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(presque) Tous les schéma de la partie "Génération".

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Georges Dupéron 2011-11-14 06:30:26 +01:00
parent 1b6a15f093
commit 753acab271
1 changed files with 316 additions and 345 deletions
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présentation.tex
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@ -114,6 +114,9 @@
);
perlin2DCosine_(\x,\y,\octave,\periode,\octaves,\persistance,\amplitude)=lazyifthenelse(\octave >= \octaves, 0, "octave2DCosine(\x,\y,\octave,\periode,\amplitude) + perlin2DCosine_(\x,\y,\octave+1,\periode*0.5,\octaves,\persistance,\amplitude*\persistance)");
perlin2DCosine(\x,\y,\periode,\octaves,\persistance,\amplitude)=perlin2DCosine_(\x,\y,0,\periode,\octaves,\persistance,\amplitude);
xpointoncircle(\t,\circler,\maxdiam)=1 + \maxdiam/2 + cos(\t)*\circler;
ypointoncircle(\t,\circler,\maxdiam)=1 + \maxdiam/2 + sin(\t)*\circler;
courbepoly(\x)=(((-12.5*\x + 26.25) * \x -16) * \x + 3.25)*\x;
}
}
\shorthandon{;?:}
@ -221,380 +224,336 @@
\end{itemize}
\end{frame}
% Macro pour la génération de dégradés.
\def\gengradient#1{
\xdef\pointa{0}
\xdef\pointb{1}
\pgfmathsetmacro{\posa}{\csname positions#1\endcsname[\pointa]}\xdef\posa{\posa}
\pgfmathsetmacro{\posb}{\csname positions#1\endcsname[\pointb]}\xdef\posb{\posb}
\foreach \x in {0,...,512}{
\pgfmathsetmacro{\v}{max(0,min(1,\x/512))}
\pgfmathparse{\v > \posb}
\ifnum 1=\pgfmathresult
\xdef\pointa{\pointb}
\xdef\posa{\posb}
\setintmacro{\pointb}{\pointb+1}\xdef\pointb{\pointb}
\pgfmathsetmacro{\posb}{\csname positions#1\endcsname[\pointb]}\xdef\posb{\posb}
\fi
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\setcache{gradient,#1,\x}{gradient#1\pointa!\mix!gradient#1\pointb}
}
}
% Génération du dégradé "terrain"
\definecolor{gradientterrain0}{rgb}{0,0,0.5}
\definecolor{gradientterrain1}{rgb}{0.2,0.2,1}
\definecolor{gradientterrain2}{rgb}{0.9,0.6,0.1}
\definecolor{gradientterrain3}{rgb}{0.1,0.6,0.2}
\definecolor{gradientterrain4}{rgb}{0.6,0.3,0.05}
\definecolor{gradientterrain5}{rgb}{1,1,1}
\def\positionsterrain{{0,0.3,0.4,0.88,0.94,1}}
\gengradient{terrain}
\definecolor{gradientnuage0}{rgb}{0,0,1}
\definecolor{gradientnuage1}{rgb}{0,0.3,1}
\definecolor{gradientnuage2}{rgb}{0.7,0.7,1}
\definecolor{gradientnuage3}{rgb}{1,1,1}
\def\positionsnuage{{0,0.1,0.9,1}}
\gengradient{nuage}
\definecolor{gradientmarbre0}{rgb}{1,1,1}
\definecolor{gradientmarbre1}{rgb}{0.6,0.3,0.05} % rose
\definecolor{gradientmarbre2}{rgb}{1,0.95,0.8} % beige/gris
\definecolor{gradientmarbre3}{rgb}{0.8,0.7,0.4} % beige/gris
\definecolor{gradientmarbre4}{rgb}{0.5,0.5,0.5} % gris
\definecolor{gradientmarbre5}{rgb}{0,0,0} % noir
\def\positionsmarbre{{0,0.4,0.6,0.88,0.96,1}}
\gengradient{marbre}
% Génération du perlin 2D
\xdef\twodperlinsize{8}
\xdef\maxvtwodperlin{0}
\xdef\minvtwodperlin{0}
\def\maxradius{32}
\def\ncircles{10}
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Perlin 2D line \y/\twodperlinsize.}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{-perlin2DCosine(\x,\y,16,3,0.5,50)}
\setcache{vtwodperlin,\x,\y}{\v}
\pgfmathparse{max(\maxvtwodperlin,\v)}
