2]+m],this.board)};e.prepareUpdate().update();return e};JXG.JSXGraph.registerElement("sector",JXG.createSector);JXG.createCircumcircleSector=function(e,b,a){var d,g,f="",c;a=JXG.checkAttributes(a,{withLabel:JXG.readOption(e.options,"sector","withLabel"),layer:null});if(a.id!=null){f=a.id+"_mp"}if((JXG.isPoint(b[0]))&&(JXG.isPoint(b[1]))&&(JXG.isPoint(b[2]))){g=e.create("circumcirclemidpoint",[b[0],b[1],b[2]],{id:f,withLabel:false,visible:false});a.useDirection=true;d=e.create("sector",[g,b[0],b[2],b[1]],a)}else{throw new Error("JSXGraph: Can't create circumcircle sector with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"' and '"+(typeof b[2])+"'.")}return d};JXG.JSXGraph.registerElement("circumcirclesector",JXG.createCircumcircleSector);JXG.createAngle=function(k,n,f){var b,a,d,v,r,s,m=["&alpha;","&beta;","&gamma;","&delta;","&epsilon;","&zeta;","&eta","&theta;","&iota;","&kappa;","&lambda;","&mu;","&nu;","&xi;","&omicron;","&pi;","&rho;","&sigmaf;","&sigma;","&tau;","&upsilon;","&phi;","&chi;","&psi;","&omega;"],h=0,g,e,l,c,q,u;d={withLabel:JXG.readOption(k.options,"elements","withLabel"),layer:JXG.readOption(k.options,"layer","angle"),radius:JXG.readOption(k.options,"angle","radius"),text:""};v=k.options.angle;for(r in v){d[r]=v[r]}f=JXG.checkAttributes(f,d);if((JXG.isPoint(n[0]))&&(JXG.isPoint(n[1]))&&(JXG.isPoint(n[2]))){s=f.text;if(s==""){while(h<m.length){e=h;l=m[h];for(b in k.objects){if(k.objects[b].type==JXG.OBJECT_TYPE_ANGLE){if(k.objects[b].text==l){h++;break}}}if(h==e){s=l;h=m.length+1}}if(h==m.length){c="&alpha;_{";q="}";u=false;e=0;while(!u){for(b in k.objects){if(k.objects[b].type==JXG.OBJECT_TYPE_ANGLE){if(k.objects[b].text==(c+e+q)){u=true;break}}}if(u){u=false}else{u=true;s=(c+e+q)}}}}a=k.create("point",[function(){var w=n[0],z=n[1],x=f.radius,y=z.Dist(w);return[z.X()+(w.X()-z.X())*x/y,z.Y()+(w.Y()-z.Y())*x/y]}],{withLabel:false,visible:false});for(h=0;h<3;h++){JXG.getReference(k,n[h]).addChild(a)}b=k.create("sector",[n[1],a,n[2]],f);b.type=JXG.OBJECT_TYPE_ANGLE;if(b.withLabel){b.label.content.setText(s)}JXG.getReference(k,n[0]).addChild(b);b.getLabelAnchor=function(){var y=JXG.Math.Geometry.rad(this.point2,this.point1,this.point3),G=10/(this.board.stretchX),E=10/(this.board.stretchY),C=this.point2.coords.usrCoords,w=this.point1.coords.usrCoords,x=C[1]-w[1],F=C[2]-w[2],D,A,z,B;if(this.label.content!=null){this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board)}D=new JXG.Coords(JXG.COORDS_BY_USER,[w[1]+Math.cos(y*0.5*1.125)*x-Math.sin(y*0.5*1.125)*F,w[2]+Math.sin(y*0.5*1.125)*x+Math.cos(y*0.5*1.125)*F],this.board);A=D.usrCoords[1]-w[1];z=D.usrCoords[2]-w[2];B=Math.sqrt(A*A+z*z);A=A*(B+G)/B;z=z*(B+E)/B;return new JXG.Coords(JXG.COORDS_BY_USER,[w[1]+A,w[2]+z],this.board)}}else{throw new Error("JSXGraph: Can't create angle with parent types '"+(typeof n[0])+"' and '"+(typeof n[1])+"' and '"+(typeof n[2])+"'.")}return b};JXG.JSXGraph.registerElement("angle",JXG.createAngle);JXG.Algebra=function(a){this.board=a;this.eps=JXG.Math.eps};JXG.Algebra.prototype.angle=function(a,c,b){return JXG.Math.Geometry.angle(a,c,b)};JXG.Algebra.prototype.trueAngle=function(a,c,b){return this.rad(a,c,b)*57.29577951308232};JXG.Algebra.prototype.rad=function(a,c,b){return JXG.Math.Geometry.rad(a,c,b)};JXG.Algebra.prototype.angleBisector=function(a,c,b){return JXG.Math.Geometry.angleBisector(a,c,b,this.board)};JXG.Algebra.prototype.reflection=function(b,a){return JXG.Math.Geometry.reflection(b,a,this.board)};JXG.Algebra.prototype.rotation=function(b,a,c){return JXG.Math.Geometry.rotation(b,a,c,this.board)};JXG.Algebra.prototype.perpendicular=function(b,a){return JXG.Math.Geometry.perpendicular(b,a,this.board)};JXG.Algebra.prototype.circumcenterMidpoint=function(c,b,a){return JXG.Math.Geometry.circumcenterMidpoint(c,b,a,this.board)};JXG.Algebra.prototype.intersectLineLine=function(b,a){return JXG.Math.Geometry.intersectLineLine(b,a,this.board)};JXG.Algebra.prototype.intersectCircleLine=function(b,a){return JXG.Math.Geometry.intersectCircleLine(b,a,this.board)};JXG.Algebra.prototype.intersectCircleCircle=function(b,a){return JXG.Math.Geometry.intersectCircleCircle(b,a,this.board)};JXG.Algebra.prototype.projectPointToCircle=function(a,b){return JXG.Math.Geometry.projectPointToCircle(a,b,this.board)};JXG.Algebra.prototype.projectPointToLine=function(a,b){return JXG.Math.Geometry.projectPointToLine(a,b,this.board)};JXG.Algebra.prototype.projectPointToCurve=function(a,b){return JXG.Math.Geometry.projectPointToCurve(a,b,this.board)};JXG.Algebra.prototype.projectCoordsToCurve=function(a,d,b,c){return JXG.Math.Geometry.projectCoordsToCurve(a,d,b,c,this.board)};JXG.Algebra.prototype.projectPointToTurtle=function(a,b){return JXG.Math.Geometry.projectPointToTurtle(a,b,this.board)};JXG.Algebra.prototype.replacePow=function(a){return JXG.GeonextParser.replacePow(a)};JXG.Algebra.prototype.replaceIf=function(a){return JXG.GeonextParser.replaceIf(a)};JXG.Algebra.prototype.replaceSub=function(a){return JXG.GeonextParser.replaceSub(a)};JXG.Algebra.prototype.replaceSup=function(a){return JXG.GeonextParser.replaceSup(a)};JXG.Algebra.prototype.replaceNameById=function(a){return JXG.GeonextParser.replaceNameById(a,this.board)};JXG.Algebra.prototype.replaceIdByObj=function(a){return JXG.GeonextParser.replaceIdByObj(a)};JXG.Algebra.prototype.geonext2JS=function(a){return JXG.GeonextParser.geonext2JS(a,this.board)};JXG.Algebra.prototype.findDependencies=function(b,a){JXG.GeonextParser.findDependencies(b,a,this.board)};JXG.Algebra.prototype.distance=function(b,a){return JXG.Math.Geometry.distance(b,a)};JXG.Algebra.prototype.affineDistance=function(b,a){return JXG.Math.Geometry.affineDistance(b,a)};JXG.Algebra.prototype.pow=function(d,c){return JXG.Math.pow(d,c)};JXG.Algebra.prototype.meet=function(c,a,b){return JXG.Math.Geometry.meet(c,a,b,this.board)};JXG.Algebra.prototype.meetLineLine=function(b,a,c){return JXG.Math.Geometry.meetLineLine(b,a,c,this.board)};JXG.Algebra.prototype.meetLineCircle=function(c,b,a){return JXG.Math.Geometry.meetLineCircle(c,b,a,this.board)};JXG.Algebra.prototype.meetCircleCircle=function(c,a,b){return JXG.Math.Geometry.meetCircleCircle(c,a,b,this.board)};JXG.Algebra.prototype.normalize=function(a){return JXG.Math.normalize(a)};JXG.Algebra.prototype.meetCurveCurve=function(c,b,a,d){return JXG.Math.Geometry.meetCurveCurve(c,b,a,d,this.board)};JXG.Algebra.prototype.meetCurveLine=function(b,a,c){return JXG.Math.Geometry.meetCurveLine(b,a,c,this.board)};JXG.Intersection=function(e,b,d,c,g,f,m,l){this.constructor();this.board=e;this.id=b;this.name=this.id;this.visProp={};this.visProp.visible=true;this.show=true;this.real=true;this.notExistingParents={};this.intersect1=JXG.getReference(this.board,d);this.intersect2=JXG.getReference(this.board,c);this.type=JXG.OBJECT_TYPE_INTERSECTION;if(((this.intersect1=="")||(this.intersect1==undefined))&&((this.intersect2=="")||(this.intersect2==undefined))){return}if(((this.intersect1.type==this.intersect2.type)&&(this.intersect1.type==JXG.OBJECT_TYPE_LINE||this.intersect1.type==JXG.OBJECT_TYPE_ARROW))||((this.intersect1.type==JXG.OBJECT_TYPE_LINE)&&(this.intersect2.type==JXG.OBJECT_TYPE_ARROW))||((this.intersect2.type==JXG.OBJECT_TYPE_LINE)&&(this.intersect1.type==JXG.OBJECT_TYPE_ARROW))){var h=JXG.Math.Geometry.intersectLineLine(this.intersect1,this.intersect2,this.board).usrCoords.slice(1);this.p=new JXG.Point(this.board,h,g,m,true);this.p.fixed=true;this.addChild(this.p);this.real=true;this.update=function(){if(this.needsUpdate){this.p.coords=JXG.Math.Geometry.intersectLineLine(this.intersect1,this.intersect2,this.board);this.needsUpdate=false}};this.hideElement=function(){this.visProp.visible=false;this.p.hideElement()};this.showElement=function(){this.visProp.visible=true;this.p.showElement()};this.hideChild=function(q){this.notExistingParents[q]=this.board.objects[q];for(var n in this.descendants){if(this.descendants[n].visProp.visible&&this.descendants[n].type!=JXG.OBJECT_TYPE_INTERSECTION){if(this.descendants[n].type!=JXG.OBJECT_TYPE_TEXT){this.descendants[n].hideElement();this.descendants[n].visProp.visible=true}else{if(!this.descendants[n].isLabel){this.descendants[n].hideElement();this.descendants[n].visProp.visible=true}}}this.descendants[n].notExistingParents[q]=this.board.objects[q]}};this.showChild=function(q){for(var n in this.board.objects){delete (this.board.objects[n].notExistingParents[q]);if(this.board.objects[n].visProp.visible&&JXG.keys(this.board.objects[n].notExistingParents).length==0){if(this.board.objects[n].type!=JXG.OBJECT_TYPE_INTERSECTION){this.board.objects[n].showElement()}}}}}else{if(((d.type==c.type)&&(d.type==JXG.OBJECT_TYPE_CIRCLE||d.type==JXG.OBJECT_TYPE_ARC))||(d.type==JXG.OBJECT_TYPE_CIRCLE&&c.type==JXG.OBJECT_TYPE_ARC)||(c.type==JXG.OBJECT_TYPE_CIRCLE&&d.type==JXG.OBJECT_TYPE_ARC)){this.p1=new JXG.Point(this.board,[0,0],g,m,false);this.p1.fixed=true;this.p1.label.content.visProp.visible=true;this.p2=new JXG.Point(this.board,[0,0],f,l,false);this.p2.fixed=true;this.p2.label.content.visProp.visible=true;this.addChild(this.p1);this.addChild(this.p2);var k=JXG.Math.Geometry.intersectCircleCircle(this.intersect1,this.intersect2,this.board);if(k[0]==1){this.p1.coords=k[1];this.p1.showElement();this.p1.updateRenderer();this.p2.coords=k[2];this.p2.showElement();this.p2.updateRenderer();this.real=true}else{this.real=false}this.update=function(){if(!this.needsUpdate){return}var r=JXG.Math.Geometry.intersectCircleCircle(this.intersect1,this.intersect2,this.board);var q=this.p1.visProp.visible;var n=this.p2.visProp.visible;if(r[0]==0){if(this.real){this.hideChild(this.id);this.p1.visProp.visible=q;this.p2.visProp.visible=n;this.real=false}}else{this.p1.coords=r[1];this.p2.coords=r[2];if(!this.real){this.showChild(this.id);this.real=true}}this.needsUpdate=false};this.hideElement=function(){this.visProp.visible=false;this.p1.hideElement();this.p2.hideElement()};this.showElement=function(){this.visProp.visible=true;this.p1.showElement();this.p2.showElement()};this.hideChild=function(q){this.notExistingParents[q]=this.board.objects[q];for(var n in this.descendants){if(this.descendants[n].visProp.visible&&this.descendants[n].type!=JXG.OBJECT_TYPE_INTERSECTION){if(this.descendants[n].type!=JXG.OBJECT_TYPE_TEXT){this.descendants[n].hideElement();this.descendants[n].visProp.visible=true}else{if(!this.descendants[n].isLabel){this.descendants[n].hideElement();this.descendants[n].visProp.visible=true}}}this.descendants[n].notExistingParents[q]=this.board.objects[q]}};this.showChild=function(q){var n;for(n in this.board.objects){delete (this.board.objects[n].notExistingParents[q]);if(this.board.objects[n].visProp.visible&&JXG.keys(this.board.objects[n].notExistingParents).length==0){if(this.board.objects[n].type!=JXG.OBJECT_TYPE_INTERSECTION){this.board.objects[n].showElement()}}}}}else{this.p1=new JXG.Point(this.board,[0,0],g,m,false);this.p1.fixed=true;this.p1.label.content.visProp.visible=true;this.p2=new JXG.Point(this.board,[0,0],f,l,false);this.p2.fixed=true;this.p2.label.content.visProp.visible=true;this.addChild(this.p1);this.addChild(this.p2);if(this.intersect1.type==JXG.OBJECT_TYPE_LINE||this.intersect1.type==JXG.OBJECT_TYPE_ARROW){var a=this.intersect1;this.intersect1=this.intersect2;this.intersect2=a}var k=JXG.Math.Geometry.intersectCircleLine(this.intersect1,this.intersect2,this.board);if(k[0]==1){this.p1.coords=k[1];this.p1.showElement();this.p1.update()}else{if(k[0]==2){this.p1.coords=k[1];this.p1.showElement();this.p2.coords=k[2];this.p2.showElement();this.p1.updateRenderer();this.p2.updateRenderer();this.real=true}else{this.real=false}}this.update=function(){if(!this.needsUpdate){return}var r=JXG.Math.Geometry.intersectCircleLine(this.intersect1,this.intersect2,this.board);var q=this.p1.visProp.visible;var n=this.p2.visProp.visible;if(r[0]==0){if(this.real){this.hideChild(this.id);this.p1.visProp.visible=q;this.p2.visProp.visible=n;this.real=false}}else{if(r[0]==2){this.p1.coords=r[1];this.p2.coords=r[2];if(!this.real){this.showChild(this.id);this.real=true}}}this.needsUpdate=false};this.hideElement=function(){this.visProp.visible=false;this.p1.hideElement();this.p2.hideElement()};this.showElement=function(){this.visProp.visible=true;this.p1.showElement();this.p2.showElement()};this.hideChild=function(q){this.notExistingParents[q]=this.board.objects[q];for(var n in this.descendants){if(this.descendants[n].visProp.visible&&this.descendants[n].type!=JXG.OBJECT_TYPE_INTERSECTION){if(this.descendants[n].type!=JXG.OBJECT_TYPE_TEXT){this.descendants[n].hideElement();this.descendants[n].visProp.visible=true}else{if(!this.descendants[n].isLabel){this.descendants[n].hideElement();this.descendants[n].visProp.visible=true}}}this.descendants[n].notExistingParents[q]=this.board.objects[q]}};this.showChild=function(q){var n;for(n in this.board.objects){delete (this.board.objects[n].notExistingParents[q]);if(this.board.objects[n].visProp.visible&&JXG.keys(this.board.objects[n].notExistingParents).length==0){if(this.board.objects[n].type!=JXG.OBJECT_TYPE_INTERSECTION){this.board.objects[n].showElement()}}}}}}this.id=this.board.addIntersection(this)};JXG.Intersection.prototype=new JXG.GeometryElement();JXG.Intersection.prototype.update=function(){return};JXG.Intersection.prototype.hasPoint=function(a,b){return false};JXG.Intersection.prototype.hideChild=function(a){};JXG.Intersection.prototype.showChild=function(a){};JXG.Intersection.prototype.remove=function(){if(this.p!=undefined){this.board.removeObject(this.p)}if(this.p1!=undefined){this.board.removeObject(this.p1)}if(this.p2!=undefined){this.board.removeObject(this.p2)}return};JXG.Intersection.prototype.updateRenderer=function(){};JXG.createPerpendicularPoint=function(c,f,e){var a,d,b;if(JXG.isPoint(f[0])&&f[1].type==JXG.OBJECT_TYPE_LINE){d=f[0];a=f[1]}else{if(JXG.isPoint(f[1])&&f[0].type==JXG.OBJECT_TYPE_LINE){d=f[1];a=f[0]}else{throw new Error("JSXGraph: Can't create perpendicular point with parent types '"+(typeof f[0])+"' and '"+(typeof f[1])+"'.\nPossible parent types: [point,line]")}}b=JXG.createPoint(c,[function(){return JXG.Math.Geometry.perpendicular(a,d,c)[0]}],{fixed:true,name:e.name,id:e.id});d.addChild(b);a.addChild(b);b.update();b.generatePolynomial=function(){var h=a.point1.symbolic.x;var g=a.point1.symbolic.y;var r=a.point2.symbolic.x;var q=a.point2.symbolic.y;var u=d.symbolic.x;var s=d.symbolic.y;var m=b.symbolic.x;var k=b.symbolic.y;var n="("+g+")*("+m+")-("+g+")*("+r+")+("+k+")*("+r+")-("+h+")*("+k+")+("+h+")*("+q+")-("+m+")*("+q+")";var l="("+s+")*("+g+")-("+s+")*("+q+")-("+k+")*("+g+")+("+k+")*("+q+")+("+u+")*("+h+")-("+u+")*("+r+")-("+m+")*("+h+")+("+m+")*("+r+")";return[n,l]};return b};JXG.createPerpendicular=function(e,h,g){var f,a,b,d,c;h[0]=JXG.getReference(e,h[0]);h[1]=JXG.getReference(e,h[1]);if(JXG.isPoint(h[0])&&h[1].elementClass==JXG.OBJECT_CLASS_LINE){a=h[1];f=h[0]}else{if(JXG.isPoint(h[1])&&h[0].elementClass==JXG.OBJECT_CLASS_LINE){a=h[0];f=h[1]}else{throw new Error("JSXGraph: Can't create perpendicular with parent types '"+(typeof h[0])+"' and '"+(typeof h[1])+"'.\nPossible parent types: [line,point]")}}if(!JXG.isArray(g.id)){g.id=["",""]}if(!JXG.isArray(g.name)){g.name=["",""]}d=JXG.createPerpendicularPoint(e,[a,f],{fixed:true,name:g.name[1],id:g.id[1],visible:false});b=JXG.createSegment(e,[function(){return(JXG.Math.Geometry.perpendicular(a,f,e)[1]?[d,f]:[f,d])}],{name:g.name[0],id:g.id[0]});c=[b,d];c.line=b;c.point=d;c.multipleElements=true;return c};JXG.createMidpoint=function(f,h,g){var d,c,e;if(h.length==2&&JXG.isPoint(h[0])&&JXG.isPoint(h[1])){d=h[0];c=h[1]}else{if(h.length==1&&h[0].elementClass==JXG.OBJECT_CLASS_LINE){d=h[0].point1;c=h[0].point2}else{throw new Error("JSXGraph: Can't create midpoint.\nPossible parent types: [point,point], [line]")}}if(g){g.fixed=true}else{g={fixed:true}}e=f.create("point",[function(){return(d.coords.usrCoords[1]+c.coords.usrCoords[1])/2},function(){return(d.coords.usrCoords[2]+c.coords.usrCoords[2])/2}],g);d.addChild(e);c.addChild(e);e.update();e.generatePolynomial=function(){var k=d.symbolic.x;var b=d.symbolic.y;var m=c.symbolic.x;var l=c.symbolic.y;var q=e.symbolic.x;var n=e.symbolic.y;var a="("+b+")*("+q+")-("+b+")*("+m+")+("+n+")*("+m+")-("+k+")*("+n+")+("+k+")*("+l+")-("+q+")*("+l+")";var r="("+k+")^2 - 2*("+k+")*("+q+")+("+b+")^2-2*("+b+")*("+n+")-("+m+")^2+2*("+m+")*("+q+")-("+l+")^2+2*("+l+")*("+n+")";return[a,r]};if(JXG.nullAtts){g=null}return e};JXG.createParallelPoint=function(f,l,k){var e,d,h,g;if(l.length==3&&l[0].elementClass==JXG.OBJECT_CLASS_POINT&&l[1].elementClass==JXG.OBJECT_CLASS_POINT&&l[2].elementClass==JXG.OBJECT_CLASS_POINT){e=l[0];d=l[1];h=l[2]}else{if(l[0].elementClass==JXG.OBJECT_CLASS_POINT&&l[1].elementClass==JXG.OBJECT_CLASS_LINE){h=l[0];e=l[1].point1;d=l[1].point2}else{if(l[1].elementClass==JXG.OBJECT_CLASS_POINT&&l[0].elementClass==JXG.OBJECT_CLASS_LINE){h=l[1];e=l[0].point1;d=l[0].point2}else{throw new Error("JSXGraph: Can't create parallel point with parent types '"+(typeof l[0])+"', '"+(typeof l[1])+"' and '"+(typeof l[2])+"'.