var Transform = require('./transform.js');

var ANGLES = 12;
var CROWD = 4;
var LOOSE = 6;
var SMALL = 1e-4
function cross(z1, z2, z3){
	return (z2.x - z1.x) * (z3.y - z1.y) - (z3.x - z1.x) * (z2.y - z1.y)
};
function dot(z1, z2, z3){
	return (z2.x - z1.x) * (z3.x - z1.x) + (z3.y - z1.y) * (z2.y - z1.y)
};
function solveTS(a, b, c, out, flag){
	var delta = b * b - 4 * a * c;
	if(delta > 0){
		var t1 = (Math.sqrt(delta) - b) / (2 * a)
		var t2 = (-Math.sqrt(delta) - b) / (2 * a)
		if(flag){
			if(t1 >= 0 && t1 <= 1) out.push(t1)
			if(t2 >= 0 && t2 <= 1) out.push(t2)
		} else {
			if(t1 > 0 && t1 < 1) out.push(t1)
			if(t2 > 0 && t2 < 1) out.push(t2)
		}
	} else if (delta === 0){
		var t = -b / (2 * a)
		if(flag){
			if(t >= 0 && t <= 1) out.push(t)
		} else {
			if(t > 0 && t < 1) out.push(t)
		}
	};
}
function findExtrema(z1, z2, z3, z4, out){
	var a = 3 * (-z1.y + 3 * z2.y - 3 * z3.y + z4.y);
	var b = 6 * (z1.y - 2 * z2.y + z3.y);
	var c = 3 * (z2.y - z1.y);
	solveTS(a, b, c, out);
};
function findInflections(z1, z2, z3, z4, out){
	var ax = z2.x - z1.x;
	var ay = z2.y - z1.y;
	var bx = z3.x - z2.x - ax;
	var by = z3.y - z2.y - ay;
	var cx = z4.x - z3.x - ax - 2 * bx;
	var cy = z4.y - z3.y - ay - 2 * by;
	solveTS(bx * cy - by * cx, ax * cy - ay * cx, ax * by - ay * bx, out, true)
}
function rotate(z, angle){
	var c = Math.cos(angle), s = Math.sin(angle);
	return {
		x: c * z.x + s * z.y,
		y : -s * z.x + c * z.y
	}
};
function ASCEND(a, b){ return a - b }
function fineAllExtremae(z1, z2, z3, z4, angles){
	var exs = [];
	findInflections(z1, z2, z3, z4, exs);
	for(var a = 0; a < angles; a += 1){
		findExtrema(z1, z2, z3, z4, exs);
		z1 = rotate(z1, Math.PI / angles);
		z2 = rotate(z2, Math.PI / angles);
		z3 = rotate(z3, Math.PI / angles);
		z4 = rotate(z4, Math.PI / angles);
	}
	return exs.sort(ASCEND)
};
function mix(z1, z2, t){
	return {x: (1 - t) * z1.x + t * z2.x, y: (1 - t) * z1.y + t * z2.y}
};
function bez2(z1, z2, z3, t){
	return {
		x: (1 - t) * (1 - t) * z1.x + 2 * (1 - t) * t * z2.x + t * t * z3.x,
		y: (1 - t) * (1 - t) * z1.y + 2 * (1 - t) * t * z2.y + t * t * z3.y
	}
};
function bez3(z1, z2, z3, z4, t){
	return {
		x: (1 - t) * (1 - t) * (1 - t) * z1.x
			+ 3 * t * (1 - t) * (1 - t) * z2.x
			+ 3 * t * t * (1 - t) * z3.x
			+ t * t * t *z4.x,
		y: (1 - t) * (1 - t) * (1 - t) * z1.y
			+ 3 * t * (1 - t) * (1 - t) * z2.y
			+ 3 * t * t * (1 - t) * z3.y
			+ t * t * t *z4.y
	}
};
function splitBefore(z1, z2, z3, z4, t){
	return [z1, mix(z1, z2, t), bez2(z1, z2, z3, t), bez3(z1, z2, z3, z4, t)]
};
function splitAfter(z1, z2, z3, z4, t){
	return [bez3(z1, z2, z3, z4, t), bez2(z2, z3, z4, t), mix(z3, z4, t), z4]
};
function splitAtExtremae(z1, z2, z3, z4, angles, splitpoints){