\xdef\maxvtwodperlin{\pgfmathresult}
\pgfmathparse{min(\minvtwodperlin,\v)}
\xdef\minvtwodperlin{\pgfmathresult}
}
}
% Génération du craters
\xdef\craterssize{4}
\xdef\maxvcraters{0}
\xdef\minvcraters{0}
\def\maxradius{32}
\def\ncircles{10}
\foreach \y in {1,2,...,\craterssize}{
\foreach \x in {1,2,...,\craterssize}{
\setcache{vcraters,\x,\y}{0}
}
}
\foreach \c in {1,...,\ncircles}{
\setintmacro{\circlex}{noise1D(\c,0)*\craterssize}
\setintmacro{\circley}{noise1D(\c,1)*\craterssize}
\setintmacro{\circler}{1+noise1D(\c,2)*\maxradius}
\message{Circle number \c/\ncircles, center (\circlex, \circley), radius \circler}
\foreach \dy in {-\circler,...,\circler}{
\setintmacro{\y}{\circley+\dy}
\pgfmathparse{(\y > 0) && (\y <= \craterssize)}
\ifnum 1=\pgfmathresult
\foreach \dx in {-\circler,...,\circler}{
\setintmacro{\x}{\circlex+\dx}
\pgfmathparse{(\x > 0) && (\x <= \craterssize)}
\ifnum 1=\pgfmathresult
\xdef\oldv{\getcache{vcraters,\x,\y}}
\pgfmathsetmacro{\v}{\oldv - max(0,\circler - ((\dx*\dx + \dy*\dy)/\circler))}
\setcache{vcraters,\x,\y}{\v}
\pgfmathparse{max(\maxvcraters,\v)}
\xdef\maxvcraters{\pgfmathresult}
\pgfmathparse{min(\minvcraters,\v)}
\xdef\minvcraters{\pgfmathresult}
\fi
}
\fi
}
}
% Génération du perlin + craters
\xdef\cratersperlinsize{\twodperlinsize}
\xdef\maxvcratersperlin{\maxvtwodperlin}
\xdef\minvcratersperlin{\minvtwodperlin}
\def\maxradius{32}
\def\ncircles{20}
\foreach \y in {1,2,...,\cratersperlinsize}{
\foreach \x in {1,2,...,\cratersperlinsize}{
\setcache{vcratersperlin,\x,\y}{\getcache{vtwodperlin,\x,\y}}
}
}
\foreach \c in {1,...,\ncircles}{
\setintmacro{\circlex}{noise1D(\c,0)*\cratersperlinsize}
\setintmacro{\circley}{noise1D(\c,1)*\cratersperlinsize}
\setintmacro{\circler}{1+noise1D(\c,2)*\maxradius}
\message{Circle number \c/\ncircles, center (\circlex, \circley), radius \circler}
\foreach \dy in {-\circler,...,\circler}{
\setintmacro{\y}{\circley+\dy}
\pgfmathparse{(\y > 0) && (\y <= \cratersperlinsize)}
\ifnum 1=\pgfmathresult
\foreach \dx in {-\circler,...,\circler}{
\setintmacro{\x}{\circlex+\dx}
\pgfmathparse{(\x > 0) && (\x <= \cratersperlinsize)}
\ifnum 1=\pgfmathresult
\xdef\oldv{\getcache{vcratersperlin,\x,\y}}
\pgfmathparse{\oldv - max(0,\circler - ((\dx*\dx + \dy*\dy)/\circler))}
\setcache{vcratersperlin,\x,\y}{\pgfmathresult}
\pgfmathparse{max(\maxvcratersperlin,\pgfmathresult)}
\xdef\maxvcratersperlin{\pgfmathresult}
\pgfmathparse{min(\minvcratersperlin,\pgfmathresult)}
\xdef\minvcratersperlin{\pgfmathresult}
\fi
}
\fi
}
}
\begin{frame}
\frametitle{Perlin noise (Variations)}
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\path (300,0) ++(128,128) ++(1.5,1.5) rectangle (0,0);
\only<1-5>{
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Gradient line \y/\twodperlinsize...}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
\only<5>{ \pgfmathsetmacro{\v}{1-2*abs(\v-0.5)} }
\setintmacro{\v}{max(0,min(512,int(\v*512)))}
\only<2-5>{ \path[fill=\getcache{gradient,nuage,\v}] (\x,\y) rectangle ++(1.5,1.5); }
\only<3-5>{ \path[fill=\getcache{gradient,marbre,\v}] (150+\x,\y) rectangle ++(1.5,1.5); }
\only<4-5>{ \path[fill=\getcache{gradient,terrain,\v}] (300+\x,\y) rectangle ++(1.5,1.5); }
}
}
}