\nPossible parent types: [line,point], [point,point,point]")}}}g=f.create("point",[function(){return h.coords.usrCoords[1]+d.coords.usrCoords[1]-e.coords.usrCoords[1]},function(){return h.coords.usrCoords[2]+d.coords.usrCoords[2]-e.coords.usrCoords[2]}],k);h.addChild(g);g.update();g.generatePolynomial=function(){var b=e.symbolic.x;var a=e.symbolic.y;var v=d.symbolic.x;var u=d.symbolic.y;var m=h.symbolic.x;var c=h.symbolic.y;var r=g.symbolic.x;var n=g.symbolic.y;var s="("+u+")*("+r+")-("+u+")*("+m+")-("+a+")*("+r+")+("+a+")*("+m+")-("+n+")*("+v+")+("+n+")*("+b+")+("+c+")*("+v+")-("+c+")*("+b+")";var q="("+n+")*("+b+")-("+n+")*("+m+")-("+u+")*("+b+")+("+u+")*("+m+")-("+r+")*("+a+")+("+r+")*("+c+")+("+v+")*("+a+")-("+v+")*("+c+")";return[s,q]};return g};JXG.createParallel=function(d,b,k){var h,a,c,f;f={name:null,id:null,fixed:true,visible:false};if(JXG.isArray(k.name)&&k.name.length==2){f.name=k.name[1];k.name=k.name[0]}else{f.name=k.name+"p2"}if(JXG.isArray(k.id)&&k.id.length==2){f.id=k.id[1];k.id=k.id[0]}else{f.id=k.id+"p2"}try{a=JXG.createParallelPoint(d,b,f)}catch(g){throw new Error("JSXGraph: Can't create parallel with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"'.\nPossible parent types: [line,point], [point,point,point]")}h=null;if(b.length==3){h=b[2]}else{if(b[0].elementClass==JXG.OBJECT_CLASS_POINT){h=b[0]}else{if(b[1].elementClass==JXG.OBJECT_CLASS_POINT){h=b[1]}}}c=d.create("line",[h,a],k);return c};JXG.createArrowParallel=function(c,b,g){var a,d;try{a=JXG.createParallel(c,b,g)}catch(f){throw new Error("JSXGraph: Can't create arrowparallel with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"'.\nPossible parent types: [line,point], [point,point,point]")}a.setStraight(false,false);a.setArrow(false,true);return a};JXG.createNormal=function(d,b,a){var k;var l;if(b.length==1){k=b[0];l=k.slideObject}else{if(b.length==2){if(JXG.isPoint(b[0])){k=b[0];l=b[1]}else{if(JXG.isPoint(b[1])){l=b[0];k=b[1]}else{throw new Error("JSXGraph: Can't create normal with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"'.\nPossible parent types: [point,line], [point,circle], [glider]")}}}else{throw new Error("JSXGraph: Can't create normal with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"'.\nPossible parent types: [point,line], [point,circle], [glider]")}}if(l.elementClass==JXG.OBJECT_CLASS_LINE){return d.create("line",[function(){return l.stdform[1]*k.Y()-l.stdform[2]*k.X()},function(){return l.stdform[2]*k.Z()},function(){return -l.stdform[1]*k.Z()}],a)}else{if(l.elementClass==JXG.OBJECT_CLASS_CIRCLE){return d.create("line",[l.midpoint,k],a)}else{if(l.elementClass==JXG.OBJECT_CLASS_CURVE){if(l.curveType!="plot"){var e=l.X;var h=l.Y;return d.create("line",[function(){return -k.X()*d.D(e)(k.position)-k.Y()*d.D(h)(k.position)},function(){return d.D(e)(k.position)},function(){return d.D(h)(k.position)}],a)}else{return d.create("line",[function(){var f=Math.floor(k.position);var c=k.position-f;if(f==l.numberPoints-1){f--;c=1}if(f<0){return 1}return(l.Y(f)+c*(l.Y(f+1)-l.Y(f)))*(l.Y(f)-l.Y(f+1))-(l.X(f)+c*(l.X(f+1)-l.X(f)))*(l.X(f+1)-l.X(f))},function(){var c=Math.floor(k.position);if(c==l.numberPoints-1){c--}if(c<0){return 0}return l.X(c+1)-l.X(c)},function(){var c=Math.floor(k.position);if(c==l.numberPoints-1){c--}if(c<0){return 0}return l.Y(c+1)-l.Y(c)}],a)}}else{if(l.type==JXG.OBJECT_TYPE_TURTLE){return d.create("line",[function(){var g=Math.floor(k.position);var c=k.position-g;var m,f;for(f=0;f<l.objects.length;f++){m=l.objects[f];if(m.type==JXG.OBJECT_TYPE_CURVE){if(g<m.numberPoints){break}g-=m.numberPoints}}if(g==m.numberPoints-1){g--;c=1}if(g<0){return 1}return(m.Y(g)+c*(m.Y(g+1)-m.Y(g)))*(m.Y(g)-m.Y(g+1))-(m.X(g)+c*(m.X(g+1)-m.X(g)))*(m.X(g+1)-m.X(g))},function(){var f=Math.floor(k.position);var g,c;for(c=0;c<l.objects.length;c++){g=l.objects[c];if(g.type==JXG.OBJECT_TYPE_CURVE){if(f<g.numberPoints){break}f-=g.numberPoints}}if(f==g.numberPoints-1){f--}if(f<0){return 0}return g.X(f+1)-g.X(f)},function(){var f=Math.floor(k.position);var g,c;for(c=0;c<l.objects.length;c++){g=l.objects[c];if(g.type==JXG.OBJECT_TYPE_CURVE){if(f<g.numberPoints){break}f-=g.numberPoints}}if(f==g.numberPoints-1){f--}if(f<0){return 0}return g.Y(f+1)-g.Y(f)}],a)}else{throw new Error("JSXGraph: Can't create normal with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"'.\nPossible parent types: [point,line], [point,circle], [glider]")}}}}};JXG.createBisector=function(c,g,f){var e,a,d,b;if(g[0].elementClass==JXG.OBJECT_CLASS_POINT&&g[1].elementClass==JXG.OBJECT_CLASS_POINT&&g[2].elementClass==JXG.OBJECT_CLASS_POINT){d={name:"",id:null,fixed:true,visible:false};if(f){d=JXG.cloneAndCopy(f,d)}e=c.create("point",[function(){return JXG.Math.Geometry.angleBisector(g[0],g[1],g[2],c)}],d);for(b=0;b<3;b++){g[b].addChild(e)}if(typeof f.straightFirst=="undefined"){f.straightFirst=false}if(typeof f.straightLast=="undefined"){f.straightLast=true}a=JXG.createLine(c,[g[1],e],f);return a}else{throw new Error("JSXGraph: Can't create angle bisector with parent types '"+(typeof g[0])+"' and '"+(typeof g[1])+"'.\nPossible parent types: [point,point,point]")}};JXG.createAngularBisectorsOfTwoLines=function(g,k,d){var c=JXG.getReference(g,k[0]),b=JXG.getReference(g,k[1]),m="",l="",h="",e="",f;if(c.elementClass!=JXG.OBJECT_CLASS_LINE||b.elementClass!=JXG.OBJECT_CLASS_LINE){throw new Error("JSXGraph: Can't create angle bisectors of two lines with parent types '"+(typeof k[0])+"' and '"+(typeof k[1])+"'.\nPossible parent types: [line,line]")}d=JXG.checkAttributes(d,{});if(d.id!=null){if(JXG.isArray(d.id)){m=d.id[0];l=d.id[1]}else{m=d.id;l=d.id}}if(d.name!=null){if(JXG.isArray(d.name)){h=d.name[0];e=d.name[1]}else{h=d.name;e=d.name}}d.id=m;d.name=h;var a=g.create("line",[function(){var r=Math.sqrt(c.stdform[1]*c.stdform[1]+c.stdform[2]*c.stdform[2]);var q=Math.sqrt(b.stdform[1]*b.stdform[1]+b.stdform[2]*b.stdform[2]);return c.stdform[0]/r-b.stdform[0]/q},function(){var r=Math.sqrt(c.stdform[1]*c.stdform[1]+c.stdform[2]*c.stdform[2]);var q=Math.sqrt(b.stdform[1]*b.stdform[1]+b.stdform[2]*b.stdform[2]);return c.stdform[1]/r-b.stdform[1]/q},function(){var r=Math.sqrt(c.stdform[1]*c.stdform[1]+c.stdform[2]*c.stdform[2]);var q=Math.sqrt(b.stdform[1]*b.stdform[1]+b.stdform[2]*b.stdform[2]);return c.stdform[2]/r-b.stdform[2]/q}],d);d.id=l;d.name=e;var n=g.create("line",[function(){var r=Math.sqrt(c.stdform[1]*c.stdform[1]+c.stdform[2]*c.stdform[2]);var q=Math.sqrt(b.stdform[1]*b.stdform[1]+b.stdform[2]*b.stdform[2]);return c.stdform[0]/r+b.stdform[0]/q},function(){var r=Math.sqrt(c.stdform[1]*c.stdform[1]+c.stdform[2]*c.stdform[2]);var q=Math.sqrt(b.stdform[1]*b.stdform[1]+b.stdform[2]*b.stdform[2]);return c.stdform[1]/r+b.stdform[1]/q},function(){var r=Math.sqrt(c.stdform[1]*c.stdform[1]+c.stdform[2]*c.stdform[2]);var q=Math.sqrt(b.stdform[1]*b.stdform[1]+b.stdform[2]*b.stdform[2]);return c.stdform[2]/r+b.stdform[2]/q}],d);f=[a,n];f.lines=[a,n];f.line1=a;f.line2=n;f.multipleElements=true;return f};JXG.createCircumcircleMidpoint=function(b,e,d){var c,a;if(e[0].elementClass==JXG.OBJECT_CLASS_POINT&&e[1].elementClass==JXG.OBJECT_CLASS_POINT&&e[2].elementClass==JXG.OBJECT_CLASS_POINT){d.fixed=d.fixed||true;c=JXG.createPoint(b,[function(){return JXG.Math.Geometry.circumcenterMidpoint(e[0],e[1],e[2],b)}],d);for(a=0;a<3;a++){e[a].addChild(c)}return c}else{throw new Error("JSXGraph: Can't create circumcircle midpoint with parent types '"+(typeof e[0])+"', '"+(typeof e[1])+"' and '"+(typeof e[2])+"'.\nPossible parent types: [point,point,point]")}};JXG.createCircumcircle=function(b,l,k){var g,h,d,a;d=JXG.clone(k);if(k.name&&JXG.isArray(k.name)){d.name=k.name[0];k.name=k.name[1]}if(k.id&&JXG.isArray(k.id)){d.id=k.id[0];k.id=k.id[1]}try{g=JXG.createCircumcircleMidpoint(b,l,d);h=JXG.createCircle(b,[g,l[0]],k)}catch(f){throw new Error("JSXGraph: Can't create circumcircle with parent types '"+(typeof l[0])+"', '"+(typeof l[1])+"' and '"+(typeof l[2])+"'.\nPossible parent types: [point,point,point]")}a=[g,h];a.point=g;a.circle=h;a.multipleElements=true;return a};JXG.createReflection=function(b,f,e){var a,d,c;if(f[0].elementClass==JXG.OBJECT_CLASS_POINT&&f[1].elementClass==JXG.OBJECT_CLASS_LINE){d=f[0];a=f[1]}else{if(f[1].elementClass==JXG.OBJECT_CLASS_POINT&&f[0].elementClass==JXG.OBJECT_CLASS_LINE){d=f[1];a=f[0]}else{throw new Error("JSXGraph: Can't create reflection point with parent types '"+(typeof f[0])+"' and '"+(typeof f[1])+"'.\nPossible parent types: [line,point]")}}e.fixed=true;c=JXG.createPoint(b,[function(){return JXG.Math.Geometry.reflection(a,d,b)}],e);d.addChild(c);a.addChild(c);c.update();return c};JXG.createMirrorPoint=function(a,d,c){var b;if(JXG.isPoint(d[0])&&JXG.isPoint(d[1])){c.fixed=c.fixed||true;b=JXG.createPoint(a,[function(){return JXG.Math.Geometry.rotation(d[0],d[1],Math.PI,a)}],c);for(i=0;i<2;i++){d[i].addChild(b)}}else{throw new Error("JSXGraph: Can't create mirror point with parent types '"+(typeof d[0])+"' and '"+(typeof d[1])+"'.\nPossible parent types: [point,point]")}b.update();return b};JXG.createIntegral=function(f,x,l){var w,s,q={},d=0,c=0,b,a,k,h,r=1,v,m,e,y,g,n,u;if(!JXG.isArray(l.id)||(l.id.length!=5)){l.id=["","","","",""]}if(!JXG.isArray(l.name)||(l.name.length!=5)){l.name=["","","","",""]}if(JXG.isArray(x[0])&&x[1].elementClass==JXG.OBJECT_CLASS_CURVE){w=x[0];s=x[1]}else{if(JXG.isArray(x[1])&&x[0].elementClass==JXG.OBJECT_CLASS_CURVE){w=x[1];s=x[0]}else{throw new Error("JSXGraph: Can't create integral with parent types '"+(typeof x[0])+"' and '"+(typeof x[1])+"'.\nPossible parent types: [[number|function,number|function],curve]")}}if((typeof l!="undefined")&&(l!=null)){q=JXG.cloneAndCopy(l,{name:l.name[0],id:l.id[0]})}d=w[0];c=w[1];if(JXG.isFunction(d)){b=d;a=function(){return s.yterm(b())};d=b()}else{b=d;a=s.yterm(d)}if(JXG.isFunction(d)){k=c;h=function(){return s.yterm(k())};c=k()}else{k=c;h=s.yterm(c)}if(c<d){r=-1}v=f.create("glider",[b,a,s],q);if(JXG.isFunction(b)){v.hideElement()}q.name=l.name[1];q.id=l.id[1];q.visible=false;m=f.create("point",[function(){return v.X()},0],q);q.name=l.name[2];q.id=l.id[2];q.visible=l.visible||true;e=f.create("glider",[k,h,s],q);if(JXG.isFunction(k)){e.hideElement()}q.name=l.name[3];q.id=l.id[3];q.visible=false;y=f.create("point",[function(){return e.X()},0],q);g=JXG.Math.Numerics.I([d,c],s.yterm);n=f.create("text",[function(){return e.X()+0.2},function(){return e.Y()-0.8},function(){var z=JXG.Math.Numerics.I([m.X(),y.X()],s.yterm);return"&int; = "+(z).toFixed(4)}],{labelColor:l.labelColor});q.name=l.name[4];q.id=l.id[4];q.visible=l.visible||true;q.fillColor=q.fillColor||f.options.polygon.fillColor;q.highlightFillColor=q.highlightFillColor||f.options.polygon.highlightFillColor;q.fillOpacity=q.fillOpacity||f.options.polygon.fillOpacity;q.highlightFillOpacity=q.highlightFillOpacity||f.options.polygon.highlightFillOpacity;q.strokeWidth=0;q.highlightStrokeWidth=0;q.strokeOpacity=0;u=f.create("curve",[[0],[0]],q);u.updateDataArray=function(){var z,D,B,C,A;if(m.X()<y.X()){C=m.X();A=y.X()}else{C=y.X();A=m.X()}z=[C,C];D=[0,s.yterm(C)];for(B=0;B<s.numberPoints;B++){if((C<=s.points[B].usrCoords[1])&&(s.points[B].usrCoords[1]<=A)){z.push(s.points[B].usrCoords[1]);D.push(s.points[B].usrCoords[2])}}z.push(A);D.push(s.yterm(A));z.push(A);D.push(0);z.push(C);D.push(0);this.dataX=z;this.dataY=D};v.addChild(u);e.addChild(u);v.addChild(n);e.addChild(n);return u};JXG.createLocus=function(d,b,a){var f,e;if(JXG.isArray(b)&&b.length==1&&b[0].elementClass==JXG.OBJECT_CLASS_POINT){e=b[0]}else{throw new Error("JSXGraph: Can't create locus with parent of type other than point.\nPossible parent types: [point]")}f=d.create("curve",[[null],[null]],a);f.dontCallServer=false;f.updateDataArray=function(){cb=function(g,h,c){f.dataX=g;f.dataY=h;f.eq=c;d.update()};if(d.mode==d.BOARD_MODE_NONE&&!this.dontCallServer){JXG.Math.Symbolic.geometricLocusByGroebnerBase(d,e,cb);this.dontCallServer=true}else{this.dontCallServer=false}};return f};JXG.JSXGraph.registerElement("arrowparallel",JXG.createArrowParallel);JXG.JSXGraph.registerElement("bisector",JXG.createBisector);JXG.JSXGraph.registerElement("bisectorlines",JXG.createAngularBisectorsOfTwoLines);JXG.JSXGraph.registerElement("circumcircle",JXG.createCircumcircle);JXG.JSXGraph.registerElement("circumcirclemidpoint",JXG.createCircumcircleMidpoint);JXG.JSXGraph.registerElement("integral",JXG.createIntegral);JXG.JSXGraph.registerElement("midpoint",JXG.createMidpoint);JXG.JSXGraph.registerElement("mirrorpoint",JXG.createMirrorPoint);JXG.JSXGraph.registerElement("normal",JXG.createNormal);JXG.JSXGraph.registerElement("parallel",JXG.createParallel);JXG.JSXGraph.registerElement("parallelpoint",JXG.createParallelPoint);JXG.JSXGraph.registerElement("perpendicular",JXG.createPerpendicular);JXG.JSXGraph.registerElement("perpendicularpoint",JXG.createPerpendicularPoint);JXG.JSXGraph.registerElement("reflection",JXG.createReflection);JXG.JSXGraph.registerElement("locus",JXG.createLocus);JXG.Text=function(k,q,f,n,c,a,d,m,l,h){this.constructor();this.type=JXG.OBJECT_TYPE_TEXT;this.elementClass=JXG.OBJECT_CLASS_OTHER;this.init(k,c,a);this.contentStr=q;this.plaintextStr="";if(h==null){h=k.options.layer.text}this.layer=h;this.display=l||"html";if((typeof m!="undefined")&&(m!=null)){this.isLabel=m}else{this.isLabel=false}this.visProp.strokeColor=this.board.options.text.strokeColor;this.visProp.visible=true;if(d!=null){this.digits=d}else{this.digits=2}if((this.element=this.board.objects[f])){var e;if(!this.isLabel){e=this.element.getTextAnchor()}else{e=this.element.getLabelAnchor()}this.element.addChild(this);this.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[parseFloat(n[0]),parseFloat(n[1])],this.board);this.coords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[this.relativeCoords.scrCoords[1]+e.scrCoords[1],this.relativeCoords.scrCoords[2]+e.scrCoords[2]],this.board)}else{this.X=JXG.createFunction(n[0],this.board,"");this.Y=JXG.createFunction(n[1],this.board,"");this.coords=new JXG.Coords(JXG.COORDS_BY_USER,[this.X(),this.Y()],this.board);var g="this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.X(),this.Y()]);";this.updateCoords=new Function("",g)}if(typeof this.contentStr=="function"){this.updateText=function(){this.plaintextStr=this.contentStr()}}else{var b;if(typeof this.contentStr=="number"){b=(this.contentStr).toFixed(this.digits)}else{if(this.board.options.text.useASCIIMathML){b="'`"+this.contentStr+"`'"}else{b=this.generateTerm(this.contentStr)}}this.updateText=new Function("this.plaintextStr = "+b+";")}if(!this.isLabel){this.id=this.board.addText(this)}if(typeof this.contentStr=="string"){this.notifyParents(this.contentStr)}};JXG.Text.prototype=new JXG.GeometryElement();JXG.Text.prototype.hasPoint=function(a,b){return false};JXG.Text.prototype.setText=function(b){var a;if(typeof b=="number"){a=(b).toFixed(this.digits)}else{a=this.generateTerm(b)}this.updateText=new Function("this.plaintextStr = "+a+";");this.updateText();return this};JXG.Text.prototype.setCoords=function(a,b){this.X=function(){return a};this.Y=function(){return b};this.coords=new JXG.Coords(JXG.COORDS_BY_USER,[a,b],this.board);return this};JXG.Text.prototype.update=function(){if(this.needsUpdate&&!this.frozen){if(this.relativeCoords){var a;if(!this.isLabel){a=this.element.getTextAnchor()}else{a=this.element.getLabelAnchor()}this.coords.setCoordinates(JXG.COORDS_BY_SCREEN,[this.relativeCoords.scrCoords[1]+a.scrCoords[1],this.relativeCoords.scrCoords[2]+a.scrCoords[2]])}else{this.updateCoords()}}if(this.needsUpdate){this.updateText()}return this};JXG.Text.prototype.updateRenderer=function(){if(this.needsUpdate){this.board.renderer.updateText(this);this.needsUpdate=false}return this};JXG.Text.prototype.generateTerm=function(e){var d=null;var g=this.board.elementsByName;var f='""';e=e.replace(/\r/g,"");e=e.replace(/\n/g,"");e=e.replace(/\"/g,'\\"');e=e.replace(/\'/g,"\\'");e=e.replace(/&amp;arc;/g,"&ang;");e=e.replace(/<arc\s*\/>/g,"&ang;");e=e.replace(/<sqrt\s*\/>/g,"&radic;");var c;c=e.indexOf("<value>");var a=e.indexOf("</value>");if(c>=0){while(c>=0){f+=' + "'+JXG.GeonextParser.replaceSub(JXG.GeonextParser.replaceSup(e.slice(0,c)))+'"';var b=e.slice(c+7,a);var d=JXG.GeonextParser.geonext2JS(b,this.board);d=d.replace(/\\"/g,'"');d=d.replace(/\\'/g,"'");if(d.indexOf("toFixed")<0){f+="+("+d+").toFixed("+(this.digits)+")"}else{f+="+("+d+")"}e=e.slice(a+8);c=e.indexOf("<value>");a=e.indexOf("</value>")}}f+=' + "'+JXG.GeonextParser.replaceSub(JXG.GeonextParser.replaceSup(e))+'"';f=f.replace(/<overline>/g,"<span style=text-decoration:overline>");f=f.replace(/<\/overline>/g,"</span>");f=f.replace(/<arrow>/g,"<span style=text-decoration:overline>");f=f.replace(/<\/arrow>/g,"</span>");f=f.replace(/&amp;/g,"&");return f};JXG.Text.prototype.notifyParents=function(c){var b=null;var d=this.board.elementsByName;do{var a=/<value>([\w\s\*\/\^\-\+\(\)\[\],<>=!]