	var ts = fineAllExtremae(z1, z2, z3, z4, angles);
	if(ts[0] < SMALL) {
		ts[0] = 0;
	} else {
		ts.unshift(0);
	}
	if(ts[ts.length - 1] > 1 - SMALL) {
		ts[ts.length - 1] = 1;
	} else {
		ts.push(1);
	};
	for(var k = 0; k < ts.length; k++){
		if(k > 0){
			var t1 = ts[k - 1]; var t2 = ts[k];
			var bef = splitBefore(z1, z2, z3, z4, t2);
			var seg = splitAfter(bef[0], bef[1], bef[2], bef[3], t1 / t2);
			seg[1].onCurve = seg[2].onCurve = false;
			seg[1].cubic = seg[2].cubic = true;
			seg[3].onCurve = true;
			splitpoints.push(seg[1],seg[2],seg[3]);
		}
	};
};
function splitSegment(z1, z2, z3, z4, angles, splitpoints){
	var ts = [];
	var inflectAtEnd = false;
	findInflections(z1, z2, z3, z4, ts);
	ts = ts.sort(ASCEND);
	if(ts[0] < SMALL) {
		ts[0] = 0;
		splitpoints[splitpoints.length - 1].inflect = true;
	} else {
		ts.unshift(0);
	}
	if(ts[ts.length - 1] > 1 - SMALL) {
		inflectAtEnd = true;
		ts[ts.length - 1] = 1;
	} else {
		ts.push(1);
	};
	for(var k = 0; k < ts.length; k++){
		if(k > 0) {
			var t1 = ts[k - 1]; var t2 = ts[k];
			var bef = splitBefore(z1, z2, z3, z4, t2);
			var seg = splitAfter(bef[0], bef[1], bef[2], bef[3], t1 / t2);
			splitAtExtremae(seg[0], seg[1], seg[2], seg[3], angles, splitpoints);
			if(t2 < 1 || inflectAtEnd) splitpoints[splitpoints.length - 1].inflect = true;
		}
	};
};
function fitpts(p1, c1, c2, p2){
	var d1 = {x : c1.x - p1.x, y: c1.y - p1.y}
	var d2 = {x : c2.x - p2.x, y: c2.y - p2.y}
	
	var det = d2.x * d1.y - d2.y * d1.x;
	if(Math.abs(det) < 1e-6) return null;
	var u = ((p2.y - p1.y) * d2.x - (p2.x - p1.x) * d2.y) / det
	var v = ((p2.y - p1.y) * d1.x - (p2.x - p1.x) * d1.y) / det
	if(u <= 0 || v <= 0) return null;
	var mid = {
		x: p1.x + d1.x * u,
		y: p1.y + d1.y * u
	}
	return [mix(mid, p1, 1/3), mix(mid, p2, 1/3)]
};
function close(z1, z2){
	return (z1.x - z2.x) * (z1.x - z2.x) + (z1.y - z2.y) * (z1.y - z2.y) <= SMALL
}
function fairify(scurve, gizmo, angles){
	angles = angles || ANGLES
	for(var j = 0; j < scurve.length; j++){
		scurve[j] = Transform.untransform(gizmo, scurve[j])
	}
	var splitpoints = [scurve[0]];
	var last = scurve[0];
	for(var j = 1; j < scurve.length; j++){
		if(scurve[j].onCurve){
			splitpoints.push(last = scurve[j])
		} else if(scurve[j].cubic) {
			var z1 = last, z2 = scurve[j], z3 = scurve[j + 1], z4 = scurve[j + 2];
			if(!(close(z1, z2) && close(z2, z3) && close(z3, z4))) {
				splitSegment(z1, z2, z3, z4, ANGLES, splitpoints);
				last = z4;
			}
			j += 2;
		} else {
			var z1 = last, zm = scurve[j], z4 = scurve[j + 1]
			if(!(close(z1, zm) && close(zm, z4))) {
				var z2 = mix(zm, z1, 1/3);
				var z3 = mix(zm, z4, 1/3);
				splitSegment(z1, z2, z3, z4, ANGLES, splitpoints);
				last = z4;
			}
			j += 1;
		}
	};
	// Mark infections and extremae