\only<6-8>{
\node[coordinate] (p0) at (150,64) {};
\node[coordinate] (p8) at (150+128,64) {};
\node[coordinate] (m4) at ($ .5*(p0) + .5*(p8) $) {};
\node[coordinate] (p4) at ($ (m4) + (0,{noise1D(64,0)*64-32}) $) {};
\node[coordinate] (m2) at ($ .5*(p0) + .5*(p4) $) {};
\node[coordinate] (p2) at ($ (m2) + (0,{noise1D(32,0)*32-16}) $) {};
\node[coordinate] (m6) at ($ .5*(p4) + .5*(p8) $) {};
\node[coordinate] (p6) at ($ (m6) + (0,{noise1D(96,0)*32-16}) $) {};
\node[coordinate] (m1) at ($ .5*(p0) + .5*(p2) $) {};
\node[coordinate] (p1) at ($ (m1) + (0,{noise1D(16,0)*16-8}) $) {};
\node[coordinate] (m3) at ($ .5*(p2) + .5*(p4) $) {};
\node[coordinate] (p3) at ($ (m3) + (0,{noise1D(48,0)*16-8}) $) {};
\node[coordinate] (m5) at ($ .5*(p4) + .5*(p6) $) {};
\node[coordinate] (p5) at ($ (m5) + (0,{noise1D(80,0)*16-8}) $) {};
\node[coordinate] (m7) at ($ .5*(p6) + .5*(p8) $) {};
\node[coordinate] (p7) at ($ (m7) + (0,{noise1D(112,0)*16-8}) $) {};
}
\tikzset{shortdash/.style={dash pattern=on 1pt off 1pt}}
\only<6>{
\draw[gray!50] (p0) -- (p8);
\draw[shortdash,gray] (p4) -- (m4);
\draw (p0) -- (p4) -- (p8);
}
\only<7>{
\draw[gray!25] (p0) -- (p8);
\draw[gray!50] (p0) -- (p4) -- (p8);
\draw[shortdash,gray] (p2) -- (m2);
\draw[shortdash,gray] (p6) -- (m6);
\draw (p0) -- (p2) -- (p4) -- (p6) -- (p8);
}
\only<8>{
\draw[gray!12.5] (p0) -- (p8);
\draw[gray!25] (p0) -- (p4) -- (p8);
\draw[gray!50] (p0) -- (p2) -- (p4) -- (p6) -- (p8);
\draw[shortdash,gray] (p1) -- (m1);
\draw[shortdash,gray] (p3) -- (m3);
\draw[shortdash,gray] (p5) -- (m5);
\draw[shortdash,gray] (p7) -- (m7);
\draw (p0) -- (p1) -- (p2) -- (p3) -- (p4) -- (p5) -- (p6) -- (p7) -- (p8);
}
\end{tikzpicture}
\end{figure}
\begin{itemize}
\item<1-> Bruit $n$D et voxels~: cavernes\only<2->{, nuages}\only<3->{, textures}\only<4->{, terrains.}
\only<2>{
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\xdef\twodperlinsize{64}
\xdef\maxvtwodperlin{0}
\xdef\minvtwodperlin{0}
\def\maxradius{32}
\def\ncircles{10}
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Perlin 2D line \y/\twodperlinsize.}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{-perlin2DCosine(\x,\y,16,3,0.5,50}
\setcache{vtwodperlin,\x,\y}{\v}
\pgfmathparse{max(\maxvtwodperlin,\v)}
\xdef\maxvtwodperlin{\pgfmathresult}
\pgfmathparse{min(\minvtwodperlin,\v)}
\xdef\minvtwodperlin{\pgfmathresult}
}
}
\definecolor{gradientpoint0}{rgb}{0,0,1}
\definecolor{gradientpoint1}{rgb}{0,0.3,1}
\definecolor{gradientpoint2}{rgb}{0.3,0.3,1}
\definecolor{gradientpoint3}{rgb}{1,1,1}
\def\positions{{0,0.1,0.9,1}}
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Gradient line \y/\twodperlinsize...}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
\pgfmathsetmacro{\v}{max(0,min(1,\v))}
\foreach \pointb in {1,...,3}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v <= \posb}
\ifnum 1=\pgfmathresult
\setintmacro{\pointa}{\pointb-1}
\pgfmathsetmacro{\posa}{\positions[\pointa]}
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\xdef\colora{gradientpoint\pointa}
\xdef\colorb{gradientpoint\pointb}
\xdef\mix{\mix}
\breakforeach
\fi
}
\path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
\end{figure}
}
\only<3>{