+)<\/value>/;b=a.exec(c);if(b!=null){JXG.GeonextParser.findDependencies(this,b[1],this.board);c=c.substr(b.index);c=c.replace(a,"")}}while(b!=null);return this};JXG.createText=function(a,c,b){b=JXG.checkAttributes(b,{layer:null,display:a.options.text.defaultDisplay,parent:null});if(b.parent!=null){b.parent=b.parent.id}return new JXG.Text(a,c[c.length-1],b.parent,c,b.id,b.name,b.digits,false,b.display,b.layer)};JXG.JSXGraph.registerElement("text",JXG.createText);JXG.Image=function(f,b,g,d,c,h,a,e){this.type=JXG.OBJECT_TYPE_IMAGE;this.elementClass=JXG.OBJECT_CLASS_OTHER;this.transformations=[];this.init(f,h,a);this.coords=new JXG.Coords(JXG.COORDS_BY_USER,g,this.board);this.initialCoords=new JXG.Coords(JXG.COORDS_BY_USER,g,this.board);this.size=[d[0]*f.stretchX,d[1]*f.stretchY];this.url=b;if(c==null){c=f.options.layer.image}this.layer=c;this.parent=e;this.visProp.visible=true;this.id=this.board.addImage(this)};JXG.Image.prototype=new JXG.GeometryElement;JXG.Image.prototype.hasPoint=function(a,b){return false};JXG.Image.prototype.updateRenderer=function(){this.updateTransform();this.board.renderer.updateImage(this)};JXG.Image.prototype.updateTransform=function(){if(this.transformations.length==0){return}for(var a=0;a<this.transformations.length;a++){this.transformations[a].update()}};JXG.Image.prototype.addTransform=function(a){if(JXG.isArray(a)){for(var b=0;b<a.length;b++){this.transformations.push(a[b])}}else{this.transformations.push(a)}};JXG.createImage=function(c,b,d){var a;if(d==null){d={}}else{if(d.imageString!=null){a=d.imageString}}if(typeof d.layer=="undefined"){d.layer=null}return new JXG.Image(c,b[0],b[1],b[2],d.layer,false,false,undefined)};JXG.JSXGraph.registerElement("image",JXG.createImage);JXG.createSlider=function(m,z,v){var h,f,y,k,A,q,c,b,x,B,l,e,d,a,w,u,r,s,g;h=z[0];f=z[1];y=z[2][0];k=z[2][1];A=z[2][2];q=A-y;v=JXG.checkAttributes(v,{strokeColor:"#000000",fillColor:"#ffffff",withTicks:true});g=JXG.str2Bool(v.fixed);c=m.create("point",h,{visible:!g,fixed:g,name:"",withLabel:false,face:"<>",size:5,strokeColor:"#000000",fillColor:"#ffffff"});b=m.create("point",f,{visible:!g,fixed:g,name:"",withLabel:false,face:"<>",size:5,strokeColor:"#000000",fillColor:"#ffffff"});m.create("group",[c,b]);x=m.create("segment",[c,b],{strokewidth:1,name:"",withLabel:false,strokeColor:v.strokeColor});if(v.withTicks){B=2;l=m.create("ticks",[x,b.Dist(c)/B],{insertTicks:true,minorTicks:0,drawLabels:false,drawZero:true})}if(g){c.needsRegularUpdate=false;b.needsRegularUpdate=false;x.needsRegularUpdate=false}e=h[0]+(f[0]-h[0])*(k-y)/(A-y);d=h[1]+(f[1]-h[1])*(k-y)/(A-y);if(v.snapWidth!=null){s=v.snapWidth}if(v.snapwidth!=null){s=v.snapwidth}a=m.create("glider",[e,d,x],{style:6,strokeColor:v.strokeColor,fillColor:v.fillColor,showInfobox:false,name:v.name,withLabel:false,snapWidth:s});w=m.create("line",[c,a],{straightFirst:false,straightLast:false,strokewidth:3,strokeColor:v.strokeColor,name:"",withLabel:false});a.Value=function(){return this.position*q+y};a._smax=A;a._smin=y;if(typeof v.withLabel=="undefined"||v.withLabel==true){if(v.name&&v.name!=""){u=v.name+" = "}else{u=""}r=m.create("text",[function(){return(b.X()-c.X())*0.05+b.X()},function(){return(b.Y()-c.Y())*0.05+b.Y()},function(){return u+(a.Value()).toFixed(2)}],{name:""})}return a};JXG.JSXGraph.registerElement("slider",JXG.createSlider);JXG.Chart=function(h,m,e){this.constructor();if(m.length==0){return}this.elements=[];var d=e.id||"";var b=e.name||"";this.init(h,d,b);var n,l,f;if(m.length>0&&(typeof m[0]=="number")){l=m;n=[];for(f=0;f<l.length;f++){n[f]=f+1}}else{if(m.length==1){l=m[0];n=[];var g;if(JXG.isFunction(l)){g=l().length}else{g=l.length}for(f=0;f<g;f++){n[f]=f+1}}if(m.length==2){n=m[0];l=m[1]}}if(e==undefined){e={}}var a=e.chartStyle||"line";a=a.replace(/ /g,"");a=a.split(",");var k;for(f=0;f<a.length;f++){switch(a[f]){case"bar":k=this.drawBar(h,[n,l],e);break;case"line":k=this.drawLine(h,[n,l],e);break;case"fit":k=this.drawFit(h,[n,l],e);break;case"spline":k=this.drawSpline(h,[n,l],e);break;case"pie":k=this.drawPie(h,[l],e);break;case"point":k=this.drawPoints(h,[n,l],e);break;case"radar":k=this.drawRadar(h,m,e);break}this.elements.push(k)}this.id=this.board.addChart(this);return this.elements};JXG.Chart.prototype=new JXG.GeometryElement;JXG.Chart.prototype.drawLine=function(f,e,b){var d=e[0],a=e[1];b.fillColor="none";b.highlightFillColor="none";var g=f.create("curve",[d,a],b);this.rendNode=g.rendNode;return g};JXG.Chart.prototype.drawSpline=function(f,d,b){var a=d[0],h=d[1],e;b.fillColor="none";b.highlightFillColor="none";var g=f.create("spline",[a,h],b);this.rendNode=g.rendNode;return g};JXG.Chart.prototype.drawFit=function(f,e,d){var a=e[0],k=e[1],g=(((typeof d.degree=="undefined")||(parseInt(d.degree)==NaN)||(parseInt(d.degree)<1))?1:parseInt(d.degree));d.fillColor="none";d.highlightFillColor="none";var b=JXG.Math.Numerics.regressionPolynomial(g,a,k);var h=f.create("functiongraph",[b],d);this.rendNode=h.rendNode;return h};JXG.Chart.prototype.drawBar=function(h,l,f){var g,e=[],m=l[0],k=l[1],n,c,u,s,b,a,q,d=[],r;if(f.fillOpacity==undefined){f.fillOpacity=0.6}if(f&&f.width){n=f.width}else{if(m.length<=1){n=1}else{n=m[1]-m[0];for(g=1;g<m.length-1;g++){n=(m[g+1]-m[g]<n)?(m[g+1]-m[g]):n}}n*=0.8}r=f.fillColor;for(g=0;g<m.length;g++){if(JXG.isFunction(m[g])){c=function(){return m[g]()-n*0.5};u=function(){return m[g]()};s=function(){return m[g]()+n*0.5}}else{c=m[g]-n*0.5;u=m[g];s=m[g]+n*0.5}if(JXG.isFunction(k[g])){a=b}else{a=k[g]+0.2}b=k[g];if(f.dir=="horizontal"){d[0]=h.create("point",[0,c],{name:"",fixed:true,visible:false});d[1]=h.create("point",[b,c],{name:"",fixed:true,visible:false});d[2]=h.create("point",[b,s],{name:"",fixed:true,visible:false});d[3]=h.create("point",[0,s],{name:"",fixed:true,visible:false});if(f.labels&&f.labels[g]){h.create("text",[b,s,f.labels[g]],f)}}else{d[0]=h.create("point",[c,0],{name:"",fixed:true,visible:false});d[1]=h.create("point",[c,b],{name:"",fixed:true,visible:false});d[2]=h.create("point",[s,b],{name:"",fixed:true,visible:false});d[3]=h.create("point",[s,0],{name:"",fixed:true,visible:false});if(f.labels&&f.labels[g]){h.create("text",[s,b,f.labels[g]],f)}}f.withLines=false;if(!r){q=f.colorArray||["#B02B2C","#3F4C6B","#C79810","#D15600","#FFFF88","#C3D9FF","#4096EE","#008C00"];f.fillColor=q[g%q.length]}e[g]=h.create("polygon",d,f)}this.rendNode=e[0].rendNode;return e};JXG.Chart.prototype.drawPoints=function(g,d,c){var e;var f=[];c.fixed=true;c.name="";var b=JXG.isArray(c.infoboxArray)?c.infoboxArray||false:false;var a=d[0];var h=d[1];for(e=0;e<a.length;e++){c.infoboxtext=b?b[e%b.length]:false;f[e]=g.create("point",[a[e],h[e]],c)}this.rendNode=f[0].rendNode;return f};JXG.Chart.prototype.drawPie=function(d,w,f){var g=w[0];if(g.length<=0){return}if(typeof g[0]=="function"){return}var v;var q=[];var e=[];var k=JXG.Math.Statistics.sum(g);var c=f.colorArray||["#B02B2C","#3F4C6B","#C79810","#D15600","#FFFF88","#C3D9FF","#4096EE","#008C00"];var A=f.highlightColorArray||["#FF7400"];var r=new Array(g.length);for(v=0;v<g.length;v++){r[v]=""}var l=f.labelArray||r;var b=f.radius||4;var z={};if(typeof f.highlightOnSector=="undefined"){f.highlightOnSector=false}z.name=f.name;z.id=f.id;z.strokeWidth=f.strokeWidth||1;z.strokeColor=f.strokeColor||"none";z.straightFirst=false;z.straightLast=false;z.fillColor=f.fillColor||"#FFFF88";z.fillOpacity=f.fillOpacity||0.6;z.highlightFillColor=f.highlightFillColor||"#FF7400";z.highlightStrokeColor=f.highlightStrokeColor||"#FFFFFF";z.gradient=f.gradient||"none";var n=f.center||[0,0];var u=n[0];var a=n[1];var x=d.create("point",[u,a],{name:"",fixed:true,visible:false});q[0]=d.create("point",[b+u,0+a],{name:"",fixed:true,visible:false});var B=0;for(v=0;v<g.length;v++){B+=(k!=0)?(2*Math.PI*g[v]/k):0;var h=b*Math.cos(B)+u;var m=b*Math.sin(B)+a;q[v+1]=d.create("point",[h,m],{name:"",fixed:true,visible:false,withLabel:false});z.fillColor=c[v%c.length];z.name=l[v];if(z.name!=""){z.withLabel=true}else{z.withLabel=false}z.labelColor=c[v%c.length];z.highlightfillColor=A[v%A.length];e[v]=d.create("sector",[x,q[v],q[v+1]],z);if(f.highlightOnSector){e[v].hasPoint=e[v].hasPointSector}}this.rendNode=e[0].rendNode;return{arcs:e,points:q,midpoint:x}};JXG.Chart.prototype.drawRadar=function(k,L,G){if(L.length<=0){alert("No data");return}var W=G.paramArray;if(W==undefined){alert("Need paramArray attribute");return}var I=W.length;if(I<=1){alert("Need more than 1 param");return}var V,T;for(V=0;V<L.length;V++){if(I!=L[V].length){alert("Use data length equal to number of params ("+L[V].length+" != "+I+")");return}}maxes=new Array(I);mins=new Array(I);for(T=0;T<I;T++){maxes[T]=L[0][T];mins[T]=maxes[T]}for(V=1;V<L.length;V++){for(T=0;T<I;T++){if(L[V][T]>maxes[T]){maxes[T]=L[V][T]}if(L[V][T]<mins[T]){mins[T]=L[V][T]}}}var F=new Array(L.length);var q=new Array(L.length);for(V=0;V<L.length;V++){F[V]="";q[V]=[]}var c=new Array(I);var H=new Array(I);var z=G.startShiftRatio||0;var w=G.endShiftRatio||0;for(V=0;V<I;V++){c[V]=(maxes[V]-mins[V])*z;H[V]=(maxes[V]-mins[V])*w}var A=G.startShiftArray||c;var y=G.endShiftArray||H;var d=G.startArray||mins;if(G.start!=undefined){for(var V=0;V<I;V++){d[V]=G.start}}var U=G.endArray||maxes;if(G.end!=undefined){for(var V=0;V<I;V++){U[V]=G.end}}if(A.length!=I){alert("Start shifts length is not equal to number of parameters");return}if(y.length!=I){alert("End shifts length is not equal to number of parameters");return}if(d.length!=I){alert("Starts length is not equal to number of parameters");return}if(U.length!=I){alert("Ends length is not equal to number of parameters");return}var r=G.labelArray||F;var n=G.colorArray||["#B02B2C","#3F4C6B","#C79810","#D15600","#FFFF88","#C3D9FF","#4096EE","#008C00"];var s=G.highlightColorArray||["#FF7400"];var K=G.radius||10;var u={};if(typeof G.highlightOnSector=="undefined"){G.highlightOnSector=false}u.name=G.name;u.id=G.id;u.strokeWidth=G.strokeWidth||1;u.polyStrokeWidth=G.polyStrokeWidth||2*u.strokeWidth;u.strokeColor=G.strokeColor||"black";u.straightFirst=false;u.straightLast=false;u.fillColor=G.fillColor||"#FFFF88";u.fillOpacity=G.fillOpacity||0.4;u.highlightFillColor=G.highlightFillColor||"#FF7400";u.highlightStrokeColor=G.highlightStrokeColor||"black";u.gradient=G.gradient||"none";var R=G.center||[0,0];var N=R[0];var B=R[1];var a=k.createElement("point",[N,B],{name:"",fixed:true,withlabel:false,visible:false});var h=Math.PI/2-Math.PI/I;if(G.startAngle||G.startAngle===0){h=G.startAngle}var b=h;var Q=[];var g=[];var S=function(){var ac,ab,ae,ad,af=[].concat(this.labelOffsets);ac=this.point1.X();ab=this.point2.X();ae=this.point1.Y();ad=this.point2.Y();if(ab<ac){af[0]=-af[0]}if(ad<ae){af[1]=-af[1]}this.setLabelRelativeCoords(af);return new JXG.Coords(JXG.COORDS_BY_USER,[this.point2.X(),this.point2.Y()],this.board)};var E=function(af,ac){var ab;var ae;var ad;ab=k.createElement("transform",[-(d[ac]-A[ac]),0],{type:"translate"});ae=k.createElement("transform",[K/((U[ac]+y[ac])-(d[ac]-A[ac])),1],{type:"scale"});ab.melt(ae);ad=k.createElement("transform",[af],{type:"rotate"});ab.melt(ad);return ab};var J;for(V=0;V<I;V++){b+=2*Math.PI/I;var m=K*Math.cos(b)+N;var P=K*Math.sin(b)+B;Q[V]=k.createElement("point",[m,P],{name:"",fixed:true,withlabel:false,visible:false});g[V]=k.createElement("line",[a,Q[V]],{name:W[V],strokeColor:u.strokeColor,strokeWidth:u.strokeWidth,strokeOpacity:1,straightFirst:false,straightLast:false,withLabel:true,highlightStrokeColor:u.highlightStrokeColor});g[V].getLabelAnchor=S;J=E(b,V);for(T=0;T<L.length;T++){var Y=L[T][V];q[T][V]=k.createElement("point",[Y,0],{name:"",fixed:true,withlabel:false,visible:false});q[T][V].addTransform(q[T][V],J)}}var aa=new Array(L.length);for(V=0;V<L.length;V++){u.labelColor=n[V%n.length];u.strokeColor=n[V%n.length];u.fillColor=n[V%n.length];aa[V]=k.createElement("polygon",q[V],{withLines:true,withLabel:false,fillColor:u.fillColor,fillOpacity:u.fillOpacity});for(T=0;T<I;T++){aa[V].borders[T].setProperty("strokeColor:"+n[V%n.length]);aa[V].borders[T].setProperty("strokeWidth:"+u.polyStrokeWidth)}}var v=G.legendPosition||"none";switch(v){case"right":var C=G.legendLeftOffset||2;var X=G.legendTopOffset||1;this.legend=k.createElement("legend",[N+K+C,B+K-X],{labelArray:r,colorArray:n});break;case"none":break;default:alert("Unknown legend position")}var f=[];if(G.showCircles!=false){var l=[];for(V=0;V<6;V++){l[V]=20*V}l[0]="0";var D=G.circleLabelArray||l;var O=D.length;if(O<2){alert("Too less circles");return}var Z=[];var x=h+Math.PI/I;J=E(x,0);u.fillColor="none";u.highlightFillColor="none";u.strokeColor=G.strokeColor||"black";u.strokeWidth=G.circleStrokeWidth||0.5;var e=(U[0]-d[0])/(O-1);for(V=0;V<O;V++){Z[V]=k.createElement("point",[d[0]+V*e,0],{name:D[V],size:0,withLabel:true,visible:true});Z[V].addTransform(Z[V],J);f[V]=k.createElement("circle",[a,Z[V]],u)}}this.rendNode=aa[0].rendNode;return{circles:f,lines:g,points:q,midpoint:a,polygons:aa}};JXG.Chart.prototype.updateRenderer=function(){};JXG.Chart.prototype.update=function(){if(this.needsUpdate){this.updateDataArray()}};JXG.Chart.prototype.updateDataArray=function(){};JXG.createChart=function(e,u,f){if((u.length==1)&&(typeof u[0]=="string")){var s=document.getElementById(u[0]),A,d,n,m,c,a,r=[],h,g,z,y,B,k,b,l,v,q;if(typeof s!="undefined"){f=JXG.checkAttributes(f,{withHeader:true});s=(new JXG.DataSource()).loadFromTable(u[0],f.withHeader,f.withHeader);A=s.data;c=s.columnHeader;d=s.rowHeader;y=f.width;B=f.name;k=f.strokeColor;b=f.fillColor;l=f.highlightStrokeColor;v=f.highlightFillColor;e.suspendUpdate();q=A.length;z=[];if(f.rows&&JXG.isArray(f.rows)){for(n=0;n<q;n++){for(m=0;m<f.rows.length;m++){if((f.rows[m]==n)||(f.withHeaders&&f.rows[m]==d[n])){z.push(A[n]);break}}}}else{z=A}q=z.length;for(n=0;n<q;n++){g=[];if(f.chartStyle&&f.chartStyle.indexOf("bar")!=-1){if(y){h=y}else{h=0.8}g.push(1-h/2+(n+0.5)*h/(1*q));for(m=1;m<z[n].length;m++){g.push(g[m-1]+1)}f.width=h/(1*q)}if(B&&B.length==q){f.name=B[n]}else{if(f.withHeaders){f.name=c[n]}}if(k&&k.length==q){f.strokeColor=k[n]}else{f.strokeColor=JXG.hsv2rgb(((n+1)/(1*q))*360,0.9,0.6)}if(b&&b.length==q){f.fillColor=b[n]}else{f.fillColor=JXG.hsv2rgb(((n+1)/(1*q))*360,0.9,1)}if(l&&l.length==q){f.highlightStrokeColor=l[n]}else{f.highlightStrokeColor=JXG.hsv2rgb(((n+1)/(1*q))*360,0.9,1)}if(v&&v.length==q){f.highlightFillColor=v[n]}else{f.highlightFillColor=JXG.hsv2rgb(((n+1)/(1*q))*360,0.9,0.6)}if(f.chartStyle&&f.chartStyle.indexOf("bar")!=-1){r.push(new JXG.Chart(e,[g,z[n]],f))}else{r.push(new JXG.Chart(e,[z[n]],f))}}e.unsuspendUpdate()}return r}else{return new JXG.Chart(e,u,f)}};JXG.JSXGraph.registerElement("chart",JXG.createChart);JXG.Legend=function(c,d,a){this.constructor();this.board=c;this.coords=new JXG.Coords(JXG.COORDS_BY_USER,d,this.board);this.myAtts={};this.label_array=a.labelArray||["1","2","3","4","5","6","7","8"];this.color_array=a.colorArray||["#B02B2C","#3F4C6B","#C79810","#D15600","#FFFF88","#C3D9FF","#4096EE","#008C00"];var b;this.lines=[];this.myAtts.strokeWidth=a.strokeWidth||5;this.myAtts.straightFirst=false;this.myAtts.straightLast=false;this.myAtts.withLabel=true;this.style=a.legendStyle||"vertical";switch(this.style){case"vertical":this.drawVerticalLegend(a);break;default:alert("Unknown legend style"+this.style);break}};JXG.Legend.prototype=new JXG.GeometryElement;JXG.Legend.prototype.drawVerticalLegend=function(c){var b=c.lineLength||1;var a=(c.rowHeight||20)/this.board.stretchY;for(i=0;i<this.label_array.length;i++){this.myAtts.strokeColor=this.color_array[i];this.myAtts.highlightStrokeColor=this.color_array[i];this.myAtts.name=this.label_array[i];this.myAtts.labelOffsets=[10,0];this.lines[i]=board.createElement("line",[[this.coords.usrCoords[1],this.coords.usrCoords[2]-i*a],[this.coords.usrCoords[1]+b,this.coords.usrCoords[2]-i*a]],this.myAtts);this.lines[i].getLabelAnchor=function(){this.setLabelRelativeCoords(this.labelOffsets);return new JXG.Coords(JXG.COORDS_BY_USER,[this.point2.X(),this.point2.Y()],this.board)}}};JXG.createLegend=function(c,b,a){var d=[0,0];if(b!=undefined){if(b.length==2){d=b}}return new JXG.Legend(c,d,a)};JXG.JSXGraph.registerElement("legend",JXG.createLegend);JXG.Transformation=function(b,a,c){this.elementClass=JXG.OBJECT_CLASS_OTHER;this.matrix=[[1,0,0],[0,1,0],[0,0,1]];this.board=b;this.isNumericMatrix=false;this.setMatrix(b,a,c)};JXG.Transformation.prototype={};JXG.Transformation.prototype.update=function(){};JXG.Transformation.prototype.setMatrix=function(c,b,d){var a;this.isNumericMatrix=true;for(a=0;a<d.length;a++){if(typeof d[a]!