dojox/gfx/bezierutils.js

Dojo eXtensions, a rollup of many useful sub-projects and varying states of maturity – from very stable and robust, to alpha and experimental. See individual projects contain README files for details.

define([
	"./_base"
], function(gfx){

	var bu = gfx.bezierutils = {},
		error = 0.1;

	var tAtLength = bu.tAtLength = function(points, length){
		// summary:
		//		Returns the t corresponding to the given length for the specified bezier curve.
		// points: Number[]
		//		The bezier points. Should be [p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y] for a cubic
		//		bezier curve or [p1x, p1y, cx, cy, p2x, p2y] for a quadratic bezier curve.
		// length: Number
		//		The length.
		var t = 0,
			quadratic = points.length == 6,
			currentLen = 0,
			splitCount = 0,
			splitFunc = quadratic ? splitQBezierAtT : splitBezierAtT;
		var _compute = function(p, error){
			// control points polygon length
			var pLen = 0;
			for(var i = 0; i < p.length-2; i+=2)
				pLen += distance(p[i],p[i+1],p[i+2],p[i+3]);
			// chord length
			var chord = quadratic ?
				distance(points[0],points[1],points[4],points[5]) :
				distance(points[0],points[1],points[6],points[7]);
			// if needs more approx. or if currentLen is greater than the target length,
			// split the curve one more time
			if(pLen - chord > error || currentLen + pLen > length + error){
				++splitCount;
				var newbezier = splitFunc(p, .5);
				// check 1st subpath
				_compute(newbezier[0], error);
				// the 1st subcurve was the good one, we stop
				if(Math.abs(currentLen - length) <= error){
					return;
				}
				// need to continue with the 2nde subcurve
				_compute(newbezier[1], error);
				return ;
			}
			currentLen += pLen;
			t += 1.0 / (1 << splitCount);
		};
		if(length)
			_compute(points, 0.5);
		return t;
	};

	var computeLength = bu.computeLength = function(/*Array*/points){
		// summary:
		//		Returns the length of the given bezier curve.
		// points: Number[]
		//		The bezier points. Should be [p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y] for a cubic
		//		bezier curve or [p1x, p1y, cx, cy, p2x, p2y] for a quadratic bezier curve.

		var quadratic = points.length == 6, pLen=0;
		// control points polygon length
		for(var i = 0; i < points.length-2; i+=2)
			pLen += distance(points[i],points[i+1],points[i+2],points[i+3]);
		// chord length
		var chord = quadratic ?
			distance(points[0],points[1],points[4],points[5]) :
			distance(points[0],points[1],points[6],points[7]);
		// split polygons until the polygon and the chord are "the same"
		if(pLen-chord>error){
			var newBeziers = quadratic ? splitQBezierAtT(points,.5) : splitCBezierAtT(points,.5);
			var length = computeLength(newBeziers[0], quadratic);
			length += computeLength(newBeziers[1], quadratic);
			return length;
		}
		// pLen is close enough, done.
		return pLen;
	};

	var distance = bu.distance = function(x1, y1, x2, y2){
		// summary:
		//		Returns the distance between the specified points.
		return Math.sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
	};

	var splitQBezierAtT = function(points, t){
		// summary:
		//		Split a quadratic bezier curve into 2 sub-quadratic beziers at the specified t.

		// de Casteljau
		var r = 1-t,
			r2 = r*r,
			t2 = t*t,
			p1x = points[0],
			p1y = points[1],
			cx = points[2],
			cy = points[3],
			p2x = points[4],
			p2y = points[5],

			ax = r*p1x + t*cx,
			ay = r*p1y + t*cy,
			bx = r*cx + t*p2x,
			by = r*cy + t*p2y,
			px = r2*p1x + 2*r*t*cx + t2*p2x,
			py = r2*p1y + 2*r*t*cy + t2*p2y;

		return [
			[
				p1x, p1y,
				ax, ay,
				px, py
			],
			[
				px, py,
				bx, by,
				p2x, p2y
			]
		];
	};

	var splitCBezierAtT = function(points, t){
		// summary:
		//		Split a cubic bezier curve into 2 sub-cubic beziers at the specified t.

		// de Casteljau
		var r = 1-t,
			r2 = r*r,
			r3 = r2*r,
			t2 = t*t,
			t3 = t2*t,
			p1x = points[0],
			p1y = points[1],
			c1x = points[2],
			c1y = points[3],
			c2x = points[4],
			c2y = points[5],
			p2x = points[6],
			p2y = points[7],

			ax = r*p1x + t*c1x,
			ay = r*p1y + t*c1y,
			cx = r*c2x + t*p2x,
			cy = r*c2y + t*p2y,
			mx = r2*p1x + 2*r*t*c1x + t2*c2x,
			my = r2*p1y + 2*r*t*c1y + t2*c2y,
			nx = r2*c1x + 2*r*t*c2x + t2*p2x,
			ny = r2*c1y + 2*r*t*c2y + t2*p2y,
			px = r3*p1x + 3*r2*t*c1x + 3*r*t2*c2x+t3*p2x,
			py = r3*p1y + 3*r2*t*c1y + 3*r*t2*c2y+t3*p2y;

		return [
			[
				p1x, p1y,
				ax, ay,
				mx, my,
				px, py
			],
			[
				px, py,
				nx, ny,
				cx, cy,
				p2x, p2y
			]
		];
	};

	var splitBezierAtT = bu.splitBezierAtT = function(points, t){
		return points.length == 6 ? splitQBezierAtT(points, t) : splitCBezierAtT(points, t);
	};
	return bu;
});