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\definecolor{gradientpoint0}{rgb}{0,0,0.5}
\definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
\definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
\definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
\definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
\definecolor{gradientpoint5}{rgb}{1,1,1}
\def\positions{{0,0.3,0.4,0.88,0.94,1}}
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Gradient line \y/\twodperlinsize...}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
\pgfmathsetmacro{\v}{max(0,min(1,\v))}
\foreach \pointb in {1,...,5}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v <= \posb}
\ifnum 1=\pgfmathresult
\setintmacro{\pointa}{\pointb-1}
\pgfmathsetmacro{\posa}{\positions[\pointa]}
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\xdef\colora{gradientpoint\pointa}
\xdef\colorb{gradientpoint\pointb}
\xdef\mix{\mix}
\breakforeach
\fi
}
\path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
\end{figure}
}
\only<4>{
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\definecolor{gradientpoint0}{rgb}{0,0,0.5}
\definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
\definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
\definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
\definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
\definecolor{gradientpoint5}{rgb}{1,1,1}
\def\positions{{0,0.3,0.4,0.88,0.94,1}}
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Gradient line \y/\twodperlinsize...}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
\pgfmathsetmacro{\v}{max(0,min(1,\v))}
\foreach \pointb in {1,...,5}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v <= \posb}
\ifnum 1=\pgfmathresult
\setintmacro{\pointa}{\pointb-1}
\pgfmathsetmacro{\posa}{\positions[\pointa]}
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\xdef\colora{gradientpoint\pointa}
\xdef\colorb{gradientpoint\pointb}
\xdef\mix{\mix}
\breakforeach
\fi
}
\path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
\end{figure}
}
\item<5-> Ridged Perlin Noise.
\only<5>{
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\definecolor{gradientpoint0}{rgb}{0,0,0.5}
\definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
\definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
\definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
\definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
\definecolor{gradientpoint5}{rgb}{1,1,1}
\def\positions{{0,0.3,0.4,0.88,0.94,1}}
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Gradient line \y/\twodperlinsize...}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
\pgfmathsetmacro{\v}{max(0,min(1,\v))}
\pgfmathsetmacro{\v}{abs(\v-0.5)*2}
\foreach \pointb in {1,...,5}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v <= \posb}
\ifnum 1=\pgfmathresult
\setintmacro{\pointa}{\pointb-1}
\pgfmathsetmacro{\posa}{\positions[\pointa]}
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\xdef\colora{gradientpoint\pointa}
\xdef\colorb{gradientpoint\pointb}
\xdef\mix{\mix}
\breakforeach
\fi
}
\path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
\end{figure}
}
\item<6-> Midpoint displacement.