="number"){this.isNumericMatrix=false;break}}if(b=="translate"){this.evalParam=JXG.createEvalFunction(c,d,2);this.update=function(){this.matrix[1][0]=this.evalParam(0);this.matrix[2][0]=this.evalParam(1)}}else{if(b=="scale"){this.evalParam=JXG.createEvalFunction(c,d,2);this.update=function(){this.matrix[1][1]=this.evalParam(0);this.matrix[2][2]=this.evalParam(1)}}else{if(b=="reflect"){if(d.length<4){d[0]=JXG.getReference(c,d[0])}if(d.length==2){d[1]=JXG.getReference(c,d[1])}if(d.length==4){this.evalParam=JXG.createEvalFunction(c,d,4)}this.update=function(){var e,k,f,h,g;if(d.length==1){e=d[0].point2.X()-d[0].point1.X();k=d[0].point2.Y()-d[0].point1.Y();f=d[0].point1.X();h=d[0].point1.Y()}else{if(d.length==2){e=d[1].X()-d[0].X();k=d[1].Y()-d[0].Y();f=d[0].X();h=d[0].Y()}else{if(d.length==4){e=this.evalParam(2)-this.evalParam(0);k=this.evalParam(3)-this.evalParam(1);f=this.evalParam(0);h=this.evalParam(1)}}}g=e*e+k*k;this.matrix[1][1]=(e*e-k*k)/g;this.matrix[1][2]=2*e*k/g;this.matrix[2][1]=2*e*k/g;this.matrix[2][2]=(-e*e+k*k)/g;this.matrix[1][0]=f*(1-this.matrix[1][1])-h*this.matrix[1][2];this.matrix[2][0]=h*(1-this.matrix[2][2])-f*this.matrix[2][1]}}else{if(b=="rotate"){if(d.length==3){this.evalParam=JXG.createEvalFunction(c,d,3)}else{if(d.length<=2){this.evalParam=JXG.createEvalFunction(c,d,1);if(d.length==2){d[1]=JXG.getReference(c,d[1])}}}this.update=function(){var g=this.evalParam(0),e,k,h=Math.cos(g),f=Math.sin(g);this.matrix[1][1]=h;this.matrix[1][2]=-f;this.matrix[2][1]=f;this.matrix[2][2]=h;if(d.length>1){if(d.length==3){e=this.evalParam(1);k=this.evalParam(2)}else{e=d[1].X();k=d[1].Y()}this.matrix[1][0]=e*(1-h)+k*f;this.matrix[2][0]=k*(1-h)-e*f}}}else{if(b=="shear"){this.evalParam=JXG.createEvalFunction(c,d,1);this.update=function(){var e=this.evalParam(0);this.matrix[1][1]=Math.tan(e)}}else{if(b=="generic"){this.evalParam=JXG.createEvalFunction(c,d,9);this.update=function(){this.matrix[0][0]=this.evalParam(0);this.matrix[0][1]=this.evalParam(1);this.matrix[0][2]=this.evalParam(2);this.matrix[1][0]=this.evalParam(3);this.matrix[1][1]=this.evalParam(4);this.matrix[1][2]=this.evalParam(5);this.matrix[2][0]=this.evalParam(6);this.matrix[2][1]=this.evalParam(7);this.matrix[2][2]=this.evalParam(8)}}}}}}}};JXG.Transformation.prototype.apply=function(a){this.update();if(arguments[1]!=null){return JXG.Math.matVecMult(this.matrix,a.initialCoords.usrCoords)}else{return JXG.Math.matVecMult(this.matrix,a.coords.usrCoords)}};JXG.Transformation.prototype.applyOnce=function(d){var e,a,b;if(!JXG.isArray(d)){this.update();e=JXG.Math.matVecMult(this.matrix,d.coords.usrCoords);d.coords.setCoordinates(JXG.COORDS_BY_USER,[e[1],e[2]])}else{a=d.length;for(b=0;b<a;b++){this.update();e=JXG.Math.matVecMult(this.matrix,d[b].coords.usrCoords);d[b].coords.setCoordinates(JXG.COORDS_BY_USER,[e[1],e[2]])}}};JXG.Transformation.prototype.bindTo=function(c){var b,a;if(JXG.isArray(c)){a=c.length;for(b=0;b<a;b++){c[b].transformations.push(this)}}else{c.transformations.push(this)}};JXG.Transformation.prototype.setProperty=function(a){};JXG.Transformation.prototype.melt=function(g){var f=[],e,a,d,b,h,c;a=g.matrix.length;d=this.matrix[0].length;for(e=0;e<a;e++){f[e]=[]}this.update();g.update();for(e=0;e<a;e++){for(c=0;c<d;c++){h=0;for(b=0;b<a;b++){h+=g.matrix[e][b]*this.matrix[b][c]}f[e][c]=h}}this.update=function(){var k=this.matrix.length,l=this.matrix[0].length;for(e=0;e<k;e++){for(c=0;c<l;c++){this.matrix[e][c]=f[e][c]}}};return true};JXG.createTransform=function(a,c,b){return new JXG.Transformation(a,b.type,c)};JXG.JSXGraph.registerElement("transform",JXG.createTransform);JXG.Turtle=function(e,d,b){var a,f,c;this.type=JXG.OBJECT_TYPE_TURTLE;this.turtleIsHidden=false;this.board=e;this.attributes=JXG.checkAttributes(b,{withLabel:false,layer:null});this.attributes.straightFirst=false;this.attributes.straightLast=false;a=0;f=0;c=90;if(d.length!=0){if(d.length==3){a=d[0];f=d[1];c=d[2]}else{if(d.length==2){if(JXG.isArray(d[0])){a=d[0][0];f=d[0][1];c=d[1]}else{a=d[0];f=d[1]}}else{a=d[0][0];f=d[0][1]}}}this.init(a,f,c);return this};JXG.Turtle.prototype=new JXG.GeometryElement;JXG.Turtle.prototype.init=function(a,d,c){this.arrowLen=20/Math.sqrt(this.board.unitX*this.board.unitX+this.board.unitY*this.board.unitY);this.pos=[a,d];this.isPenDown=true;this.dir=90;this.stack=[];this.objects=[];this.attributes.curveType="plot";this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve);this.turtle=this.board.create("point",this.pos,{fixed:true,name:" ",visible:false,withLabel:false});this.objects.push(this.turtle);this.turtle2=this.board.create("point",[this.pos[0],this.pos[1]+this.arrowLen],{fixed:true,name:" ",visible:false,withLabel:false});this.objects.push(this.turtle2);var b=this.attributes.strokeWidth||this.attributes.strokewidth||2;this.arrow=this.board.create("line",[this.turtle,this.turtle2],{strokeColor:"#ff0000",straightFirst:false,straightLast:false,strokeWidth:b,withLabel:false,lastArrow:true});this.objects.push(this.arrow);this.right(90-c);this.board.update()};JXG.Turtle.prototype.forward=function(a){if(a==0){return}var c=a*Math.cos(this.dir*Math.PI/180);var b=a*Math.sin(this.dir*Math.PI/180);if(!this.turtleIsHidden){var d=this.board.create("transform",[c,b],{type:"translate"});d.applyOnce(this.turtle);d.applyOnce(this.turtle2)}if(this.isPenDown){if(this.curve.dataX.length>=8192){this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve)}}this.pos[0]+=c;this.pos[1]+=b;if(this.isPenDown){this.curve.dataX.push(this.pos[0]);this.curve.dataY.push(this.pos[1])}this.board.update();return this};JXG.Turtle.prototype.back=function(a){return this.forward(-a)};JXG.Turtle.prototype.right=function(b){this.dir-=b;this.dir%=360;if(!this.turtleIsHidden){var a=this.board.create("transform",[-b*Math.PI/180,this.turtle],{type:"rotate"});a.applyOnce(this.turtle2)}this.board.update();return this};JXG.Turtle.prototype.left=function(a){return this.right(-a)};JXG.Turtle.prototype.penUp=function(){this.isPenDown=false;return this};JXG.Turtle.prototype.penDown=function(){this.isPenDown=true;this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve);return this};JXG.Turtle.prototype.clean=function(){for(var a=0;a<this.objects.length;a++){var b=this.objects[a];if(b.type==JXG.OBJECT_TYPE_CURVE){this.board.removeObject(b.id);this.objects.splice(a,1)}}this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve);this.board.update();return this};JXG.Turtle.prototype.clearScreen=function(){for(var a=0;a<this.objects.length;a++){var b=this.objects[a];this.board.removeObject(b.id)}this.init(0,0,90);return this};JXG.Turtle.prototype.setPos=function(a,c){if(JXG.isArray(a)){this.pos=a}else{this.pos=[a,c]}if(!this.turtleIsHidden){this.turtle.setPositionDirectly(JXG.COORDS_BY_USER,a,c);this.turtle2.setPositionDirectly(JXG.COORDS_BY_USER,a,c+this.arrowLen);var b=this.board.create("transform",[-(this.dir-90)*Math.PI/180,this.turtle],{type:"rotate"});b.applyOnce(this.turtle2)}this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve);this.board.update();return this};JXG.Turtle.prototype.setPenSize=function(a){this.attributes.strokeWidth=a;this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve);return this};JXG.Turtle.prototype.setPenColor=function(a){this.attributes.strokeColor=a;this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve);return this};JXG.Turtle.prototype.setHighlightPenColor=function(a){this.attributes.highlightStrokeColor=a;this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve);return this};JXG.Turtle.prototype.setProperty=function(){var e;var a;var c,d;var b;for(c=0;c<arguments.length;c++){a=arguments[c];if(typeof a=="string"){e=a.split(":")}else{if(!JXG.isArray(a)){for(var b in a){this.setProperty([b,a[b]])}return this}else{e=a}}this.attributes[e[0]]=e[1]}for(c=0;c<this.objects.length;c++){d=this.objects[c];if(d.type==JXG.OBJECT_TYPE_CURVE){d.setProperty(this.attributes)}}return this};JXG.Turtle.prototype.showTurtle=function(){this.turtleIsHidden=false;this.arrow.setProperty("visible:true");this.setPos(this.pos[0],this.pos[1]);this.board.update();return this};JXG.Turtle.prototype.hideTurtle=function(){this.turtleIsHidden=true;this.arrow.setProperty("visible:false");this.setPos(this.pos[0],this.pos[1]);this.board.update();return this};JXG.Turtle.prototype.home=function(){this.pos=[0,0];this.setPos(this.pos[0],this.pos[1]);return this};JXG.Turtle.prototype.pushTurtle=function(){this.stack.push([this.pos[0],this.pos[1],this.dir]);return this};JXG.Turtle.prototype.popTurtle=function(){var a=this.stack.pop();this.pos[0]=a[0];this.pos[1]=a[1];this.dir=a[2];this.setPos(this.pos[0],this.pos[1]);return this};JXG.Turtle.prototype.lookTo=function(e){if(JXG.isArray(e)){var b=this.pos[0];var a=this.pos[1];var f=e[0];var d=e[1];var c;c=Math.atan2(d-a,f-b);this.right(this.dir-(c*180/Math.PI))}else{if(JXG.isNumber(e)){this.right(this.dir-(e))}}return this};JXG.Turtle.prototype.moveTo=function(d){if(JXG.isArray(d)){var b=d[0]-this.pos[0];var a=d[1]-this.pos[1];if(!this.turtleIsHidden){var c=this.board.create("transform",[b,a],{type:"translate"});c.applyOnce(this.turtle);c.applyOnce(this.turtle2)}if(this.isPenDown){if(this.curve.dataX.length>=8192){this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.attributes);this.objects.push(this.curve)}}this.pos[0]=d[0];this.pos[1]=d[1];if(this.isPenDown){this.curve.dataX.push(this.pos[0]);this.curve.dataY.push(this.pos[1])}this.board.update()}return this};JXG.Turtle.prototype.fd=function(a){return this.forward(a)};JXG.Turtle.prototype.bk=function(a){return this.back(a)};JXG.Turtle.prototype.lt=function(a){return this.left(a)};JXG.Turtle.prototype.rt=function(a){return this.right(a)};JXG.Turtle.prototype.pu=function(){return this.penUp()};JXG.Turtle.prototype.pd=function(){return this.penDown()};JXG.Turtle.prototype.ht=function(){return this.hideTurtle()};JXG.Turtle.prototype.st=function(){return this.showTurtle()};JXG.Turtle.prototype.cs=function(){return this.clearScreen()};JXG.Turtle.prototype.push=function(){return this.pushTurtle()};JXG.Turtle.prototype.pop=function(){return this.popTurtle()};JXG.Turtle.prototype.X=function(a){return this.pos[0]};JXG.Turtle.prototype.Y=function(a){return this.pos[1]};JXG.Turtle.prototype.hasPoint=function(a,d){var b,c;for(b=0;b<this.objects.length;b++){c=this.objects[b];if(c.type==JXG.OBJECT_TYPE_CURVE){if(c.hasPoint(a,d)){return true}}}return false};JXG.createTurtle=function(c,b,a){if(b==null){b=[]}return new JXG.Turtle(c,b,a)};JXG.JSXGraph.registerElement("turtle",JXG.createTurtle);JXG.rgbParser=function(){if(arguments.length==0){return}if(arguments.length>=3){arguments[0]=[arguments[0],arguments[1],arguments[2]];arguments.length=1}var l=arguments[0];if(JXG.isArray(l)){var c=false,f;for(f=0;f<3;f++){c|=/\./.test(arguments[0][f].toString())}for(f=0;f<3;f++){c&=(arguments[0][f]>=0)&(arguments[0][f]<=1)}if(c){return[Math.ceil(arguments[0][0]*255),Math.ceil(arguments[0][1]*255),Math.ceil(arguments[0][2]*255)]}else{arguments[0].length=3;return arguments[0]}}else{if(typeof arguments[0]=="string"){l=arguments[0]}}var a,h,m;if(l.charAt(0)=="#"){l=l.substr(1,6)}l=l.replace(/ /g,"");l=l.toLowerCase();var e={aliceblue:"f0f8ff",antiquewhite:"faebd7",aqua:"00ffff",aquamarine:"7fffd4",azure:"f0ffff",beige:"f5f5dc",bisque:"ffe4c4",black:"000000",blanchedalmond:"ffebcd",blue:"0000ff",blueviolet:"8a2be2",brown:"a52a2a",burlywood:"deb887",cadetblue:"5f9ea0",chartreuse:"7fff00",chocolate:"d2691e",coral:"ff7f50",cornflowerblue:"6495ed",cornsilk:"fff8dc",crimson:"dc143c",cyan:"00ffff",darkblue:"00008b",darkcyan:"008b8b",darkgoldenrod:"b8860b",darkgray:"a9a9a9",darkgreen:"006400",darkkhaki:"bdb76b",darkmagenta:"8b008b",darkolivegreen:"556b2f",darkorange:"ff8c00",darkorchid:"9932cc",darkred:"8b0000",darksalmon:"e9967a",darkseagreen:"8fbc8f",darkslateblue:"483d8b",darkslategray:"2f4f4f",darkturquoise:"00ced1",darkviolet:"9400d3",deeppink:"ff1493",deepskyblue:"00bfff",dimgray:"696969",dodgerblue:"1e90ff",feldspar:"d19275",firebrick:"b22222",floralwhite:"fffaf0",forestgreen:"228b22",fuchsia:"ff00ff",gainsboro:"dcdcdc",ghostwhite:"f8f8ff",gold:"ffd700",goldenrod:"daa520",gray:"808080",green:"008000",greenyellow:"adff2f",honeydew:"f0fff0",hotpink:"ff69b4",indianred:"cd5c5c",indigo:"4b0082",ivory:"fffff0",khaki:"f0e68c",lavender:"e6e6fa",lavenderblush:"fff0f5",lawngreen:"7cfc00",lemonchiffon:"fffacd",lightblue:"add8e6",lightcoral:"f08080",lightcyan:"e0ffff",lightgoldenrodyellow:"fafad2",lightgrey:"d3d3d3",lightgreen:"90ee90",lightpink:"ffb6c1",lightsalmon:"ffa07a",lightseagreen:"20b2aa",lightskyblue:"87cefa",lightslateblue:"8470ff",lightslategray:"778899",lightsteelblue:"b0c4de",lightyellow:"ffffe0",lime:"00ff00",limegreen:"32cd32",linen:"faf0e6",magenta:"ff00ff",maroon:"800000",mediumaquamarine:"66cdaa",mediumblue:"0000cd",mediumorchid:"ba55d3",mediumpurple:"9370d8",mediumseagreen:"3cb371",mediumslateblue:"7b68ee",mediumspringgreen:"00fa9a",mediumturquoise:"48d1cc",mediumvioletred:"c71585",midnightblue:"191970",mintcream:"f5fffa",mistyrose:"ffe4e1",moccasin:"ffe4b5",navajowhite:"ffdead",navy:"000080",oldlace:"fdf5e6",olive:"808000",olivedrab:"6b8e23",orange:"ffa500",orangered:"ff4500",orchid:"da70d6",palegoldenrod:"eee8aa",palegreen:"98fb98",paleturquoise:"afeeee",palevioletred:"d87093",papayawhip:"ffefd5",peachpuff:"ffdab9",peru:"cd853f",pink:"ffc0cb",plum:"dda0dd",powderblue:"b0e0e6",purple:"800080",red:"ff0000",rosybrown:"bc8f8f",royalblue:"4169e1",saddlebrown:"8b4513",salmon:"fa8072",sandybrown:"f4a460",seagreen:"2e8b57",seashell:"fff5ee",sienna:"a0522d",silver:"c0c0c0",skyblue:"87ceeb",slateblue:"6a5acd",slategray:"708090",snow:"fffafa",springgreen:"00ff7f",steelblue:"4682b4",tan:"d2b48c",teal:"008080",thistle:"d8bfd8",tomato:"ff6347",turquoise:"40e0d0",violet:"ee82ee",violetred:"d02090",wheat:"f5deb3",white:"ffffff",whitesmoke:"f5f5f5",yellow:"ffff00",yellowgreen:"9acd32"};for(var n in e){if(l==n){l=e[n]}}var k=[{re:/^rgb\((\d{1,3}),\s*(\d{1,3}),\s*(\d{1,3})\)$/,example:["rgb(123, 234, 45)","rgb(255,234,245)"],process:function(b){return[parseInt(b[1]),parseInt(b[2]),parseInt(b[3])]}},{re:/^(\w{2})(\w{2})(\w{2})$/,example:["#00ff00","336699"],process:function(b){return[parseInt(b[1],16),parseInt(b[2],16),parseInt(b[3],16)]}},{re:/^(\w{1})(\w{1})(\w{1})$/,example:["#fb0","f0f"],process:function(b){return[parseInt(b[1]+b[1],16),parseInt(b[2]+b[2],16),parseInt(b[3]+b[3],16)]}}];for(var f=0;f<k.length;f++){var s=k[f].re;var d=k[f].process;var q=s.exec(l);if(q){channels=d(q);a=channels[0];h=channels[1];m=channels[2]}}a=(a<0||isNaN(a))?0:((a>255)?255:a);h=(h<0||isNaN(h))?0:((h>255)?255:h);m=(m<0||isNaN(m))?0:((m>255)?255:m);return[a,h,m]};JXG.rgb2css=function(){var d,c,a;d=JXG.rgbParser.apply(JXG.rgbParser,arguments);c=d[1];a=d[2];d=d[0];return"rgb("+d+", "+c+", "+a+")"};JXG.rgb2hex=function(){var d,c,a;d=JXG.rgbParser.apply(JXG.rgbParser,arguments);c=d[1];a=d[2];d=d[0];d=d.toString(16);c=c.toString(16);a=a.toString(16);if(d.length==1){d="0"+d}if(c.length==1){c="0"+c}if(a.length==1){a="0"+a}return"#"+d+c+a};JXG.hsv2rgb=function(m,g,e){var h,n,c,l,k,d,b,a,r;m=((m%360)+360)%360;if(g==0){if(isNaN(m)||m<JXG.Math.eps){h=e;n=e;c=e}else{return"#ffffff"}}else{if(m>=360){d=0}else{d=m}d=d/60;k=Math.floor(d);l=d-k;b=e*(1-g);a=e*(1-(g*l));r=e*(1-(g*(1-l)));switch(k){case 0:h=e;n=r;c=b;break;case 1:h=a;n=e;c=b;break;case 2:h=b;n=e;c=r;break;case 3:h=b;n=a;c=e;break;case 4:h=r;n=b;c=e;break;case 5:h=e;n=b;c=a;break}}h=Math.round(h*255).toString(16);h=(h.length==2)?h:((h.length==1)?"0"+h:"00");n=Math.round(n*255).toString(16);n=(n.length==2)?n:((n.length==1)?"0"+n:"00");c=Math.round(c*255).toString(16);c=(c.length==2)?c:((c.length==1)?"0"+c:"00");return["#",h,n,c].join("")};JXG.rgb2hsv=function(){var a,m,u,n,c,e,d,w,l,y,x,q,f,k;a=JXG.rgbParser.apply(JXG.rgbParser,arguments);m=a[1];u=a[2];a=a[0];k=JXG.Math.Statistics;n=a/255;c=m/255;e=u/255;q=k.max([a,m,u]);f=k.min([a,m,u]);d=q/255;w=f/255;x=d;y=0;if(x>0){y=(x-w)/(x*1)}l=1/(d-w);if(y>0){if(q==a){l=(c-e)*l}else{if(q==m){l=2+(e-n)*l}else{l=4+(n-c)*l}}}l*=60;if(l<0){l+=360}if(q==f){l=0}return[l,y,x]};JXG.rgb2LMS=function(){var k,h,c,d,a,f,e;matrix=[[0.05059983,0.08585369,0.0095242],[0.01893033,0.08925308,0.01370054],[0.00292202,0.00975732,0.07145979]];k=JXG.rgbParser.apply(JXG.rgbParser,arguments);h=k[1];c=k[2];k=k[0];k=Math.pow(k,0.476190476);h=Math.pow(h,0.476190476);c=Math.pow(c,0.476190476);d=k*matrix[0][0]+h*matrix[0][1]+c*matrix[0][2];a=k*matrix[1][0]+h*matrix[1][1]+c*matrix[1][2];f=k*matrix[2][0]+h*matrix[2][1]+c*matrix[2][2];e=[d,a,f];e.l=d;e.m=a;e.s=f;return e};JXG.LMS2rgb=function(d,c,f){var k,h,a,e;matrix=[[30.830854,-29.832659,1.610474],[-6.481468,17.715578,-2.532642],[-0.37569,-1.199062,14.273846]];k=d*matrix[0][0]+c*matrix[0][1]+f*matrix[0][2];h=d*matrix[1][0]+c*matrix[1][1]+f*matrix[1][2];a=d*matrix[2][0]+c*matrix[2][1]+f*matrix[2][2];lut_lookup=function(g){var l=127,b=64;while(b>0){if(Math.pow(l,0.476190476)>g){l-=b}else{if(Math.pow(l+1,0.476190476)>g){return l}l+=b}b/=2}if(l==254&&13.994955247<g){return 255}return l};k=lut_lookup(k);h=lut_lookup(h);a=lut_lookup(a);e=[k,h,a];e.r=k;e.g=h;e.b=a;return e};JXG.Board.prototype.angle=function(a,c,b){return JXG.Math.Geometry.angle(a,c,b)};JXG.Board.prototype.rad=function(a,c,b){return JXG.Math.Geometry.rad(a,c,b)};JXG.Board.prototype.distance=function(b,a){return JXG.Math.Geometry.distance(b,a)};JXG.Board.prototype.pow=function(d,c){return