	for(var j = 1; j < splitpoints.length - 1; j++) {
		if(splitpoints[j].onCurve && !splitpoints[j - 1].onCurve && !splitpoints[j + 1].onCurve){
			var z1 = splitpoints[j], z0 = splitpoints[j - 1], z2 = splitpoints[j + 1]
			if(cross(z1, z0, z2) < 1e-6 && dot(z1, z0, z2) < 0){
				var isInflection = false;
				if(j > 2 && j < splitpoints.length - 2){
					var za = bez3(z1, z0, splitpoints[j - 2], splitpoints[j - 3], SMALL);
					var zb = bez3(z1, z2, splitpoints[j + 2], splitpoints[j + 3], SMALL);
					var inflect = ((z0.y-z2.y)*(za.x-z0.x) + (z2.x-z0.x)*(za.y-z0.y)) * ((z0.y-z2.y)*(zb.x-z0.x) + (z2.x-z0.x)*(zb.y-z0.y));
					if(inflect < 0) isInflection = true;
				};
				if(!(z1.inflect || isInflection)) {
					var angle0 = Math.atan2(z2.y - z0.y, z2.x - z0.x);
					var angle = Math.abs(angle0 / Math.PI * 2 % 1);
					if(Math.abs(Math.abs(angle0) - Math.PI / 2) <= SMALL || angle <= SMALL || angle >= 1 - SMALL){
						z1.mark = true;
					}
				} else {
					z1.mark = true;
				}
			} else {
				z1.mark = true;
			}
		} else if(splitpoints[j].onCurve) {
			splitpoints[j].mark = true // corner
		}
	};
	splitpoints[0].mark = splitpoints[splitpoints.length - 1].mark = true;
	
	// Mark diagonals
	var lastmark = splitpoints[0];
	for(var j = 1; j < splitpoints.length - 1; j++) {
		if(splitpoints[j].mark){
			lastmark = splitpoints[j];
			for(var k = j + 1; k < splitpoints.length && !splitpoints[k].mark; k++);
			nextmark = splitpoints[k];
			var hspan = Math.abs(lastmark.x - nextmark.x);
			var vspan = Math.abs(lastmark.y - nextmark.y);
		}
		if(splitpoints[j].onCurve && !splitpoints[j].mark){
			var z1 = splitpoints[j], z0 = splitpoints[j - 1], z2 = splitpoints[j + 1];
			var angle0 = Math.atan2(z2.y - z0.y, z2.x - z0.x);
			var angle = Math.abs(angle0 / Math.PI * (hspan <= 10 * LOOSE || vspan <= 10 * LOOSE  ? CROWD : LOOSE) % 1);
			if(!(Math.abs(Math.abs(angle0) - Math.PI / 2) <= SMALL || angle <= SMALL || angle >= 1 - SMALL)){
				z1.remove = z0.remove = z2.remove = true;
			}
		}
	};
	for(var j = 0; j < splitpoints.length; j++) if(splitpoints[j].onCurve && !splitpoints[j].remove && splitpoints[j + 1] && !splitpoints[j + 1].onCurve){
		for(var k = j + 2; k < splitpoints.length && splitpoints[k].remove; k++);
		if(k - j > 2){
			var zs = fitpts(splitpoints[j], splitpoints[j + 1], splitpoints[k], splitpoints[k + 1]);
			if(zs){
				zs[0].onCurve = zs[1].onCurve = false;
				zs[0].cubic = zs[1].cubic = true;
				splitpoints[j + 1] = zs[0];
				splitpoints[k] = zs[1];
			}
		}
		j = k;
	};
	var ans = []
	for(var j = 0; j < splitpoints.length; j++) if(splitpoints[j] && !splitpoints[j].remove) {
		ans.push(Transform.transformPoint(gizmo, splitpoints[j]))
	}
	return ans
}
module.exports = fairify;