\only<6-8>{
\begin{figure}[h]
\centering
\begin{tikzpicture}
% TODO : figure en 3 étapes
\end{tikzpicture}
\end{figure}
}
\item<9-> Simplex noise : généralisation des triangles équilatéraux à $n$ dimensions, interpolation par rapport aux coins. $d^2$ au lieu de $2^d$.
\item<10-> Bruit répétable 1D : points sur un cercle dans un espace 2D. Généralisation à $n$ dimensions : hypercercle $n$D dans un espace $2n$D.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Perlin noise (Variations)}
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\path (0,0) -- (0,129.5);
\only<1>{
\node[coordinate] (a) at (60:64) {};
\node[coordinate] (b) at (0,0) {};
\node[coordinate] (c) at (64,0) {};
\shade[shading=axis,bottom color=white,top color=gray!50,shading angle=60] (a) -- (b) -- (c) -- cycle;
\draw (a) -- (b) -- (c) -- cycle;
\node[fill=black,circle,inner sep=1pt] (p) at (20,15) {};
\draw[gray, densely dotted] (p) -- (a);
\draw[gray, densely dotted] (p) -- (b);
\draw[gray, densely dotted] (p) -- (c);
% Tétraèdre
\node[coordinate] (3a) at (132,{23+64*sqrt(24)/6},{64*sqrt(3)/6}) {};
\node[coordinate] (3b) at (100,23,0) {};
\node[coordinate] (3c) at (164,23,0) {};
\node[coordinate] (3d) at (132,23,{64*sqrt(3)/2}) {};
\draw (3a) -- (3b);
\draw (3b) -- (3d);
\draw (3d) -- (3a);
\draw (3a) -- (3c);
\draw (3c) -- (3d);
\draw[dashed] (3b) -- (3c);
\node[fill=black,circle,inner sep=1pt] (3p) at (135,30,30) {};
\draw[gray, densely dotted] (3p) -- (3a);
\draw[gray, densely dotted] (3p) -- (3b);
\draw[gray, densely dotted] (3p) -- (3c);
\draw[gray, densely dotted] (3p) -- (3d);
}
\only<2-4>{
\pgfmathsetmacro{\xalign}{164/2-128/2}
\pgfmathsetmacro{\circler}{\twodperlinsize*0.35}
\pgfmathsetmacro{\maxdiam}{\twodperlinsize}
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Gradient line \y/\twodperlinsize...}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
\setintmacro{\v}{max(0,min(512,int(\v*512)))}
\path[fill=\getcache{gradient,terrain,\v}] (\xalign+\x,\y) rectangle ++(1.5,1.5);
}
}
% TODO : couleur de la map sur la ligne.
\draw[->,gray] (\xalign+150,0) -- (\xalign+150+140,0);
\only<2>{
\draw[red,samples at={0,3,...,60}, smooth, mark=*, mark indices={0,20}, mark size=72] plot ({\xalign+xpointoncircle(\x,\circler,\maxdiam)},{ypointoncircle(\x,\circler,\maxdiam)});
\draw[red,samples at={0,3,...,60}, smooth, mark=*, mark indices={0,20}, mark size=72] plot ({\xalign+150+\x/360*70},{perlin2DCosine(xpointoncircle(\x,\circler,\maxdiam),ypointoncircle(\x,\circler,\maxdiam),16,3,0.5,35)});
}
\only<3>{
\draw[red,samples at={0,3,...,360}, smooth, mark=*, mark indices={0,20,40}, mark size=72] plot ({\xalign+xpointoncircle(\x,\circler,\maxdiam)},{ypointoncircle(\x,\circler,\maxdiam)});
\draw[red,samples at={0,3,...,360}, smooth, mark=*, mark indices={0,20,40}, mark size=72] plot ({\xalign+150+\x/360*70},{perlin2DCosine(xpointoncircle(\x,\circler,\maxdiam),ypointoncircle(\x,\circler,\maxdiam),16,3,0.5,35)});
}
\only<4>{
\draw[red,samples at={0,3,...,360}, smooth, mark=*, mark indices={0,20,40}, mark size=72] plot ({\xalign+xpointoncircle(\x,\circler,\maxdiam)},{ypointoncircle(\x,\circler,\maxdiam)});
\draw[red,samples at={0,3,...,360}, smooth, mark=*, mark indices={0,20,40,140,160}, mark size=72] plot ({\xalign+150+\x/360*70},{perlin2DCosine(xpointoncircle(\x,\circler,\maxdiam),ypointoncircle(\x,\circler,\maxdiam),16,3,0.5,35)});
}
}
\end{tikzpicture}
\end{figure}
\begin{itemize}
\item<1-> Simplex noise. $O(d^2)$ au lieu de $O(2^d)$.