JXG.Math.pow(d,c)};JXG.Board.prototype.round=function(a,b){return(a).toFixed(b)};JXG.Board.prototype.cosh=function(a){return JXG.Math.cosh(a)};JXG.Board.prototype.sinh=function(a){return JXG.Math.sinh(a)};JXG.Board.prototype.sgn=function(a){return(a==0?0:a/(Math.abs(a)))};JXG.Board.prototype.D=function(a,b){return JXG.Math.Numerics.D(a,b)};JXG.Board.prototype.I=function(a,b){return JXG.Math.Numerics.I(a,b)};JXG.Board.prototype.root=function(b,a,c){return JXG.Math.Numerics.root(b,a,c)};JXG.Board.prototype.lagrangePolynomial=function(a){return JXG.Math.Numerics.lagrangePolynomial(a)};JXG.Board.prototype.neville=function(a){return JXG.Math.Numerics.neville(a)};JXG.Board.prototype.riemannsum=function(c,e,b,d,a){return JXG.Math.Numerics.riemannsum(c,e,b,d,a)};JXG.Board.prototype.abs=Math.abs;JXG.Board.prototype.acos=Math.acos;JXG.Board.prototype.asin=Math.asin;JXG.Board.prototype.atan=Math.atan;JXG.Board.prototype.ceil=Math.ceil;JXG.Board.prototype.cos=Math.cos;JXG.Board.prototype.exp=Math.exp;JXG.Board.prototype.floor=Math.floor;JXG.Board.prototype.log=Math.log;JXG.Board.prototype.max=Math.max;JXG.Board.prototype.min=Math.min;JXG.Board.prototype.random=Math.random;JXG.Board.prototype.sin=Math.sin;JXG.Board.prototype.sqrt=Math.sqrt;JXG.Board.prototype.tan=Math.tan;JXG.Board.prototype.trunc=Math.ceil;JXG.Board.prototype.factorial=function(a){return JXG.Math.factorial(a)};JXG.Board.prototype.binomial=function(b,a){return JXG.Math.binomial(b,a)};JXG.Point.prototype.setPositionX=function(c,a){var b=(c==JXG.COORDS_BY_USER)?this.coords.usrCoords[2]:this.coords.scrCoords[2];this.setPosition(c,a,b)};JXG.Point.prototype.setPositionY=function(c,b){var a=(c==JXG.COORDS_BY_USER)?this.coords.usrCoords[1]:this.coords.scrCoords[1];this.setPosition(c,a,b)};JXG.Board.prototype.getElement=function(a){return JXG.getReference(this,a)};JXG.Board.prototype.intersectionOptions=["point",[[JXG.OBJECT_CLASS_LINE,JXG.OBJECT_CLASS_LINE],[JXG.OBJECT_CLASS_LINE,JXG.OBJECT_CLASS_CIRCLE],[JXG.OBJECT_CLASS_CIRCLE,JXG.OBJECT_CLASS_CIRCLE]]];JXG.Board.prototype.intersection=function(d,b,c,a){d=JXG.getReference(this,d);b=JXG.getReference(this,b);if(d.elementClass==JXG.OBJECT_CLASS_CURVE&&b.elementClass==JXG.OBJECT_CLASS_CURVE){return function(){return JXG.Math.Geometry.meetCurveCurve(d,b,c,a,d.board)}}else{if((d.elementClass==JXG.OBJECT_CLASS_CURVE&&b.elementClass==JXG.OBJECT_CLASS_LINE)||(b.elementClass==JXG.OBJECT_CLASS_CURVE&&d.elementClass==JXG.OBJECT_CLASS_LINE)){return function(){return JXG.Math.Geometry.meetCurveLine(d,b,c,d.board)}}else{return function(){return JXG.Math.Geometry.meet(d.stdform,b.stdform,c,d.board)}}}};JXG.Board.prototype.intersectionFunc=function(d,b,c,a){return this.intersection(d,b,c,a)};JXG.Board.prototype.otherIntersection=function(b,a,c){b=JXG.getReference(this,b);a=JXG.getReference(this,a);return function(){var d=JXG.Math.Geometry.meet(b.stdform,a.stdform,0,b.board);if(Math.abs(c.X()-d.usrCoords[1])>JXG.Math.eps||Math.abs(c.Y()-d.usrCoords[2])>JXG.Math.eps||Math.abs(c.Z()-d.usrCoords[0])>JXG.Math.eps){return d}else{return JXG.Math.Geometry.meet(b.stdform,a.stdform,1,b.board)}}};JXG.Board.prototype.pointFunc=function(){return[null]};JXG.Board.prototype.pointOptions=["point",[[JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.lineFunc=function(){return arguments};JXG.Board.prototype.lineOptions=["line",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.linesegmentFunc=function(){return arguments};JXG.Board.prototype.linesegmentOptions=["line",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.linesegmentAtts={straightFirst:false,straightLast:false};JXG.Board.prototype.arrowFunc=function(){return arguments};JXG.Board.prototype.arrowOptions=["arrow",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.circleFunc=function(){return arguments};JXG.Board.prototype.circleOptions=["circle",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT],[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE],[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_CIRCLE]]];JXG.Board.prototype.arrowparallelOptions=["arrowparallel",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]];JXG.Board.prototype.arrowparallelFunc=function(){return arguments};JXG.Board.prototype.bisectorOptions=["bisector",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.bisectorFunc=function(){return arguments};JXG.Board.prototype.circumcircleOptions=["circumcircle",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.circumcircleFunc=function(){return arguments};JXG.Board.prototype.circumcirclemidpointOptions=["circumcirclemidpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.circumcirclemidpointFunc=function(){return arguments};JXG.Board.prototype.integralOptions=["integral",[[]]];JXG.Board.prototype.integralFunc=function(){return arguments};JXG.Board.prototype.midpointOptions=["midpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT],[JXG.OBJECT_CLASS_LINE]]];JXG.Board.prototype.midpointFunc=function(){return arguments};JXG.Board.prototype.mirrorpointOptions=["mirrorpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.mirrorpointFunc=function(){return arguments};JXG.Board.prototype.normalOptions=["normal",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]];JXG.Board.prototype.normalFunc=function(){return arguments};JXG.Board.prototype.parallelOptions=["parallel",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]];JXG.Board.prototype.parallelFunc=function(){return arguments};JXG.Board.prototype.parallelpointOptions=["parallelpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]];JXG.Board.prototype.parallelpointFunc=function(){return arguments};JXG.Board.prototype.perpendicularOptions=["perpendicular",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]];JXG.Board.prototype.perpendicularFunc=function(){return arguments};JXG.Board.prototype.perpendicularpointOptions=["perpendicularpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]];JXG.Board.prototype.perpendicularpointFunc=function(){return arguments};JXG.Board.prototype.reflectionOptions=["reflection",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]];JXG.Board.prototype.reflectionFunc=function(){return arguments};JXG.Board.prototype.pstricks={};JXG.Board.prototype.pstricks.givePsTricksToDiv=function(a,b){JXG.PsTricks.givePsTricksToDiv(a,b)};JXG.Ticks=function(a,f,e,g,b,h,c,d){this.constructor();this.type=JXG.OBJECT_TYPE_TICKS;this.elementClass=JXG.OBJECT_CLASS_OTHER;this.line=a;this.board=this.line.board;this.ticksFunction=null;this.fixedTicks=null;this.equidistant=false;if(JXG.isFunction(f)){this.ticksFunction=f;throw new Error("Function arguments are no longer supported.")}else{if(JXG.isArray(f)){this.fixedTicks=f}else{if(Math.abs(f)<JXG.Math.eps){f=this.board.options.line.ticks.defaultDistance}this.ticksFunction=function(k){return f};this.equidistant=true}}this.minorTicks=((e==null)?this.board.options.line.ticks.minorTicks:e);if(this.minorTicks<0){this.minorTicks=-this.minorTicks}this.majorHeight=((g==null)||(g==0)?this.board.options.line.ticks.majorHeight:g);if(this.majorHeight<0){this.majorHeight=-this.majorHeight}this.minorHeight=((b==null)||(b==0)?this.board.options.line.ticks.minorHeight:b);if(this.minorHeight<0){this.minorHeight=-this.minorHeight}this.minTicksDistance=this.board.options.line.ticks.minTicksDistance;this.maxTicksDistance=this.board.options.line.ticks.maxTicksDistance;this.insertTicks=this.board.options.line.ticks.insertTicks;this.drawZero=this.board.options.line.ticks.drawZero;this.drawLabels=this.board.options.line.ticks.drawLabels;this.labels=[];this.init(this.board,h,c);this.visProp.visible=true;this.visProp.fillColor=this.line.visProp.fillColor;this.visProp.highlightFillColor=this.line.visProp.highlightFillColor;this.visProp.strokeColor=this.line.visProp.strokeColor;this.visProp.highlightStrokeColor=this.line.visProp.highlightStrokeColor;this.visProp.strokeWidth=this.line.visProp.strokeWidth;this.id=this.line.addTicks(this)};JXG.Ticks.prototype=new JXG.GeometryElement;JXG.Ticks.prototype.hasPoint=function(a,b){return false};JXG.Ticks.prototype.calculateTicksCoordinates=function(){var L=this.line.point1,K=this.line.point2,d=L.coords.distance(JXG.COORDS_BY_USER,K.coords),h=(K.coords.usrCoords[1]-L.coords.usrCoords[1])/d,g=(K.coords.usrCoords[2]-L.coords.usrCoords[2])/d,s=L.coords.distance(JXG.COORDS_BY_SCREEN,new JXG.Coords(JXG.COORDS_BY_USER,[L.coords.usrCoords[1]+h,L.coords.usrCoords[2]+g],this.board)),B=(this.equidistant?this.ticksFunction(1):1),H=5,w,u,N=1,k,q,y,n,I,C,P=function(W,Q,T,S,V){var U,R;U=W.toString();if(U.length>5){U=W.toPrecision(3).toString()}R=new JXG.Text(T,U,null,[Q.usrCoords[1],Q.usrCoords[2]],V+I+"Label","",null,true,T.options.text.defaultDisplay);R.distanceX=0;R.distanceY=-10;R.setCoords(Q.usrCoords[1]*1+R.distanceX/(T.stretchX),Q.usrCoords[2]*1+R.distanceY/(T.stretchY));if(S){R.visProp.visible=true}else{R.visProp.visible=false}return R},a=function(Q){return Math.floor(Q)-(Math.floor(Q)%B)},x=JXG.Math.eps,r=-this.line.getSlope(),J=this.majorHeight/2,e=this.minorHeight/2,c=0,A=0,z=0,O=0;if(Math.abs(r)<x){c=0;A=J;z=0;O=e}else{if((Math.abs(r)>1/x)||(isNaN(r))){c=J;A=0;z=e;O=0}else{c=-J/Math.sqrt(1/(r*r)+1);A=c/r;z=-e/Math.sqrt(1/(r*r)+1);O=z/r}}if(this.ticks!=null){for(var G=0;G<this.ticks.length;G++){if(this.labels[G]!=null){if(this.labels[G].visProp.visible){this.board.renderer.remove(this.labels[G].rendNode)}}}}this.ticks=new Array();this.labels=new Array();w=new JXG.Coords(JXG.COORDS_BY_USER,[L.coords.usrCoords[1],L.coords.usrCoords[2]],this.board);u=new JXG.Coords(JXG.COORDS_BY_USER,[K.coords.usrCoords[1],K.coords.usrCoords[2]],this.board);this.board.renderer.calcStraight(this.line,w,u);if(!this.equidistant){var m=L.coords.usrCoords[1]-w.usrCoords[1];var l=L.coords.usrCoords[2]-w.usrCoords[2];var v=Math.sqrt(m*m+l*l);var f=L.coords.usrCoords[1]-u.usrCoords[1];var D=L.coords.usrCoords[2]-u.usrCoords[2];var b=Math.sqrt(f*f+D*D);var F=0;var E=0;for(var I=0;I<this.fixedTicks.length;I++){if((-v<=this.fixedTicks[I])&&(this.fixedTicks[I]<=b)){if(this.fixedTicks[I]<0){F=Math.abs(m)*this.fixedTicks[I]/v;E=Math.abs(l)*this.fixedTicks[I]/v}else{F=Math.abs(f)*this.fixedTicks[I]/b;E=Math.abs(D)*this.fixedTicks[I]/b}y=new JXG.Coords(JXG.COORDS_BY_USER,[L.coords.usrCoords[1]+F,L.coords.usrCoords[2]+E],this.board);this.ticks.push(y);this.ticks[this.ticks.length-1].major=true;this.labels.push(P(this.fixedTicks[I],y,this.board,this.drawLabels,this.id))}}this.board.renderer.updateTicks(this,c,A,z,O);return}while(s>4*this.minTicksDistance){B/=10;h/=10;g/=10;s=L.coords.distance(JXG.COORDS_BY_SCREEN,new JXG.Coords(JXG.COORDS_BY_USER,[L.coords.usrCoords[1]+h,L.coords.usrCoords[2]+g],this.board))}while(s<this.minTicksDistance){B*=H;h*=H;g*=H;H=(H==5?2:5);s=L.coords.distance(JXG.COORDS_BY_SCREEN,new JXG.Coords(JXG.COORDS_BY_USER,[L.coords.usrCoords[1]+h,L.coords.usrCoords[2]+g],this.board))}if(this.board.renderer.isSameDirection(L.coords,w,u)){k=a(L.coords.distance(JXG.COORDS_BY_USER,w));q=L.coords.distance(JXG.COORDS_BY_USER,u);if(this.board.renderer.isSameDirection(L.coords,K.coords,w)){if(this.line.visProp.straightFirst){k-=2*B}}else{q=-1*q;k=-1*k;if(this.line.visProp.straightFirst){k-=2*B}}}else{if(!this.line.visProp.straightFirst){k=0}else{k=-a(L.coords.distance(JXG.COORDS_BY_USER,w))-2*B}if(!this.line.visProp.straightLast){q=d}else{q=L.coords.distance(JXG.COORDS_BY_USER,u)}}n=new JXG.Coords(JXG.COORDS_BY_USER,[L.coords.usrCoords[1]+k*h/B,L.coords.usrCoords[2]+k*g/B],this.board);y=new JXG.Coords(JXG.COORDS_BY_USER,[L.coords.usrCoords[1]+k*h/B,L.coords.usrCoords[2]+k*g/B],this.board);h/=this.minorTicks+1;g/=this.minorTicks+1;I=0;C=k;while(n.distance(JXG.COORDS_BY_USER,y)<Math.abs(q-k)+JXG.Math.eps){if(I%(this.minorTicks+1)==0){y.major=true;this.labels.push(P(C,y,this.board,this.drawLabels,this.id));C+=B}else{y.major=false;this.labels.push(null)}I++;this.ticks.push(y);y=new JXG.Coords(JXG.COORDS_BY_USER,[y.usrCoords[1]+h,y.usrCoords[2]+g],this.board);if(!this.drawZero&&y.distance(JXG.COORDS_BY_USER,L.coords)<=JXG.Math.eps){I++;C+=B;y=new JXG.Coords(JXG.COORDS_BY_USER,[y.usrCoords[1]+h,y.usrCoords[2]+g],this.board)}}this.board.renderer.updateTicks(this,c,A,z,O);return};JXG.Ticks.prototype.updateRenderer=function(){if(this.needsUpdate){this.calculateTicksCoordinates();this.needsUpdate=false}};JXG.createTicks=function(d,b,a){var c;a=JXG.checkAttributes(a,{layer:null});if((b[0].elementClass==JXG.OBJECT_CLASS_LINE)&&(JXG.isFunction(b[1])||JXG.isArray(b[1])||JXG.isNumber(b[1]))){c=new JXG.Ticks(b[0],b[1],a.minorTicks,a.majHeight,a.minHeight,a.id,a.name,a.layer)}else{throw new Error("JSXGraph: Can't create Ticks with parent types '"+(typeof b[0])+"' and '"+(typeof b[1])+"' and '"+(typeof b[2])+"'.")}return c};JXG.JSXGraph.registerElement("ticks",JXG.createTicks);JXG.Util={};JXG.Util.Unzip=function(W){var q=[],I="",G=false,D,J=0,T=[],v,h=new Array(32768),ab=0,O=false,Y,K,aa=[0,128,64,192,32,160,96,224,16,144,80,208,48,176,112,240,8,136,72,200,40,168,104,232,24,152,88,216,56,184,120,248,4,132,68,196,36,164,100,228,20,148,84,212,52,180,116,244,12,140,76,204,44,172,108,236,28,156,92,220,60,188,124,252,2,130,66,194,34,162,98,226,18,146,82,210,50,178,114,242,10,138,74,202,42,170,106,234,26,154,90,218,58,186,122,250,6,134,70,198,38,166,102,230,22,150,86,214,54,182,118,246,14,142,78,206,46,174,110,238,30,158,94,222,62,190,126,254,1,129,65,193,33,161,97,225,17,145,81,209,49,177,113,241,9,137,73,201,41,169,105,233,25,153,89,217,57,185,121,249,5,133,69,197,37,165,101,229,21,149,85,213,53,181,117,245,13,141,77,205,45,173,109,237,29,157,93,221,61,189,125,253,3,131,67,195,35,163,99,227,19,147,83,211,51,179,115,243,11,139,75,203,43,171,107,235,27,155,91,219,59,187,123,251,7,135,71,199,39,167,103,231,23,151,87,215,55,183,119,247,15,143,79,207,47,175,111,239,31,159,95,223,63,191,127,255],ae=[3,4,5,6,7,8,9,10,11,13,15,17,19,23,27,31,35,43,51,59,67,83,99,115,131,163,195,227,258,0,0],V=[0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,0,99,99],P=[1,2,3,4,5,7,9,13,17,25,33,49,65,97,129,193,257,385,513,769,1025,1537,2049,3073,4097,6145,8193,12289,16385,24577],C=[0,0,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13],r=[16,17,18,0,8,7,9,6,10,5,11,4,12,3,13,2,14,1,15],z=W,b=0,g=0,af=1,a=0,ad=256,f=[],l;function d(){a+=8;if(b<z.length){return z[b++]}else{return -1}}function s(){af=1}function Z(){var ah;a++;ah=(af&1);af>>=1;if(af==0){af=d();ah=(af&1);af=(af>>1)|128}return ah}function X(ah){var aj=0,ai=ah;while(ai--){aj=(aj<<1)|Z()}if(ah){aj=aa[aj]>>(8-ah)}return aj}function c(){ab=0}function A(ah){K++;h[ab++]=ah;q.push(String.fromCharCode(ah));if(ab==32768){ab=0}}function n(){this.b0=0;this.b1=0;this.jump=null;this.jumppos=-1}var e=288;var y=new Array(e);var R=new Array(32);var L=0;var ac=null;var u=null;var Q=new Array(64);var N=new Array(64);var B=0;var F=new Array(17);F[0]=0;var S;var x;function k(){while(1){if(F[B]>=x){return -1}if(S[F[B]]==B){return F[B]++}F[B]++}}function H(){var ai=ac[L];var ah;if(G){document.write("<br>len:"+B+" treepos:"+L)}if(B==17){return -1}L++;B++;ah=k();if(G){document.write("<br>IsPat "+ah)}if(ah>=0){ai.b0=ah;if(G){document.write("<br>b0 "+ai.b0)}}else{ai.b0=32768;if(G){document.write("<br>b0 "+ai.b0)}if(H()){return -1}}ah=k();if(ah>=0){ai.b1=ah;if(G){document.write("<br>b1 "+ai.b1)}ai.jump=null}else{ai.b1=32768;if(G){document.write("<br>b1 "+ai.b1)}ai.jump=ac[L];ai.jumppos=L;if(H()){return -1}}B--;return 0}function m(al,aj,am,ai){var ak;if(G){document.write("currentTree "+al+" numval "+aj+" lengths "+am+" show "+ai)}ac=al;L=0;S=am;x=aj;for(ak=0;ak<17;ak++){F[ak]=0}B=0;if(H()){if(G){alert("invalid huffman tree\n")}return -1}if(G){document.write("<br>Tree: "+ac.length);for(var ah=0;ah<32;ah++){document.write("Places["+ah+"].b0="+ac[ah].b0+"<br>");document.write("Places["+ah+"].b1="+ac[ah].b1+"<br>")}}return 0}function E(ak){var ai,aj,am=0,al=ak[am],ah;while(1){ah=Z();if(G){document.write("b="+ah)}if(ah){if(!(al.b1&32768)){if(G){document.write("ret1")}return al.b1}al=al.jump;ai=ak.length;for(aj=0;aj<ai;aj++){if(ak[aj]===al){am=aj;break}}}else{if(!(al.b0&32768)){if(G){document.write("ret2")}return al.b0}am++;al=ak[am]}}if(G){document.write("ret3")}return -1}function ag(){var al,ay,ai,aw,ax;do{al=Z();ai=X(2);switch(ai){case 0:if(G){alert("Stored\n")}break;case 1:if(G){alert("Fixed Huffman codes\n")}break;case 2:if(G){alert("Dynamic Huffman codes\n")}break;case 3:if(G){alert("Reserved block type!!\n")}break;default:if(G){alert("Unexpected value %d!\n",ai)}break}if(ai==0){var au,ah;s();au=d();au|=(d()<<8);ah=d();ah|=(d()<<8);if(((au^~ah)&65535)){document.write("BlockLen checksum mismatch\n")}while(au--){ay=d();A(ay)}}else{if(ai==1){var av;while(1){av=(aa[X(7)]>>1);if(av>23){av=(av<<1)|Z();if(av>199){av-=128;av=(av<<1)|Z()}else{av-=48;if(av>143){av=av+136}}}else{av+=256}if(av<256){A(av)}else{if(av==256){break}else{var ax,aq;av-=256+1;ax=X(V[av])+ae[av];av=aa[X(5)]>>3;if(C[av]>8){aq=X(8);aq|=(X(C[av]-8)<<8)}else{aq=X(C[av])}aq+=P[av];for(av=0;av<ax;av++){var ay=h[(ab-aq)&32767];A(ay)}}}}}else{if(ai==2){var av,ar,aj,ao,ap;var an=new Array(288+32);aj=257+X(5);ao=1+X(5);ap=4+X(4);for(av=0;av<19;av++){an[av]=0}for(av=0;av<ap;av++){an[r[av]]=X(3)}ax=R.length;for(aw=0;aw<ax;aw++){R[aw]=new n()}if(m(R,19,an,0)){c();return 1}if(G){document.write("<br>distanceTree");for(var az=0;az<R.length;az++){document.write("<br>"+R[az].b0+" "+R[az].b1+" "+R[az].jump+" "+R[az].jumppos)}}ar=aj+ao;aw=0;var ak=-1;if(G){document.write("<br>n="+ar+" bits: "+a+"<br>")}while(aw<ar){ak++;av=E(R);if(G){document.write("<br>"+ak+" i:"+aw+" decode: "+av+" bits "+a+"<br>")}if(av<16){an[aw++]=av}else{if(av==16){var at;av=3+X(2);if(aw+av>ar){c();return 1}at=aw?an[aw-1]:0;while(av--){an[aw++]=at}}else{if(av==17){av=3+X(3)}else{av=11+X(7)}if(aw+av>ar){c();return 1}while(av--){an[aw++]=0}}}}ax=y.length;for(aw=0;aw<ax;aw++){y[aw]=new n()}if(m(y,aj,an,0)){c();return 1}ax=y.length;for(aw=0;aw<ax;aw++){R[aw]=new n()}var am=new Array();for(aw=aj;aw<an.length;aw++){am[aw-aj]=an[aw]}if(m(R,ao,am,0)){c();return 1}if(G){document.write("<br>literalTree")}while(1){av=E(y);if(av>=256){var ax,aq;av-=256;if(av==0){break}av--;ax=X(V[av])+ae[av];av=E(R);if(C[av]>8){aq=X(8);aq|=(X(C[av]-8)<<8)}else{aq=X(C[av])}aq+=P[av];while(ax--){var ay=h[(ab-aq)&32767];A(ay)}}else{A(av)}}}}}}while(!al);c();s();return 0}JXG.Util.Unzip.prototype.unzipFile=function(ah){var ai;this.unzip();for(ai=0;ai<T.length;ai++){if(T[ai][1]==ah){return T[ai][0]}}};JXG.Util.Unzip.prototype.unzip=function(){if(G){alert(z)}w();return T};function w(){if(G){alert("NEXTFILE")}q=[];var al=[];O=false;al[0]=d();al[1]=d();if(G){alert("type: "+al[0]+" "+al[1])}if(al[0]==parseInt("78",16)&&al[1]==parseInt("da",16)){if(G){alert("GEONExT-GZIP")}ag();if(G){alert(q.join(""))}T[J]=new Array(2);T[J][0]=q.join("");T[J][1]="geonext.gxt";J++}if(al[0]==parseInt("1f",16)&&al[1]==parseInt("8b",16)){if(G){alert("GZIP")}U();if(G){alert(q.join(""))}T[J]=new Array(2);T[J][0]=q.join("");T[J][1]="file";J++}if(al[0]==parseInt("50",16)&&al[1]==parseInt("4b",16)){O=true;al[2]=d();al[3]=d();if(al[2]==parseInt("3",16)&&al[3]==parseInt("4",16)){al[0]=d();al[1]=d();if(G){alert("ZIP-Version: "+al[1]+" "+al[0]/10+"."+al[0]%10)}D=d();D|=(d()<<8);if(G){alert("gpflags: "+D)}var ah=d();ah|=(d()<<8);if(G){alert("method: "+ah)}d();d();d();d();var am=d();am|=(d()<<8);am|=(d()<<16);am|=(d()<<24);var ak=d();ak|=(d()<<8);ak|=(d()<<16);ak|=(d()<<24);var ap=d();ap|=(d()<<8);ap|=(d()<<16);ap|=(d()<<24);if(G){alert("local CRC: "+am+"\nlocal Size: "+ap+"\nlocal CompSize: "+ak)}var ai=d();ai|=(d()<<8);var ao=d();ao|=(d()<<8);if(G){alert("filelen "+ai)}aj=0;f=[];while(ai--){var an=d();if(an=="/"|an==":"){aj=0}else{if(aj<ad-1){f[aj++]=String.fromCharCode(an)}}}if(G){alert("nameBuf: "+f)}if(!l){l=f}var aj=0;while(aj<ao){an=d();aj++}Y=4294967295;K=0;if(ap=0&&fileOut.charAt(l.length-1)=="/"){if(G){alert("skipdir")}}if(ah==8){ag();if(G){alert(q.join(""))}T[J]=new Array(2);T[J][0]=q.join("");T[J][1]=f.join("");J++}U()}}}function U(){var am,aj=[],ak,ai,al,ah,an;if((D&8)){aj[0]=d();aj[1]=d();aj[2]=d();aj[3]=d();if(aj[0]==parseInt("50",16)&&aj[1]==parseInt("4b",16)&&aj[2]==parseInt("07",16)&&aj[3]==parseInt("08",16)){am=d();am|=(d()<<8);am|=(d()<<16);am|=(d()<<24)}else{am=aj[0]|(aj[1]<<8)|(aj[2]<<16)|(aj[3]<<24)}ak=d();ak|=(d()<<8);ak|=(d()<<16);ak|=(d()<<24);ai=d();ai|=(d()<<8);ai|=(d()<<16);ai|=(d()<<24);if(G){alert("CRC:")}}if(O){w()}aj[0]=d();if(aj[0]!=8){if(G){alert("Unknown compression method!")}return 0}D=d();if(G){if((D&~(parseInt("1f",16)))){alert("Unknown flags set!")}}d();d();d();d();d();al=d();if((D&4)){aj[0]=d();aj[2]=d();B=aj[0]+256*aj[1];if(G){alert("Extra field size: "+B)}for(ah=0;ah<B;ah++){d()}}if((D&8)){ah=0;f=[];while(an=d()){if(an=="7"||an==":"){ah=0}if(ah<ad-1){f[ah++]=an}}if(G){alert("original file name: "+f)}}if((D&16)){while(an=d()){}}if((D&2)){d();d()}ag();am=d();am|=(d()<<8);am|=(d()<<16);am|=(d()<<24);ai=d();ai|=(d()<<8);ai|=(d()<<16);ai|=(d()<<24);if(O){w()}}};JXG.Util.Base64={_keyStr:"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",encode:function(c){var a=[],l,h,f,k,g,e,d,b=0;c=JXG.Util.Base64._utf8_encode(c);while(b<c.length){l=c.charCodeAt(b++);h=c.charCodeAt(b++);f=c.charCodeAt(b++);k=l>>2;g=((l&3)<<4)|(h>>4);e=((h&15)<<2)|(f>>6);d=f&63;if(isNaN(h)){e=d=64}else{if(isNaN(f)){d=64}}a.push([this._keyStr.charAt(k),this._keyStr.charAt(g),this._keyStr.charAt(e),this._keyStr.charAt(d)].join(""))}return a.join("")},decode:function(d,c){var a=[],m,k,g,l,h,f,e,b=0;d=d.replace(/[^A-Za-z0-9\+\/\=]/g,"");while(b<d.length){l=this._keyStr.indexOf(d.charAt(b++));h=this._keyStr.indexOf(d.charAt(b++));f=this._keyStr.indexOf(d.charAt(b++));e=this._keyStr.indexOf(d.charAt(b++));m=(l<<2)|(h>>4);k=((h&15)<<4)|(f>>2);g=((f&3)<<6)|e;a.push(String.fromCharCode(m));if(f!=64){a.push(String.fromCharCode(k))}if(e!=64){a.push(String.fromCharCode(g))}}a=a.join("");if(c){a=JXG.Util.Base64._utf8_decode(a)}return a},_utf8_encode:function(b){b=b.replace(/\r\n/g,"\n");var a="";for(var e=0;e<b.length;e++){var d=b.charCodeAt(e);if(d<128){a+=String.fromCharCode(d)}else{if((d>127)&&(d<2048)){a+=String.fromCharCode((d>>6)|192);a+=String.fromCharCode((d&63)|128)}else{a+=String.fromCharCode((d>>12)|224);a+=String.fromCharCode(((d>>6)&63)|128);a+=String.fromCharCode((d&63)|128)}}}return a},_utf8_decode:function(a){var d=[],f=0,g=0,e=0,b=0;while(f<a.length){g=a.charCodeAt(f);if(g<128){d.push(String.fromCharCode(g));f++}else{if((g>191)&&(g<224)){e=a.charCodeAt(f+1);d.push(String.fromCharCode(((g&31)<<6)|(e&63)));f+=2}else{e=a.charCodeAt(f+1);b=a.charCodeAt(f+2);d.push(String.fromCharCode(((g&15)<<12)|((e&63)<<6)|(b&63)));f+=3}}}return d.join("")},_destrip:function(f,d){var b=[],e,c,a=[];if(d==null){d=76}f.replace(/ /g,"");e=f.length/d;for(c=0;c<e;c++){b[c]=f.substr(c*d,d)}if(e!=f.length/d){b[b.length]=f.substr(e*d,f.length-(e*d))}for(c=0;c<b.length;c++){a.push(b[c])}return a.join("\n")},decodeAsArray:function(b){var d=this.decode(b),a=[],c;for(c=0;c<d.length;c++){a[c]=d.charCodeAt(c)}return a},decodeGEONExT:function(a){return decodeAsArray(destrip(a),false)}};JXG.Util.asciiCharCodeAt=function(b,a){var d=b.charCodeAt(a);if(d>255){switch(d){case 8364:d=128;break;case 8218:d=130;break;case 402:d=131;break;case 8222:d=132;break;case 8230:d=133;break;case 8224:d=134;break;case 8225:d=135;break;case 710:d=136;break;case 8240:d=137;break;case 352:d=138;break;case 8249:d=139;break;case 338:d=140;break;case 381:d=142;break;case 8216:d=145;break;case 8217:d=146;break;case 8220:d=147;break;case 8221:d=148;break;case 8226:d=149;break;case 8211:d=150;break;case 8212:d=151;break;case 732:d=152;break;case 8482:d=153;break;case 353:d=154;break;case 8250:d=155;break;case 339:d=156;break;case 382:d=158;break;case 376:d=159;break;default:break}}return d};JXG.Util.utf8Decode=function(a){var b=[];var e=0;var g=0,f=0,d=0;while(e<a.length){g=a.charCodeAt(e);if(g<128){b.push(String.fromCharCode(g));e++}else{if((g>191)&&(g<224)){d=a.charCodeAt(e+1);b.push(String.fromCharCode(((g&31)<<6)|(d&63)));e+=2}else{d=a.charCodeAt(e+1);c3=a.charCodeAt(e+2);b.push(String.fromCharCode(((g&15)<<12)|((d&63)<<6)|(c3&63)));e+=3}}}return b.join("")};JXG.PsTricks=new function(){this.psTricksString=""};JXG.PsTricks.convertBoardToPsTricks=function(b){var d=new JXG.Coords(JXG.COORDS_BY_SCREEN,[b.canvasWidth,b.canvasHeight],b);var c=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],b);this.psTricksString="\\begin{pspicture*}("+c.usrCoords[1]+","+d.usrCoords[2]+")("+d.usrCoords[1]+","+c.usrCoords[2]+")\n";for(var a in b.objects){var e=b.objects[a];if(e.type==JXG.OBJECT_TYPE_ARC){if(e.visProp.visible){this.addSector(e)}}}for(var a in b.objects){var e=b.objects[a];if(e.type==JXG.OBJECT_TYPE_POLYGON){if(e.visProp.visible){this.addPolygon(e)}}}for(var a in b.objects){var e=b.objects[a];if(e.type==JXG.OBJECT_TYPE_ANGLE){if(e.visProp.visible){this.addAngle(e)}}}for(var a in b.objects){var e=b.objects[a];if(e.type==JXG.OBJECT_TYPE_CIRCLE){if(e.visProp.visible){this.addCircle(e)}}}for(var a in b.objects){var e=b.objects[a];if(e.type==JXG.OBJECT_TYPE_ARC){if(e.visProp.visible){this.addArc(e)}}}for(var a in b.objects){var e=b.objects[a];if(e.type==JXG.OBJECT_TYPE_LINE){if(e.visProp.visible){this.addLine(e)}}}for(var a in b.objects){var e=b.objects[a];if(e.type==JXG.OBJECT_TYPE_POINT){if(e.visProp.visible){this.addPoint(e)}}}this.psTricksString+="\\end{pspicture*}"};JXG.PsTricks.givePsTricksToDiv=function(a,b){this.convertBoardToPsTricks(b);document.getElementById(a).innerHTML=this.psTricksString};JXG.PsTricks.addPoint=function(a){this.psTricksString+="\\psdot";this.psTricksString+="[linecolor="+this.parseColor(a.visProp.strokeColor)+",";this.psTricksString+="dotstyle=";if(a.visProp.face=="cross"){this.psTricksString+="x, dotsize=";if(a.visProp.size==2){this.psTricksString+="2pt 2"}else{if(a.visProp.size==3){this.psTricksString+="5pt 2"}else{if(a.visProp.size>=4){this.psTricksString+="5pt 3"}}}}else{if(a.visProp.face=="circle"){this.psTricksString+="*, dotsize=";if(a.visProp.size==1){this.psTricksString+="2pt 2"}else{if(a.visProp.size==2){this.psTricksString+="4pt 2"}else{if(a.visProp.size==3){this.psTricksString+="6pt 2"}else{if(a.visProp.size>=4){this.psTricksString+="6pt 3"}}}}}else{if(a.visProp.face=="square"){this.psTricksString+="square*, dotsize=";if(a.visProp.size==2){this.psTricksString+="2pt 2"}else{if(a.visProp.size==3){this.psTricksString+="5pt 2"}else{if(a.visProp.size>=4){this.psTricksString+="5pt 3"}}}}else{if(a.visProp.face=="plus"){this.psTricksString+="+, dotsize=";if(a.visProp.size==2){this.psTricksString+="2pt 2"}else{if(a.visProp.size==3){this.psTricksString+="5pt 2"}else{if(a.visProp.size>=4){this.psTricksString+="5pt 3"}}}}}}}this.psTricksString+="]";this.psTricksString+="("+a.coords.usrCoords[1]+","+a.coords.usrCoords[2]+")\n";this.psTricksString+="\\rput("+(a.coords.usrCoords[1]+15/a.board.stretchY)+","+(a.coords.usrCoords[2]+15/a.board.stretchY)+"){\\small $"+a.name+"$}\n"};JXG.PsTricks.addLine=function(c){var b=new JXG.Coords(JXG.COORDS_BY_USER,c.point1.coords.usrCoords,c.board);var a=new JXG.Coords(JXG.COORDS_BY_USER,c.point2.coords.usrCoords,c.board);if(c.visProp.straightFirst||c.visProp.straightLast){c.board.renderer.calcStraight(c,b,a)}this.psTricksString+="\\psline";this.psTricksString+="[linecolor="+this.parseColor(c.visProp.strokeColor)+", linewidth="+c.visProp.strokeWidth+"px";this.psTricksString+="]";if(c.visProp.firstArrow){if(c.visProp.lastArrow){this.psTricksString+="{<->}"}else{this.psTricksString+="{<-}"}}else{if(c.visProp.lastArrow){this.psTricksString+="{->}"}}this.psTricksString+="("+b.usrCoords[1]+","+b.usrCoords[2]+")("+a.usrCoords[1]+","+a.usrCoords[2]+")\n"};JXG.PsTricks.addCircle=function(b){var a=b.Radius();this.psTricksString+="\\pscircle";this.psTricksString+="[linecolor="+this.parseColor(b.visProp.strokeColor)+", linewidth="+b.visProp.strokeWidth+"px";if(b.visProp.fillColor!="none"&&b.visProp.fillOpacity!=0){this.psTricksString+=", fillstyle=solid, fillcolor="+this.parseColor(b.visProp.fillColor)+", opacity="+JXG.Math.round(b.visProp.fillOpacity,5)}this.psTricksString+="]";this.psTricksString+="("+b.midpoint.coords.usrCoords[1]+","+b.midpoint.coords.usrCoords[2]+"){"+a+"}\n"};JXG.PsTricks.addPolygon=function(b){this.psTricksString+="\\pspolygon";this.psTricksString+="[linestyle=none, fillstyle=solid, fillcolor="+this.parseColor(b.visProp.fillColor)+", opacity="+JXG.Math.round(b.visProp.fillOpacity,5)+"]";for(var a=0;a<b.vertices.length;a++){this.psTricksString+="("+b.vertices[a].coords.usrCoords[1]+","+b.vertices[a].coords.usrCoords[2]+")"}this.psTricksString+="\n"};JXG.PsTricks.addArc=function(b){var a=b.Radius();var d={};d.coords=new JXG.Coords(JXG.COORDS_BY_USER,[b.board.canvasWidth/(b.board.stretchY),b.midpoint.coords.usrCoords[2]],b.board);var c=JXG.Math.round(JXG.Math.Geometry.trueAngle(d,b.midpoint,b.point2),4);var e=JXG.Math.round(JXG.Math.Geometry.trueAngle(d,b.midpoint,b.point3),4);this.psTricksString+="\\psarc";this.psTricksString+="[linecolor="+this.parseColor(b.visProp.strokeColor)+", linewidth="+b.visProp.strokeWidth+"px";this.psTricksString+="]";if(b.visProp.lastArrow){if(b.visProp.firstArrow){this.psTricksString+="{<->}"}else{this.psTricksString+="{<-}"}}else{if(b.visProp.firstArrow){this.psTricksString+="{->}"}}this.psTricksString+="("+b.midpoint.coords.usrCoords[1]+","+b.midpoint.coords.usrCoords[2]+"){"+a+"}{"+c+"}{"+e+"}\n"};JXG.PsTricks.addSector=function(b){var a=b.Radius();var d={};d.coords=new JXG.Coords(JXG.COORDS_BY_USER,[b.board.canvasWidth/(b.board.stretchY),b.midpoint.coords.usrCoords[2]],b.board);var c=JXG.Math.round(JXG.Math.Geometry.trueAngle(d,b.midpoint,b.point2),4);var e=JXG.Math.round(JXG.Math.Geometry.trueAngle(d,b.midpoint,b.point3),4);if(b.visProp.fillColor!="none"&&b.visProp.fillOpacity!=0){this.psTricksString+="\\pswedge";this.psTricksString+="[linestyle=none, fillstyle=solid, fillcolor="+this.parseColor(b.visProp.fillColor)+", opacity="+JXG.Math.round(b.visProp.fillOpacity,5)+"]";this.psTricksString+="("+b.midpoint.coords.usrCoords[1]+","+b.midpoint.coords.usrCoords[2]+"){"+a+"}{"+c+"}{"+e+"}\n"}};JXG.PsTricks.addAngle=function(b){var a=b.radius;var d={};d.coords=new JXG.Coords(JXG.COORDS_BY_USER,[b.board.canvasWidth/(b.board.stretchY),b.point2.coords.usrCoords[2]],b.board);var c=JXG.Math.round(JXG.Math.Geometry.trueAngle(d,b.point2,b.point1),4);var e=JXG.Math.round(JXG.Math.Geometry.trueAngle(d,b.point2,b.point3),4);if(b.visProp.fillColor!="none"&&b.visProp.fillOpacity!=0){this.psTricksString+="\\pswedge";this.psTricksString+="[linestyle=none, fillstyle=solid, fillcolor="+this.parseColor(b.visProp.fillColor)+", opacity="+JXG.Math.round(b.visProp.fillOpacity,5)+"]";this.psTricksString+="("+b.point2.coords.usrCoords[1]+","+b.point2.coords.usrCoords[2]+"){"+a+"}{"+c+"}{"+e+"}\n"}this.psTricksString+="\\psarc";this.psTricksString+="[linecolor="+this.parseColor(b.visProp.strokeColor)+", linewidth="+b.visProp.strokeWidth+"px";this.psTricksString+="]";this.psTricksString+="("+b.point2.coords.usrCoords[1]+","+b.point2.coords.usrCoords[2]+"){"+a+"}{"+c+"}{"+e+"}\n"};JXG.PsTricks.parseColor=function(b){var a=JXG.rgbParser(b);return"{[rgb]{"+a[0]/255+","+a[1]/255+","+a[2]/255+"}}"};JXG.Server=function(){};JXG.Server.modules=function(){};JXG.Server.runningCalls={};JXG.Server.handleError=function(a){alert("error occured, server says: "+a.message)};JXG.Server.callServer=function(action,callback,data,sync){var fileurl,passdata,AJAX,params,id,dataJSONStr,k;if(typeof sync=="undefined"||sync==null){sync=false}params="";for(k in data){params+="&"+escape(k)+"="+escape(data[k])}dataJSONStr=JXG.toJSON(data);do{id=action+Math.floor(Math.random()*4096)}while(typeof this.runningCalls[id]!="undefined");this.runningCalls[id]={action:action};if(typeof data.module!="undefined"){this.runningCalls[id].module=data.module}fileurl=JXG.serverBase+"JXGServer.py";passdata="action="+escape(action)+"&id="+id+"&dataJSON="+escape(JXG.Util.Base64.encode(dataJSONStr));this.cbp=function(d){var str,data,tmp,inject,paramlist,id,i,j;str=(new JXG.Util.Unzip(JXG.Util.Base64.decodeAsArray(d))).unzip();if(JXG.isArray(str)&&str.length>0){str=str[0][0]}if(typeof str!="string"){return}data=eval("("+str+")");if(data.type=="error"){this.handleError(data)}else{if(data.type=="response"){id=data.id;for(i=0;i<data.fields.length;i++){tmp=data.fields[i];inject=tmp.namespace+(typeof eval(tmp.namespace)=="object"?".":".prototype.")+tmp.name+" = "+tmp.value;eval(inject)}for(i=0;i<data.handler.length;i++){tmp=data.handler[i];paramlist=[];for(j=0;j<tmp.parameters.length;j++){paramlist[j]='"'+tmp.parameters[j]+'": '+tmp.parameters[j]}inject="if(typeof JXG.Server.modules."+this.runningCalls[id].module+' == "undefined")JXG.Server.modules.'+this.runningCalls[id].module+" = {};";inject+="JXG.Server.modules."+this.runningCalls[id].module+"."+tmp.name+"_cb = "+tmp.callback+";";inject+="JXG.Server.modules."+this.runningCalls[id].module+"."+tmp.name+" = function ("+tmp.parameters.join(",")+', __JXGSERVER_CB__, __JXGSERVER_SYNC) {if(typeof __JXGSERVER_CB__ == "undefined") __JXGSERVER_CB__ = JXG.Server.modules.'+this.runningCalls[id].module+"."+tmp.name+"_cb;var __JXGSERVER_PAR__ = {"+paramlist.join(",")+', "module": "'+this.runningCalls[id].module+'", "handler": "'+tmp.name+'" };JXG.Server.callServer("exec", __JXGSERVER_CB__, __JXGSERVER_PAR__, __JXGSERVER_SYNC);};';eval(inject)}delete this.runningCalls[id];callback(data.data)}}};this.cb=JXG.bind(this.cbp,this);if(window.XMLHttpRequest){AJAX=new XMLHttpRequest();AJAX.overrideMimeType("text/plain; charset=iso-8859-1")}else{AJAX=new ActiveXObject("Microsoft.XMLHTTP")}if(AJAX){AJAX.open("POST",fileurl,!sync);AJAX.setRequestHeader("Content-type","application/x-www-form-urlencoded");if(!sync){AJAX.onreadystatechange=(function(cb){return function(){switch(AJAX.readyState){case 4:if(AJAX.status!