\item<2-> Bruit répétable 1D : Cercle dans un espace 2D.\\Bruit répétable $n$D : hypercercle dans un espace $2n$D.
{\tiny\url{http://www.gamedev.net/blog/33/entry-2138456-seamless-noise/}}
\only<10-12>{
\begin{figure}[h]
\centering
\begin{tikzpicture}
% TODO : figure en 3 étapes
\end{tikzpicture}
\end{figure}
}
\end{itemize}
\end{frame}
\subsection{Craters et Hills Algorithm}
\begin{frame}
% Création du craters
\xdef\craterssize{128}
\xdef\maxvcraters{0}
\xdef\minvcraters{0}
\def\maxradius{32}
\def\ncircles{100}
\foreach \y in {1,2,...,\craterssize}{
\foreach \x in {1,2,...,\craterssize}{
\setcache{vcraters,\x,\y}{0}
}
}
\foreach \c in {1,...,\ncircles}{
\setintmacro{\circlex}{noise1D(\c,0)*\craterssize}
\setintmacro{\circley}{noise1D(\c,1)*\craterssize}
\setintmacro{\circler}{noise1D(\c,2)*\maxradius}
\message{Circle number \c/\ncircles, center (\circlex, \circley), radius \circler}
\foreach \dy in {-\circler,...,\circler}{
\setintmacro{\y}{\circley+\dy}
\pgfmathparse{(\y > 0) && (\y <= \craterssize)}
\ifnum 1=\pgfmathresult
\foreach \dx in {-\circler,...,\circler}{
\setintmacro{\x}{\circlex+\dx}
\pgfmathparse{(\x > 0) && (\x <= \craterssize)}
\ifnum 1=\pgfmathresult
\xdef\oldv{\getcache{vcraters,\x,\y}}
\pgfmathsetmacro{\v}{\oldv - max(0,\circler - ((\dx*\dx + \dy*\dy)/\circler))}
\setcache{vcraters,\x,\y}{\v}
\pgfmathparse{max(\maxvcraters,\v)}
\xdef\maxvcraters{\pgfmathresult}
\pgfmathparse{min(\minvcraters,\v)}
\xdef\minvcraters{\pgfmathresult}
\fi
}
\fi
}
}
% Création du perlin + craters
\xdef\cratersperlinsize{\twodperlinsize}
\xdef\maxvcratersperlin{\maxvtwodperlin}
\xdef\minvcratersperlin{\minvtwodperlin}
\def\maxradius{32}
\def\ncircles{20}
\foreach \y in {1,2,...,\cratersperlinsize}{
\foreach \x in {1,2,...,\cratersperlinsize}{
\setcache{vcratersperlin,\x,\y}{\getcache{vtwodperlin,\x,\y}}
}
}
\foreach \c in {1,...,\ncircles}{
\setintmacro{\circlex}{noise1D(\c,0)*\cratersperlinsize}
\setintmacro{\circley}{noise1D(\c,1)*\cratersperlinsize}
\setintmacro{\circler}{noise1D(\c,2)*\maxradius}
\message{Circle number \c/\ncircles, center (\circlex, \circley), radius \circler}
\foreach \dy in {-\circler,...,\circler}{
\setintmacro{\y}{\circley+\dy}
\pgfmathparse{(\y > 0) && (\y <= \cratersperlinsize)}
\ifnum 1=\pgfmathresult
\foreach \dx in {-\circler,...,\circler}{
\setintmacro{\x}{\circlex+\dx}
\pgfmathparse{(\x > 0) && (\x <= \cratersperlinsize)}
\ifnum 1=\pgfmathresult
\xdef\oldv{\getcache{vcratersperlin,\x,\y}}
\pgfmathparse{\oldv - max(0,\circler - ((\dx*\dx + \dy*\dy)/\circler))}
\setcache{vcratersperlin,\x,\y}{\pgfmathresult}
\pgfmathparse{max(\maxvcratersperlin,\pgfmathresult)}
\xdef\maxvcratersperlin{\pgfmathresult}
\pgfmathparse{min(\minvcratersperlin,\pgfmathresult)}
\xdef\minvcratersperlin{\pgfmathresult}
\fi
}
\fi
}
}
\frametitle{Craters et Hills Algorithm}
\only<2->{
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\definecolor{gradientpoint0}{rgb}{0,0,0.5}
\definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
\definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
\definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
\definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