=200){}else{cb(AJAX.responseText)}break;default:return false;break}}})(this.cb)}AJAX.send(passdata);if(sync){this.cb(AJAX.responseText)}}else{return false}};JXG.Server.loadModule_cb=function(b){var a;for(a=0;a<b.length;a++){alert(b[a].name+": "+b[a].value)}};JXG.Server.loadModule=function(a){return JXG.Server.callServer("load",JXG.Server.loadModule_cb,{module:a},true)};JXG.DataSource=function(){this.data=[];this.columnHeaders=[];this.rowHeaders=[];return this};JXG.DataSource.prototype.loadFromArray=function(e,f,d){var c,b,a;if(typeof f=="undefined"){f=false}if(typeof d=="undefined"){d=false}if(JXG.isArray(f)){this.columnHeader=f;f=false}if(JXG.isArray(d)){this.rowHeader=d;d=false}this.data=[];if(f){this.columnHeader=[]}if(d){this.rowHeader=[]}if(typeof e!="undefined"){this.data=new Array(e.length);for(c=0;c<e.length;c++){this.data[c]=new Array(e[c].length);for(b=0;b<e[c].length;b++){a=e[c][b];if(""+parseFloat(a)==a){this.data[c][b]=parseFloat(a)}else{if(a!="-"){this.data[c][b]=a}else{this.data[c][b]=NaN}}}}if(f){this.columnHeader=this.data[0].slice(1);this.data=this.data.slice(1)}if(d){this.rowHeader=new Array();for(c=0;c<this.data.length;c++){this.rowHeader.push(this.data[c][0]);this.data[c]=this.data[c].slice(1)}}}return this};JXG.DataSource.prototype.loadFromTable=function(h,c,f){var k,e,d,b,g,a;if(typeof c=="undefined"){c=false}if(typeof f=="undefined"){f=false}if(JXG.isArray(c)){this.columnHeader=c;c=false}if(JXG.isArray(f)){this.rowHeader=f;f=false}this.data=[];if(c){this.columnHeader=[]}if(f){this.rowHeader=[]}h=document.getElementById(h);if(typeof h!="undefined"){k=h.getElementsByTagName("tr");this.data=new Array(k.length);for(e=0;e<k.length;e++){b=k[e].getElementsByTagName("td");this.data[e]=new Array(b.length);for(d=0;d<b.length;d++){g=b[d].innerHTML;if(""+parseFloat(g)==g){this.data[e][d]=parseFloat(g)}else{if(g!="-"){this.data[e][d]=g}else{this.data[e][d]=NaN}}}}if(c){this.columnHeader=this.data[0].slice(1);this.data=this.data.slice(1)}if(f){this.rowHeader=new Array();for(e=0;e<this.data.length;e++){this.rowHeader.push(this.data[e][0]);this.data[e]=this.data[e].slice(1)}}}return this};JXG.DataSource.prototype.addColumn=function(a,c,b){};JXG.DataSource.prototype.addRow=function(a,c,b){};JXG.DataSource.prototype.getColumn=function(b){var a=new Array(this.data.length),c;if(typeof b=="string"){for(c=0;c<this.columnHeader.length;c++){if(b==this.columnHeader[c]){b=c;break}}}for(c=0;c<this.data.length;c++){if(this.data[c].length>b){a[c]=this.data[c][b]}}return a};JXG.DataSource.prototype.getRow=function(c){var a,b;if(typeof c=="string"){for(b=0;b<this.rowHeader.length;b++){if(c==this.rowHeader[b]){c=b;break}}}a=new Array(this.data[c].length);for(b=0;b<this.data[c].length;b++){a[b]=this.data[c][b]}return a};JXG.SVGRenderer=function(a){var b;this.constructor();this.svgRoot=null;this.suspendHandle=null;this.svgNamespace="http://www.w3.org/2000/svg";this.xlinkNamespace="http://www.w3.org/1999/xlink";this.container=a;this.container.style.MozUserSelect="none";this.container.style.overflow="hidden";if(this.container.style.position==""){this.container.style.position="relative"}this.svgRoot=this.container.ownerDocument.createElementNS(this.svgNamespace,"svg");this.svgRoot.style.overflow="hidden";this.svgRoot.style.width=this.container.style.width;this.svgRoot.style.height=this.container.style.height;this.container.appendChild(this.svgRoot);this.defs=this.container.ownerDocument.createElementNS(this.svgNamespace,"defs");this.svgRoot.appendChild(this.defs);this.filter=this.container.ownerDocument.createElementNS(this.svgNamespace,"filter");this.filter.setAttributeNS(null,"id",this.container.id+"_f1");this.filter.setAttributeNS(null,"width","300%");this.filter.setAttributeNS(null,"height","300%");this.feOffset=this.container.ownerDocument.createElementNS(this.svgNamespace,"feOffset");this.feOffset.setAttributeNS(null,"result","offOut");this.feOffset.setAttributeNS(null,"in","SourceAlpha");this.feOffset.setAttributeNS(null,"dx","5");this.feOffset.setAttributeNS(null,"dy","5");this.filter.appendChild(this.feOffset);this.feGaussianBlur=this.container.ownerDocument.createElementNS(this.svgNamespace,"feGaussianBlur");this.feGaussianBlur.setAttributeNS(null,"result","blurOut");this.feGaussianBlur.setAttributeNS(null,"in","offOut");this.feGaussianBlur.setAttributeNS(null,"stdDeviation","3");this.filter.appendChild(this.feGaussianBlur);this.feBlend=this.container.ownerDocument.createElementNS(this.svgNamespace,"feBlend");this.feBlend.setAttributeNS(null,"in","SourceGraphic");this.feBlend.setAttributeNS(null,"in2","blurOut");this.feBlend.setAttributeNS(null,"mode","normal");this.filter.appendChild(this.feBlend);this.defs.appendChild(this.filter);this.layer=[];for(b=0;b<JXG.Options.layer.numlayers;b++){this.layer[b]=this.container.ownerDocument.createElementNS(this.svgNamespace,"g");this.svgRoot.appendChild(this.layer[b])}this.dashArray=["2, 2","5, 5","10, 10","20, 20","20, 10, 10, 10","20, 5, 10, 5"]};JXG.SVGRenderer.prototype=new JXG.AbstractRenderer;JXG.SVGRenderer.prototype.setShadow=function(a){if(a.visPropOld.shadow==a.visProp.shadow){return}if(a.rendNode!=null){if(a.visProp.shadow){a.rendNode.setAttributeNS(null,"filter","url(#f1)")}else{a.rendNode.removeAttributeNS(null,"filter")}}a.visPropOld.shadow=a.visProp.shadow};JXG.SVGRenderer.prototype.setGradient=function(c){var m=c.rendNode,d,f,e,l,k,b,a,h,g;if(typeof c.visProp.fillOpacity=="function"){f=c.visProp.fillOpacity()}else{f=c.visProp.fillOpacity}f=(f>0)?f:0;if(typeof c.visProp.fillColor=="function"){d=c.visProp.fillColor()}else{d=c.visProp.fillColor}if(c.visProp.gradient=="linear"){e=this.createPrim("linearGradient",c.id+"_gradient");b="0%";a="100%";h="0%";g="0%";e.setAttributeNS(null,"x1",b);e.setAttributeNS(null,"x2",a);e.setAttributeNS(null,"y1",h);e.setAttributeNS(null,"y2",g);l=this.createPrim("stop",c.id+"_gradient1");l.setAttributeNS(null,"offset","0%");l.setAttributeNS(null,"style","stop-color:"+d+";stop-opacity:"+f);k=this.createPrim("stop",c.id+"_gradient2");k.setAttributeNS(null,"offset","100%");k.setAttributeNS(null,"style","stop-color:"+c.visProp.gradientSecondColor+";stop-opacity:"+c.visProp.gradientSecondOpacity);e.appendChild(l);e.appendChild(k);this.defs.appendChild(e);m.setAttributeNS(null,"style","fill:url(#"+this.container.id+"_"+c.id+"_gradient)");c.gradNode1=l;c.gradNode2=k}else{if(c.visProp.gradient=="radial"){e=this.createPrim("radialGradient",c.id+"_gradient");e.setAttributeNS(null,"cx","50%");e.setAttributeNS(null,"cy","50%");e.setAttributeNS(null,"r","50%");e.setAttributeNS(null,"fx",c.visProp.gradientPositionX*100+"%");e.setAttributeNS(null,"fy",c.visProp.gradientPositionY*100+"%");l=this.createPrim("stop",c.id+"_gradient1");l.setAttributeNS(null,"offset","0%");l.setAttributeNS(null,"style","stop-color:"+c.visProp.gradientSecondColor+";stop-opacity:"+c.visProp.gradientSecondOpacity);k=this.createPrim("stop",c.id+"_gradient2");k.setAttributeNS(null,"offset","100%");k.setAttributeNS(null,"style","stop-color:"+d+";stop-opacity:"+f);e.appendChild(l);e.appendChild(k);this.defs.appendChild(e);m.setAttributeNS(null,"style","fill:url(#"+this.container.id+"_"+c.id+"_gradient)");c.gradNode1=l;c.gradNode2=k}else{m.removeAttributeNS(null,"style")}}};JXG.SVGRenderer.prototype.updateGradient=function(d){var b=d.gradNode1,a=d.gradNode2,c,e;if(b==null||a==0){return}if(typeof d.visProp.fillOpacity=="function"){e=d.visProp.fillOpacity()}else{e=d.visProp.fillOpacity}e=(e>0)?e:0;if(typeof d.visProp.fillColor=="function"){c=d.visProp.fillColor()}else{c=d.visProp.fillColor}if(d.visProp.gradient=="linear"){b.setAttributeNS(null,"style","stop-color:"+c+";stop-opacity:"+e);a.setAttributeNS(null,"style","stop-color:"+d.visProp.gradientSecondColor+";stop-opacity:"+d.visProp.gradientSecondOpacity)}else{if(d.visProp.gradient=="radial"){b.setAttributeNS(null,"style","stop-color:"+d.visProp.gradientSecondColor+";stop-opacity:"+d.visProp.gradientSecondOpacity);a.setAttributeNS(null,"style","stop-color:"+c+";stop-opacity:"+e)}}};JXG.SVGRenderer.prototype.displayCopyright=function(c,d){var b=this.createPrim("text","licenseText"),a;b.setAttributeNS(null,"x","20");b.setAttributeNS(null,"y",2+d);b.setAttributeNS(null,"style","font-family:Arial,Helvetica,sans-serif; font-size:"+d+"px; fill:#356AA0; opacity:0.3;");a=document.createTextNode(c);b.appendChild(a);this.appendChildPrim(b,0)};JXG.SVGRenderer.prototype.drawInternalText=function(a){var b=this.createPrim("text",a.id);b.setAttributeNS(null,"class","JXGtext");b.setAttributeNS(null,"style","'alignment-baseline:middle;");a.rendNodeText=document.createTextNode("");b.appendChild(a.rendNodeText);this.appendChildPrim(b,9);return b};JXG.SVGRenderer.prototype.updateInternalText=function(a){a.rendNode.setAttributeNS(null,"x",(a.coords.scrCoords[1])+"px");a.rendNode.setAttributeNS(null,"y",(a.coords.scrCoords[2])+"px");a.updateText();if(a.htmlStr!=a.plaintextStr){a.rendNodeText.data=a.plaintextStr;a.htmlStr=a.plaintextStr}};JXG.SVGRenderer.prototype.drawTicks=function(a){var b=this.createPrim("path",a.id);this.appendChildPrim(b,a.layer);this.appendNodesToElement(a,"path")};JXG.SVGRenderer.prototype.updateTicks=function(e,f,a,h,b){var g="",k,m,d,l=e.ticks.length;for(k=0;k<l;k++){m=e.ticks[k].scrCoords;if(e.ticks[k].major){if(e.labels[k].visProp.visible){this.drawText(e.labels[k])}g+="M "+(m[1]+f)+" "+(m[2]-a)+" L "+(m[1]-f)+" "+(m[2]+a)+" "}else{g+="M "+(m[1]+h)+" "+(m[2]-b)+" L "+(m[1]-h)+" "+(m[2]+b)+" "}}d=this.getElementById(e.id);if(d==null){d=this.createPrim("path",e.id);this.appendChildPrim(d,e.layer);this.appendNodesToElement(e,"path")}d.setAttributeNS(null,"stroke",e.visProp.strokeColor);d.setAttributeNS(null,"stroke-opacity",e.visProp.strokeOpacity);d.setAttributeNS(null,"stroke-width",e.visProp.strokeWidth);this.updatePathPrim(d,g,e.board)};JXG.SVGRenderer.prototype.drawImage=function(b){var a=b.url,c=this.createPrim("image",b.id);c.setAttributeNS(this.xlinkNamespace,"xlink:href",a);c.setAttributeNS(null,"preserveAspectRatio","none");this.appendChildPrim(c,b.layer);b.rendNode=c;this.updateImage(b)};JXG.SVGRenderer.prototype.transformImage=function(b,a){var c=b.rendNode,d=c.getAttributeNS(null,"transform");d+=" "+this.joinTransforms(b,a);c.setAttributeNS(null,"transform",d)};JXG.SVGRenderer.prototype.joinTransforms=function(e,c){var f="",b,d,a=c.length;for(b=0;b<a;b++){d=c[b].matrix[1][1]+","+c[b].matrix[2][1]+","+c[b].matrix[1][2]+","+c[b].matrix[2][2]+","+c[b].matrix[1][0]+","+c[b].matrix[2][0];f+="matrix("+d+") "}return f};JXG.SVGRenderer.prototype.transformImageParent=function(c,a){var b,d;if(a!=null){b=a[1][1]+","+a[2][1]+","+a[1][2]+","+a[2][2]+","+a[1][0]+","+a[2][0];d="matrix("+b+")"}else{d=""}c.rendNode.setAttributeNS(null,"transform",d)};JXG.SVGRenderer.prototype.setArrowAtts=function(a,d,b){if(!a){return}a.setAttributeNS(null,"stroke",d);a.setAttributeNS(null,"stroke-opacity",b);a.setAttributeNS(null,"fill",d);a.setAttributeNS(null,"fill-opacity",b)};JXG.SVGRenderer.prototype.setObjectStrokeColor=function(el,color,opacity){var c=this.eval(color),o=this.eval(opacity),node;o=(o>0)?o:0;if(el.visPropOld.strokeColor==c&&el.visPropOld.strokeOpacity==o){return}node=el.rendNode;if(el.type==JXG.OBJECT_TYPE_TEXT){if(el.display=="html"){node.style.color=c}else{node.setAttributeNS(null,"style","fill:"+c)}}else{node.setAttributeNS(null,"stroke",c);node.setAttributeNS(null,"stroke-opacity",o)}if(el.type==JXG.OBJECT_TYPE_ARROW){this.setArrowAtts(el.rendNodeTriangle,c,o)}else{if(el.elementClass==JXG.OBJECT_CLASS_CURVE||el.elementClass==JXG.OBJECT_CLASS_LINE){if(el.visProp.firstArrow){this.setArrowAtts(el.rendNodeTriangleStart,c,o)}if(el.visProp.lastArrow){this.setArrowAtts(el.rendNodeTriangleEnd,c,o)}}}el.visPropOld.strokeColor=c;el.visPropOld.strokeOpacity=o};JXG.SVGRenderer.prototype.setObjectFillColor=function(el,color,opacity){var node,c=this.eval(color),o=this.eval(opacity);o=(o>0)?o:0;if(el.visPropOld.fillColor==c&&el.visPropOld.fillOpacity==o){return}node=el.rendNode;node.setAttributeNS(null,"fill",c);node.setAttributeNS(null,"fill-opacity",o);if(el.visProp.gradient!=null){this.updateGradient(el)}el.visPropOld.fillColor=c;el.visPropOld.fillOpacity=o};JXG.SVGRenderer.prototype.setObjectStrokeWidth=function(el,width){var w=this.eval(width),node;try{if(el.visPropOld.strokeWidth==w){return}}catch(e){}node=el.rendNode;this.setPropertyPrim(node,"stroked","true");if(w!=null){this.setPropertyPrim(node,"stroke-width",w)}el.visPropOld.strokeWidth=w};JXG.SVGRenderer.prototype.hide=function(a){var b;if(a==null){return}b=a.rendNode;b.setAttributeNS(null,"display","none");b.style.visibility="hidden"};JXG.SVGRenderer.prototype.show=function(a){var b=a.rendNode;b.setAttributeNS(null,"display","inline");b.style.visibility="inherit"};JXG.SVGRenderer.prototype.remove=function(a){if(a!=null&&a.parentNode!=null){a.parentNode.removeChild(a)}};JXG.SVGRenderer.prototype.suspendRedraw=function(){if(true){this.suspendHandle=this.svgRoot.suspendRedraw(10000)}};JXG.SVGRenderer.prototype.unsuspendRedraw=function(){if(true){this.svgRoot.unsuspendRedraw(this.suspendHandle);this.svgRoot.forceRedraw()}};JXG.SVGRenderer.prototype.setDashStyle=function(b,a){var d=b.visProp.dash,c=b.rendNode;if(b.visProp.dash>0){c.setAttributeNS(null,"stroke-dasharray",this.dashArray[d-1])}else{if(c.hasAttributeNS(null,"stroke-dasharray")){c.removeAttributeNS(null,"stroke-dasharray")}}};JXG.SVGRenderer.prototype.setGridDash=function(b){var a=this.getElementById(b);this.setPropertyPrim(a,"stroke-dasharray","5, 5")};JXG.SVGRenderer.prototype.createPrim=function(a,c){var b=this.container.ownerDocument.createElementNS(this.svgNamespace,a);b.setAttributeNS(null,"id",this.container.id+"_"+c);b.style.position="absolute";if(a=="path"){b.setAttributeNS(null,"stroke-linecap","butt");b.setAttributeNS(null,"stroke-linejoin","round")}return b};JXG.SVGRenderer.prototype.createArrowHead=function(c,e){var d=c.id+"Triangle",b,a;if(e!=null){d+=e}b=this.createPrim("marker",d);b.setAttributeNS(null,"viewBox","0 0 10 6");b.setAttributeNS(null,"refY","3");b.setAttributeNS(null,"markerUnits","strokeWidth");b.setAttributeNS(null,"markerHeight","6");b.setAttributeNS(null,"markerWidth","6");b.setAttributeNS(null,"orient","auto");b.setAttributeNS(null,"stroke",c.visProp.strokeColor);b.setAttributeNS(null,"stroke-opacity",c.visProp.strokeOpacity);b.setAttributeNS(null,"fill",c.visProp.strokeColor);b.setAttributeNS(null,"fill-opacity",c.visProp.strokeOpacity);a=this.container.ownerDocument.createElementNS(this.svgNamespace,"path");if(e=="End"){b.setAttributeNS(null,"refX","0");a.setAttributeNS(null,"d","M 0 3 L 10 6 L 10 0 z")}else{b.setAttributeNS(null,"refX","10");a.setAttributeNS(null,"d","M 0 0 L 10 3 L 0 6 z")}b.appendChild(a);return b};JXG.SVGRenderer.prototype.makeArrow=function(c,b,d){var a=this.createArrowHead(b,d);this.defs.appendChild(a);c.setAttributeNS(null,"marker-end","url(#"+this.container.id+"_"+b.id+"Triangle)");b.rendNodeTriangle=a};JXG.SVGRenderer.prototype.makeArrows=function(b){var a;if(b.visPropOld.firstArrow==b.visProp.firstArrow&&b.visPropOld.lastArrow==b.visProp.lastArrow){return}if(b.visProp.firstArrow){a=b.rendNodeTriangleStart;if(a==null){a=this.createArrowHead(b,"End");this.defs.appendChild(a);b.rendNodeTriangleStart=a;b.rendNode.setAttributeNS(null,"marker-start","url(#"+this.container.id+"_"+b.id+"TriangleEnd)")}}else{a=b.rendNodeTriangleStart;if(a!=null){this.remove(a)}}if(b.visProp.lastArrow){a=b.rendNodeTriangleEnd;if(a==null){a=this.createArrowHead(b,"Start");this.defs.appendChild(a);b.rendNodeTriangleEnd=a;b.rendNode.setAttributeNS(null,"marker-end","url(#"+this.container.id+"_"+b.id+"TriangleStart)")}}else{a=b.rendNodeTriangleEnd;if(a!=null){this.remove(a)}}b.visPropOld.firstArrow=b.visProp.firstArrow;b.visPropOld.lastArrow=b.visProp.lastArrow};JXG.SVGRenderer.prototype.updateLinePrim=function(e,b,a,d,c){e.setAttributeNS(null,"x1",b);e.setAttributeNS(null,"y1",a);e.setAttributeNS(null,"x2",d);e.setAttributeNS(null,"y2",c)};JXG.SVGRenderer.prototype.updateCirclePrim=function(c,a,d,b){c.setAttributeNS(null,"cx",(a));c.setAttributeNS(null,"cy",(d));c.setAttributeNS(null,"r",(b))};JXG.SVGRenderer.prototype.updateEllipsePrim=function(b,a,e,d,c){b.setAttributeNS(null,"cx",(a));b.setAttributeNS(null,"cy",(e));b.setAttributeNS(null,"rx",(d));b.setAttributeNS(null,"ry",(c))};JXG.SVGRenderer.prototype.updateRectPrim=function(d,a,e,b,c){d.setAttributeNS(null,"x",(a));d.setAttributeNS(null,"y",(e));d.setAttributeNS(null,"width",(b));d.setAttributeNS(null,"height",(c))};JXG.SVGRenderer.prototype.updatePathPrim=function(b,c,a){b.setAttributeNS(null,"d",c)};JXG.SVGRenderer.prototype.updatePathStringPrim=function(a){var c=" M ",d=" L ",b=c,l=5000,f="",e,h,k=(a.curveType!="plot"),g;if(a.numberPoints<=0){return""}if(k&&a.board.options.curve.RDPsmoothing){a.points=this.RamenDouglasPeuker(a.points,0.5)}g=Math.min(a.points.length,a.numberPoints);for(e=0;e<g;e++){h=a.points[e].scrCoords;if(isNaN(h[1])||isNaN(h[2])){b=c}else{if(h[1]>l){h[1]=l}else{if(h[1]<-l){h[1]=-l}}if(h[2]>l){h[2]=l}else{if(h[2]<-l){h[2]=-l}}f+=[b,h[1]," ",h[2]].join("");b=d}}return f};JXG.SVGRenderer.prototype.updatePathStringPoint=function(e,b,d){var c="",g=e.coords.scrCoords,f=b*Math.sqrt(3)*0.5,a=b*0.5;if(d=="x"){c="M "+(g[1]-b)+" "+(g[2]-b)+" L "+(g[1]+b)+" "+(g[2]+b)+" M "+(g[1]+b)+" "+(g[2]-b)+" L "+(g[1]-b)+" "+(g[2]+b)}else{if(d=="+"){c="M "+(g[1]-b)+" "+(g[2])+" L "+(g[1]+b)+" "+(g[2])+" M "+(g[1])+" "+(g[2]-b)+" L "+(g[1])+" "+(g[2]+b)}else{if(d=="diamond"){c="M "+(g[1]-b)+" "+(g[2])+" L "+(g[1])+" "+(g[2]+b)+" L "+(g[1]+b)+" "+(g[2])+" L "+(g[1])+" "+(g[2]-b)+" Z "}else{if(d=="A"){c="M "+(g[1])+" "+(g[2]-b)+" L "+(g[1]-f)+" "+(g[2]+a)+" L "+(g[1]+f)+" "+(g[2]+a)+" Z "}else{if(d=="v"){c="M "+(g[1])+" "+(g[2]+b)+" L "+(g[1]-f)+" "+(g[2]-a)+" L "+(g[1]+f)+" "+(g[2]-a)+" Z "}else{if(d==">"){c="M "+(g[1]+b)+" "+(g[2])+" L "+(g[1]-a)+" "+(g[2]-f)+" L "+(g[1]-a)+" "+(g[2]+f)+" Z "}else{if(d=="<"){c="M "+(g[1]-b)+" "+(g[2])+" L "+(g[1]+a)+" "+(g[2]-f)+" L "+(g[1]+a)+" "+(g[2]+f)+" Z "}}}}}}}return c};JXG.SVGRenderer.prototype.updatePolygonePrim=function(e,d){var f="",b,c,a=d.vertices.length;e.setAttributeNS(null,"stroke","none");for(c=0;c<a-1;c++){b=d.vertices[c].coords.scrCoords;f=f+b[1]+","+b[2];if(c<a-2){f+=" "}}e.setAttributeNS(null,"points",f)};JXG.SVGRenderer.prototype.appendChildPrim=function(a,b){if(typeof b=="undefined"){b=0}else{if(b>=JXG.Options.layer.numlayers){b=JXG.Options.layer.numlayers-1}}this.layer[b].appendChild(a)};JXG.SVGRenderer.prototype.setPropertyPrim=function(b,a,c){if(a=="stroked"){return}b.setAttributeNS(null,a,c)};JXG.SVGRenderer.prototype.drawVerticalGrid=function(d,b,f,c){var e=this.createPrim("path","gridx"),a="";while(d.scrCoords[1]<b.scrCoords[1]+f-1){a+=" M "+d.scrCoords[1]+" "+0+" L "+d.scrCoords[1]+" "+c.canvasHeight+" ";d.setCoordinates(JXG.COORDS_BY_SCREEN,[d.scrCoords[1]+f,d.scrCoords[2]])}this.updatePathPrim(e,a,c);return e};JXG.SVGRenderer.prototype.drawHorizontalGrid=function(d,b,f,c){var e=this.createPrim("path","gridy"),a="";while(d.scrCoords[2]<=b.scrCoords[2]+f-1){a+=" M "+0+" "+d.scrCoords[2]+" L "+c.canvasWidth+" "+d.scrCoords[2]+" ";d.setCoordinates(JXG.COORDS_BY_SCREEN,[d.scrCoords[1],d.scrCoords[2]+f])}this.updatePathPrim(e,a,c);return e};JXG.SVGRenderer.prototype.appendNodesToElement=function(a,b){a.rendNode=this.getElementById(a.id)};JXG.VMLRenderer=function(a){this.constructor();this.container=a;this.container.style.overflow="hidden";this.container.onselectstart=function(){return false};this.resolution=10;a.ownerDocument.namespaces.add("jxgvml","urn:schemas-microsoft-com:vml");this.container.ownerDocument.createStyleSheet().addRule(".jxgvml","behavior:url(#default#VML)");try{!a.ownerDocument.namespaces.jxgvml&&a.ownerDocument.namespaces.add("jxgvml","urn:schemas-microsoft-com:vml");this.createNode=function(c){return a.ownerDocument.createElement("<jxgvml:"+c+' class="jxgvml">')}}catch(b){this.createNode=function(c){return a.ownerDocument.createElement("<"+c+' xmlns="urn:schemas-microsoft.com:vml" class="jxgvml">')}}this.dashArray=["Solid","1 1","ShortDash","Dash","LongDash","ShortDashDot","LongDashDot"]};JXG.VMLRenderer.prototype=new JXG.AbstractRenderer;JXG.VMLRenderer.prototype.setAttr=function(c,a,f,b){try{if(document.documentMode==8){c[a]=f}else{c.setAttribute(a,f,b)}}catch(d){}};JXG.VMLRenderer.prototype.setShadow=function(a){var b=a.rendNodeShadow;if(!b){return}if(a.visPropOld.shadow==a.visProp.shadow){return}if(a.visProp.shadow){this.setAttr(b,"On","True");this.setAttr(b,"Offset","3pt,3pt");this.setAttr(b,"Opacity","60%");this.setAttr(b,"Color","#aaaaaa")}else{this.setAttr(b,"On","False")}a.visPropOld.shadow=a.visProp.shadow};JXG.VMLRenderer.prototype.setGradient=function(b){var a=b.rendNodeFill;if(b.visProp.gradient=="linear"){this.setAttr(a,"type","gradient");this.setAttr(a,"color2",b.visProp.gradientSecondColor);this.setAttr(a,"opacity2",b.visProp.gradientSecondOpacity);this.setAttr(a,"angle",b.visProp.gradientAngle)}else{if(b.visProp.gradient=="radial"){this.setAttr(a,"type","gradientradial");this.setAttr(a,"color2",b.visProp.gradientSecondColor);this.setAttr(a,"opacity2",b.visProp.gradientSecondOpacity);this.setAttr(a,"focusposition",b.visProp.gradientPositionX*100+"%,"+b.visProp.gradientPositionY*100+"%");this.setAttr(a,"focussize","0,0")}else{this.setAttr(a,"type","solid")}}};JXG.VMLRenderer.prototype.updateGradient=function(a){};JXG.VMLRenderer.prototype.addShadowToGroup=function(a,c){var b,d;if(a=="lines"){for(b in c.objects){d=c.objects[b];if(d.elementClass==JXG.OBJECT_CLASS_LINE){this.addShadowToElement(d)}}}else{if(a=="points"){for(b in c.objects){d=c.objects[b];if(d.elementClass==JXG.OBJECT_CLASS_POINT){this.addShadowToElement(d)}}}else{if(a=="circles"){for(b in c.objects){d=c.objects[b];if(d.elementClass==JXG.OBJECT_CLASS_CIRCLE){this.addShadowToElement(d)}}}}}c.fullUpdate()};JXG.VMLRenderer.prototype.displayCopyright=function(c,d){var b,a;b=this.createNode("textbox");b.style.position="absolute";this.setAttr(b,"id",this.container.id+"_licenseText");b.style.left=20;b.style.top=(2);b.style.fontSize=(d);b.style.color="#356AA0";b.style.fontFamily="Arial,Helvetica,sans-serif";this.setAttr(b,"opacity","30%");b.style.filter="alpha(opacity = 30)";a=document.createTextNode(c);b.appendChild(a);this.appendChildPrim(b,0)};JXG.VMLRenderer.prototype.drawInternalText=function(a){var b;b=this.createNode("textbox");b.style.position="absolute";if(document.documentMode==8){b.setAttribute("class","JXGtext")}else{b.setAttribute("className",9)}a.rendNodeText=document.createTextNode("");b.appendChild(a.rendNodeText);this.appendChildPrim(b,9);return b};JXG.VMLRenderer.prototype.updateInternalText=function(a){a.rendNode.style.left=(a.coords.scrCoords[1])+"px";a.rendNode.style.top=(a.coords.scrCoords[2]-this.vOffsetText)+"px";a.updateText();if(a.htmlStr!=a.plaintextStr){a.rendNodeText.data=a.plaintextStr;a.htmlStr=a.plaintextStr}};JXG.VMLRenderer.prototype.drawTicks=function(b){var a=this.createPrim("path",b.id);this.appendChildPrim(a,b.layer);this.appendNodesToElement(b,"path")};JXG.VMLRenderer.prototype.updateTicks=function(f,g,b,h,e){var d=[],k,l,m,n,a=this.resolution;l=f.ticks.length;for(k=0;k<l;k++){m=f.ticks[k].scrCoords;if(f.ticks[k].major){if(f.labels[k].visProp.visible){this.drawText(f.labels[k])}d.push(" m "+Math.round(a*(m[1]+g))+", "+Math.round(a*(m[2]-b))+" l "+Math.round(a*(m[1]-g))+", "+Math.round(a*(m[2]+b))+" ")}else{d.push(" m "+Math.round(a*(m[1]+h))+", "+Math.round(a*(m[2]-e))+" l "+Math.round(a*(m[1]-h))+", "+Math.round(a*(m[2]+e))+" ")}}n=this.getElementById(f.id);if(n==null){n=this.createPrim("path",f.id);this.appendChildPrim(n,f.layer);this.appendNodesToElement(f,"path")}this.setAttr(n,"stroked","true");this.setAttr(n,"strokecolor",f.visProp.strokeColor,1);this.setAttr(n,"strokeweight",f.visProp.strokeWidth);this.updatePathPrim(n,d,f.board)};JXG.VMLRenderer.prototype.drawImage=function(b){var c,a=b.url;c=this.container.ownerDocument.createElement("img");c.style.position="absolute";this.setAttr(c,"id",this.container.id+"_"+b.id);this.setAttr(c,"src",a);this.container.appendChild(c);this.appendChildPrim(c,b.layer);c.style.filter="progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand')";b.rendNode=c;this.updateImage(b)};JXG.VMLRenderer.prototype.transformImage=function(c,b){var d=c.rendNode,a;a=this.joinTransforms(c,b);d.style.left=(c.coords.scrCoords[1]+a[1][0])+"px";d.style.top=(c.coords.scrCoords[2]-c.size[1]+a[2][0])+"px";d.filters.item(0).M11=a[1][1];d.filters.item(0).M12=a[1][2];d.filters.item(0).M21=a[2][1];d.filters.item(0).M22=a[2][2]};JXG.VMLRenderer.prototype.joinTransforms=function(e,d){var b=[[1,0,0],[0,1,0],[0,0,1]],c,a=d.length;for(c=0;c<a;c++){b=JXG.Math.matMatMult(d[c].matrix,b)}return b};JXG.VMLRenderer.prototype.transformImageParent=function(b,a){};JXG.VMLRenderer.prototype.hide=function(a){a.rendNode.style.visibility="hidden"};JXG.VMLRenderer.prototype.show=function(a){a.rendNode.style.visibility="inherit"};JXG.VMLRenderer.prototype.setDashStyle=function(b,a){var c;if(a.dash>=0){c=b.rendNodeStroke;this.setAttr(c,"dashstyle",this.dashArray[a.dash])}};JXG.VMLRenderer.prototype.setObjectStrokeColor=function(el,color,opacity){var c=this.eval(color),o=this.eval(opacity),node,nodeStroke;o=(o>0)?o:0;if(el.visPropOld.strokeColor==c&&el.visPropOld.strokeOpacity==o){return}if(el.type==JXG.OBJECT_TYPE_TEXT){el.rendNode.style.color=c}else{node=el.rendNode;this.setAttr(node,"stroked","true");this.setAttr(node,"strokecolor",c);if(el.id=="gridx"){nodeStroke=this.getElementById("gridx_stroke")}else{if(el.id=="gridy"){nodeStroke=this.getElementById("gridy_stroke")}else{nodeStroke=el.rendNodeStroke}}if(o!=undefined){this.setAttr(nodeStroke,"opacity",(o*100)+"%")}}el.visPropOld.strokeColor=c;el.visPropOld.strokeOpacity=o};JXG.VMLRenderer.prototype.setObjectFillColor=function(el,color,opacity){var c=this.eval(color),o=this.eval(opacity);o=(o>0)?o:0;if(el.visPropOld.fillColor==c&&el.visPropOld.fillOpacity==o){return}if(c=="none"){this.setAttr(el.rendNode,"filled","false")}else{this.setAttr(el.rendNode,"filled","true");this.setAttr(el.rendNode,"fillcolor",c);if(o!=undefined&&el.rendNodeFill){this.setAttr(el.rendNodeFill,"opacity",(o*100)+"%")}}el.visPropOld.fillColor=c;el.visPropOld.fillOpacity=o};JXG.VMLRenderer.prototype.remove=function(a){if(a!=null){a.removeNode(true)}};JXG.VMLRenderer.prototype.suspendRedraw=function(){this.container.style.display="none"};JXG.VMLRenderer.prototype.unsuspendRedraw=function(){this.container.style.display=""};JXG.VMLRenderer.prototype.setAttributes=function(node,props,vmlprops,visProp){var val,i,p;len=props.length;for(i=0;i<len;i++){p=props[i];if(visProp[p]!=null){val=this.eval(visProp[p]);val=(val>0)?val:0;this.setAttr(node,vmlprops[i],val)}}};JXG.VMLRenderer.prototype.setGridDash=function(b,a){var a=this.getElementById(b+"_stroke");this.setAttr(a,"dashstyle","Dash")};JXG.VMLRenderer.prototype.setObjectStrokeWidth=function(el,width){var w=this.eval(width),node;if(el.visPropOld.strokeWidth==w){return}node=el.rendNode;this.setPropertyPrim(node,"stroked","true");if(w!=null){this.setPropertyPrim(node,"stroke-width",w)}el.visPropOld.strokeWidth=w};JXG.VMLRenderer.prototype.createPrim=function(b,g){var c,a=this.createNode("fill"),f=this.createNode("stroke"),e=this.createNode("shadow"),d;this.setAttr(a,"id",this.container.id+"_"+g+"_fill");this.setAttr(f,"id",this.container.id+"_"+g+"_stroke");this.setAttr(e,"id",this.container.id+"_"+g+"_shadow");if(b=="circle"||b=="ellipse"){c=this.createNode("oval");c.appendChild(a);c.appendChild(f);c.appendChild(e)}else{if(b=="polygon"||b=="path"||b=="shape"||b=="line"){c=this.createNode("shape");c.appendChild(a);c.appendChild(f);c.appendChild(e);d=this.createNode("path");this.setAttr(d,"id",this.container.id+"_"+g+"_path");c.appendChild(d)}else{c=this.createNode(b);c.appendChild(a);c.appendChild(f);c.appendChild(e)}}c.style.position="absolute";this.setAttr(c,"id",this.container.id+"_"+g);return c};JXG.VMLRenderer.prototype.appendNodesToElement=function(a,b){if(b=="shape"||b=="path"||b=="polygon"){a.rendNodePath=this.getElementById(a.id+"_path")}a.rendNodeFill=this.getElementById(a.id+"_fill");a.rendNodeStroke=this.getElementById(a.id+"_stroke");a.rendNodeShadow=this.getElementById(a.id+"_shadow");a.rendNode=this.getElementById(a.id)};JXG.VMLRenderer.prototype.makeArrow=function(c,b,d){var a=b.rendNodeStroke;this.setAttr(a,"endarrow","block");this.setAttr(a,"endarrowlength","long")};JXG.VMLRenderer.prototype.makeArrows=function(b){var a;if(b.visPropOld.firstArrow==b.visProp.firstArrow&&b.visPropOld.lastArrow==b.visProp.lastArrow){return}if(b.visProp.firstArrow){a=b.rendNodeStroke;this.setAttr(a,"startarrow","block");this.setAttr(a,"startarrowlength","long")}else{a=b.rendNodeStroke;if(a!=null){this.setAttr(a,"startarrow","none")}}if(b.visProp.lastArrow){a=b.rendNodeStroke;this.setAttr(a,"id",this.container.id+"_"+b.id+"stroke");this.setAttr(a,"endarrow","block");this.setAttr(a,"endarrowlength","long")}else{a=b.rendNodeStroke;if(a!=null){this.setAttr(a,"endarrow","none")}}b.visPropOld.firstArrow=b.visProp.firstArrow;b.visPropOld.lastArrow=b.visProp.lastArrow};JXG.VMLRenderer.prototype.updateLinePrim=function(h,b,a,d,c,f){var e,g=this.resolution;e=["m ",g*b,", ",g*a," l ",g*d,", ",g*c];this.updatePathPrim(h,e,f)};JXG.VMLRenderer.prototype.updateCirclePrim=function(c,a,d,b){c.style.left=(a-b)+"px";c.style.top=(d-b)+"px";c.style.width=(b*2)+"px";c.style.height=(b*2)+"px"};JXG.VMLRenderer.prototype.updateRectPrim=function(d,a,e,b,c){d.style.left=(a)+"px";d.style.top=(e)+"px";d.style.width=(b)+"px";d.style.height=(c)+"px"};JXG.VMLRenderer.prototype.updateEllipsePrim=function(b,a,e,d,c){b.style.left=(a-d)+"px";b.style.top=(e-c)+"px";b.style.width=(d*2)+"px";b.style.height=(c*2)+"px"};JXG.VMLRenderer.prototype.updatePathPrim=function(c,d,b){var a=b.canvasWidth,e=b.canvasHeight;c.style.width=a;c.style.height=e;this.setAttr(c,"coordsize",[(this.resolution*a),(this.resolution*e)].join(","));this.setAttr(c,"path",d.join(""))};JXG.VMLRenderer.prototype.updatePathStringPrim=function(b){var h=[],g,l,a=this.resolution,f=Math.round,d=" m ",e=" l ",c=d,m=(b.curveType!="plot"),k=Math.min(b.numberPoints,8192);if(b.numberPoints<=0){return""}if(m&&b.board.options.curve.RDPsmoothing){b.points=this.RamenDouglasPeuker(b.points,1)}k=Math.min(k,b.points.length);for(g=0;g<k;g++){l=b.points[g].scrCoords;if(isNaN(l[1])||isNaN(l[2])){c=d}else{if(l[1]>20000){l[1]=20000}else{if(l[1]<-20000){l[1]=-20000}}if(l[2]>20000){l[2]=20000}else{if(l[2]<-20000){l[2]=-20000}}h.push([c,f(a*l[1]),", ",f(a*l[2])].join(""));c=e}}h.push(" e");return h};JXG.VMLRenderer.prototype.updatePathStringPoint=function(e,b,d){var c=[],h=e.coords.scrCoords,g=b*Math.sqrt(3)*0.5,a=b*0.5,f=this.resolution;if(d=="x"){c.push(["m ",(f*(h[1]-b)),", ",(f*(h[2]-b))," l ",(f*(h[1]+b)),", ",(f*(h[2]+b))," m ",(f*(h[1]+b)),", ",(f*(h[2]-b))," l ",(f*(h[1]-b)),", ",(f*(h[2]+b))].join(""))}else{if(d=="+"){c.push(["m ",(f*(h[1]-b)),", ",(f*(h[2]))," l ",(f*(h[1]+b)),", ",(f*(h[2]))," m ",(f*(h[1])),", ",(f*(h[2]-b))," l ",(f*(h[1])),", ",(f*(h[2]+b))].join(""))}else{if(d=="diamond"){c.push(["m ",(f*(h[1]-b)),", ",(f*(h[2]))," l ",(f*(h[1])),", ",(f*(h[2]+b))," l ",(f*(h[1]+b)),", ",(f*(h[2]))," l ",(f*(h[1])),", ",(f*(h[2]-b))," x e "].join(""))}else{if(d=="A"){c.push(["m ",(f*(h[1])),", ",(f*(h[2]-b))," l ",Math.round(f*(h[1]-g)),", ",(f*(h[2]+a))," l ",Math.round(f*(h[1]+g)),", ",(f*(h[2]+a))," x e "].join(""))}else{if(d=="v"){c.push(["m ",(f*(h[1])),", ",(f*(h[2]+b))," l ",Math.round(f*(h[1]-g)),", ",(f*(h[2]-a))," l ",Math.round(f*(h[1]+g)),", ",(f*(h[2]-a))," x e "].join(""))}else{if(d==">"){c.push(["m ",(f*(h[1]+b)),", ",(f*(h[2]))," l ",(f*(h[1]-a)),", ",Math.round(f*(h[2]-g))," l ",(f*(h[1]-a)),", ",Math.round(f*(h[2]+g))," l ",(f*(h[1]+b)),", ",(f*(h[2]))].join(""))}else{if(d=="<"){c.push(["m ",(f*(h[1]-b)),", ",(f*(h[2]))," l ",(f*(h[1]+a)),", ",Math.round(f*(h[2]-g))," l ",(f*(h[1]+a)),", ",Math.round(f*(h[2]+g))," x e "].join(""))}}}}}}}return c};JXG.VMLRenderer.prototype.updatePolygonePrim=function(e,c){var f=c.vertices[0].coords.scrCoords[1],b=c.vertices[0].coords.scrCoords[1],d=c.vertices[0].coords.scrCoords[2],a=c.vertices[0].coords.scrCoords[2],g,k=c.vertices.length,l,n,m,h=[];this.setAttr(e,"stroked","false");for(g=1;g<k-1;g++){l=c.vertices[g].coords.scrCoords;if(l[1]<f){f=l[1]}else{if(l[1]>b){b=l[1]}}if(l[2]<d){d=l[2]}else{if(l[2]>a){a=l[2]}}}n=Math.round(b-f);m=Math.round(a-d);if(!isNaN(n)&&!isNaN(m)){e.style.width=n;e.style.height=m;this.setAttr(e,"coordsize",n+","+m)}l=c.vertices[0].coords.scrCoords;h.push(["m ",l[1],",",l[2]," l "].join(""));for(g=1;g<k-1;g++){l=c.vertices[g].coords.scrCoords;h.push(l[1]+","+l[2]);if(g<k-2){h.push(", ")}}h.push(" x e");this.setAttr(e,"path",h.join(""))};JXG.VMLRenderer.prototype.appendChildPrim=function(a,b){if(typeof b=="undefined"){b=0}a.style.zIndex=b;this.container.appendChild(a)};JXG.VMLRenderer.prototype.setPropertyPrim=function(node,key,val){var keyVml="",node2,v;switch(key){case"stroke":keyVml="strokecolor";break;case"stroke-width":keyVml="strokeweight";break;case"stroke-dasharray":keyVml="dashstyle";break}if(keyVml!=""){v=this.eval(val);this.setAttr(node,keyVml,v)}};JXG.VMLRenderer.prototype.drawVerticalGrid=function(d,b,f,c){var e=this.createPrim("path","gridx"),a=[];while(d.scrCoords[1]<b.scrCoords[1]+f-1){a.push(" m "+(this.resolution*d.scrCoords[1])+", "+0+" l "+(this.resolution*d.scrCoords[1])+", "+(this.resolution*c.canvasHeight)+" ");d.setCoordinates(JXG.COORDS_BY_SCREEN,[d.scrCoords[1]+f,d.scrCoords[2]])}this.updatePathPrim(e,a,c);return e};JXG.VMLRenderer.prototype.drawHorizontalGrid=function(d,b,f,c){var e=this.createPrim("path","gridy"),a=[];while(d.scrCoords[2]<=b.scrCoords[2]+f-1){a.push(" m "+0+", "+(this.resolution*d.scrCoords[2])+" l "+(this.resolution*c.canvasWidth)+", "+(this.resolution*d.scrCoords[2])+" ");d.setCoordinates(JXG.COORDS_BY_SCREEN,[d.scrCoords[1],d.scrCoords[2]+f])}this.updatePathPrim(e,a,c);return e};
Reference in New Issue View Git Blame Copy Permalink