\definecolor{gradientpoint5}{rgb}{1,1,1}
\def\positions{{0,0.3,0.4,0.88,0.94,1}}
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\path (300,0) ++(128,128) ++(1.5,1.5) rectangle (0,0);
\only<2->{
\foreach \y in {1,2,...,\craterssize}{
\message{Gradient line \y/\craterssize...}
\foreach \x in {1,2,...,\craterssize}{
\pgfmathsetmacro{\v}{(\getcache{vcraters,\x,\y}-\minvcraters)/max(1,\maxvcraters-\minvcraters)}
\pgfmathsetmacro{\v}{max(0,min(1,\v))}
\foreach \pointb in {1,...,5}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v < \posb}
\ifnum 1=\pgfmathresult
\setintmacro{\pointa}{\pointb-1}
\pgfmathsetmacro{\posa}{\positions[\pointa]}
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\xdef\colora{gradientpoint\pointa}
\xdef\colorb{gradientpoint\pointb}
\xdef\mix{\mix}
\breakforeach
\fi
}
\path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
\setintmacro{\v}{max(0,min(512,int(\v*512)))}
\path[fill=\getcache{gradient,terrain,\v}] (\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
\end{figure}
}
\only<3->{
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\definecolor{gradientpoint0}{rgb}{0,0,0.5}
\definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
\definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
\definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
\definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
\definecolor{gradientpoint5}{rgb}{1,1,1}
\def\positions{{0,0.3,0.4,0.88,0.94,1}}
}
\only<3->{
\foreach \y in {1,2,...,\cratersperlinsize}{
\message{Gradient line \y/\cratersperlinsize...}
\foreach \x in {1,2,...,\cratersperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vcratersperlin,\x,\y}-\minvcratersperlin)/max(1,\maxvcratersperlin-\minvcratersperlin)}
\pgfmathsetmacro{\v}{max(0,min(1,\v))}
\foreach \pointb in {1,...,5}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v <= \posb}
\ifnum 1=\pgfmathresult
\setintmacro{\pointa}{\pointb-1}
\pgfmathsetmacro{\posa}{\positions[\pointa]}
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\xdef\colora{gradientpoint\pointa}
\xdef\colorb{gradientpoint\pointb}
\xdef\mix{\mix}
\breakforeach
\fi
}
\path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
\setintmacro{\v}{max(0,min(512,int(\v*512)))}
\path[fill=\getcache{gradient,terrain,\v}] (150+\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
\end{figure}
}
\only<4->{
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
\definecolor{gradientpoint0}{rgb}{0,0,0.5}
\definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
\definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
\definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
\definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
\definecolor{gradientpoint5}{rgb}{1,1,1}
\def\positions{{0,0.3,0.4,0.88,0.94,1}}
}
\only<4->{
\foreach \y in {1,2,...,\craterssize}{
\message{Gradient line \y/\craterssize...}
\foreach \x in {1,2,...,\craterssize}{
\pgfmathsetmacro{\v}{(\getcache{vcraters,\x,\y}-\minvcraters)/max(1,\maxvcraters-\minvcraters)}
\pgfmathsetmacro{\v}{max(0,min(1,\v))}
\pgfmathsetmacro{\v}{1-\v}
\foreach \pointb in {1,...,5}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v < \posb}
\ifnum 1=\pgfmathresult
\setintmacro{\pointa}{\pointb-1}
\pgfmathsetmacro{\posa}{\positions[\pointa]}
\pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
\xdef\colora{gradientpoint\pointa}
\xdef\colorb{gradientpoint\pointb}
\xdef\mix{\mix}
\breakforeach
\fi
}
\path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
\setintmacro{\v}{max(0,min(512,int(\v*512)))}
\setintmacro{\v}{512-\v}
\path[fill=\getcache{gradient,terrain,\v}] (300+\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
\end{figure}
}
}
\end{tikzpicture}
\end{figure}
\begin{itemize}
\item<1-> Craters
\begin{itemize}
\item<1-> Soustraire des cercles au terrain ({\small $z = z - f(\text{distance au centre})$})
\item<1-> Soustraire des cercles au terrain {\small ($z = z - f(\text{distance au centre})$)}
\item<2-> Sur un terrain nu
\item<3-> Sur un terrain existant
\end{itemize}
\item<4-> Hills Algorithm~: ajouter des cercles
\item<5-> Stockage des cercles dans un arbre (BSP, Quadtree, LOD, \dots{}).
\item<5-> Stockage des cercles dans un arbre {\small (BSP, Quadtree, LOD, \dots{})}
\end{itemize}
\end{frame}
@ -608,14 +567,26 @@
\item<3-> Carte de circulation des eaux.
\item<4-> Pas temps-réel.
\item<5-6> Approximation : modification de la distribution des hauteurs.
% TODO : schéma en 2 étapes
\begin{figure}[h]
\centering
\begin{tikzpicture}
% Un dégradé vertical indiquant l'élévation de départ
% Fonction f(x) = x
% 2e dégradé indiquant le résultat.
% Même chose avec une autre fonction.
\begin{tikzpicture}[scale=0.025]
\path (300,0) ++(128,128) ++(1.5,1.5) rectangle (0,-2);
\foreach \y in {1,2,...,\twodperlinsize}{
\message{Gradient line \y/\twodperlinsize...}
\foreach \x in {1,2,...,\twodperlinsize}{
\pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
\only<6>{\pgfmathsetmacro{\v}{courbepoly(\v)}}
\setintmacro{\v}{max(0,min(512,int(\v*512)))}
\path[fill=\getcache{gradient,terrain,\v}] (\x,\y) rectangle ++(1.5,1.5);
\path[fill=\getcache{gradient,terrain,\v}] (300+\x,\y) rectangle ++(1.5,1.5);
}
}
\only<5>{ \draw[red, samples at={0,...,128}, smooth] plot (150+\x,\x); }
\only<6>{ \draw[red, samples at={0,...,128}, smooth] plot (150+\x,{courbepoly(\x/128) * 128}); }
\draw[->] (150,0) -- (150,128);
\draw[->] (150,0) -- (150+128,0);
\draw[gray!50] (150,128) -- (150+128,128);
\draw[gray!50] (150,0) -- (150+128,128);
\end{tikzpicture}
\end{figure}
\end{itemize}
@ -650,9 +621,9 @@
\frametitle{Rivières}
\begin{itemize}
\item<1-> Pathfinding {\tiny\url{http://www.umbrarumregnum.net/articles/creating-rivers}}
% Image
% TODO : Image (ne sera pas fait, manque de temps).
\item<2-4> Affinage du tracé en fonction du LOD.
% Schéma sur 3 niveaux d'affinage en 3 étapes.
% TODO : Schéma sur 3 niveaux d'affinage en 3 étapes.
\item<5-> Tracé arbitraire.
\item<6-> Intégration dans le terrain.
\end{itemize}
@ -679,7 +650,7 @@
\begin{frame}
\frametitle{Isosurfaces}
\begin{itemize}
\item Metaballs % TODO : écran de veille / screenshot.
\item Metaballs {\small \texttt{/usr/lib/xscreensaver/metaballs}}
\item Surface 2D d'un bruit 3D.
\item Simplification de nuages.
\item Surface de l'eau.