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https://github.com/scratchfoundation/paper.js.git
synced 2025-01-01 02:38:43 -05:00
Move curvature calculations into Curve.evaluate(), and define unit tests for it.
This commit is contained in:
Jürg Lehni
parent
619a8f88f8
commit
258c404b98
2 changed files with 38 additions and 57 deletions
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@ -444,14 +444,14 @@ statics: {
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cy = 3 * (c1y - p1y),
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by = 3 * (c2y - c1y) - cy,
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ay = p2y - p1y - cy - by;
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switch (type) {
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case 0: // point
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if (type === 0) {
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// Calculate the curve point at parameter value t
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x = ((ax * t + bx) * t + cx) * t + p1x;
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y = ((ay * t + by) * t + cy) * t + p1y;
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break;
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case 1: // tangent, 1st derivative
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case 2: // normal, 1st derivative
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} else {
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// 1: tangent, 1st derivative
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// 2: normal, 1st derivative
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// 3: curvature, 1st derivative & 2nd derivative
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// Prevent tangents and normals of length 0:
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// http://stackoverflow.com/questions/10506868/
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var tMin = /*#=*/ Numerical.TOLERANCE;
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@ -465,11 +465,14 @@ statics: {
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x = (3 * ax * t + 2 * bx) * t + cx;
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y = (3 * ay * t + 2 * by) * t + cy;
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}
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break;
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case 3: // 2nd derivative
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x = 6 * ax * t + 2 * bx;
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y = 6 * ay * t + 2 * by;
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break;
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if (type === 3) {
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// Calculate 2nd derivative, and curvature from there:
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// http://cagd.cs.byu.edu/~557/text/ch2.pdf page#31
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// k = |dx * d2y - dy * d2x| / (( dx^2 + dy^2 )^(3/2))
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var x2 = 6 * ax * t + 2 * bx,
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y2 = 6 * ay * t + 2 * by;
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return (x * y2 - y * x2) / Math.pow(x * x + y * y, 3 / 2);
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}
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}
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}
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// The normal is simply the rotated tangent:
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@ -771,7 +774,7 @@ statics: {
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* @bean
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* @ignore
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*/
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}), Base.each(['getPoint', 'getTangent', 'getNormal'],
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}), Base.each(['getPoint', 'getTangent', 'getNormal', 'getCurvatureAt'],
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// Note: Although Curve.getBounds() exists, we are using Path.getBounds() to
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// determine the bounds of Curve objects with defined segment1 and segment2
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// values Curve.getBounds() can be used directly on curve arrays, without
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@ -788,52 +791,6 @@ statics: {
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};
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},
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/** @lends Curve# */{
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/**
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* Calculate the curvature at the specified offset on the path.
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* Curvature indicates how sharply it curves. A straight line has zero
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* curvature where as a circle has a constant curvature.
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*
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* Curvature at a point, by definition, is a scalar value equal to
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* the reciprocal of the 'osculating circle' at that point on the path.
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*
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* Reference:
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* http://cagd.cs.byu.edu/~557/text/ch2.pdf page#31
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*
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* @param {Number} offset the offset on the curve, or the curve time
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* parameter if {@code isParameter} is {@code true}
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* @param {Boolean} [isParameter=false] pass {@code true} if {@code offset}
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* is a curve time parameter.
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* @return {Number} Curvatue of the curve at specified offset
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*/
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getCurvatureAt: function(offset, isParameter) {
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var values = this.getValues();
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if (offset === 0
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|| isParameter ? offset === 1 : offset === this.getLength()) {
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// We're at an end point:
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// k = (2/3) * h / a^2
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var line, point;
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if (offset === 0) {
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line = new Line(values[0], values[1], values[2], values[3]);
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point = new Point(values[4], values[5]);
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} else {
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line = new Line(values[6], values[7], values[4], values[5]);
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point = new Point(values[2], values[3]);
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}
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var a = line.getLength(),
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h = line.getDistance(point);
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return 2 * h / (3 * a * a);
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} else {
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// k = |dx * d2y - dy * d2x| / (( dx^2 + dy^2 )^(3/2))
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// First derivative at offset/parameter
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var dt = Curve.evaluate(values, offset, isParameter, 1),
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// Second derivative at offset/parameter
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d2t = Curve.evaluate(values, offset, isParameter, 3),
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dx = dt.x,
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dy = dt.y;
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return (dx * d2t.y - dy * d2t.x) / Math.pow(dx * dx + dy * dy, 3 / 2);
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}
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},
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/**
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* Calculates the curve time parameter of the specified offset on the path,
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* relative to the provided start parameter. If offset is a negative value,
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@ -963,6 +920,8 @@ statics: {
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/**
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* Returns the curvature vector of the curve at the specified position.
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* Curvatures indicate how sharply a curve changes direction. A straight
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* line has zero curvature where as a circle has a constant curvature.
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*
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* @name Curve#getCurvatureAt
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* @function
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@ -95,3 +95,25 @@ test('Curve#getCurvatureAt()', function() {
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'curve.getCurvatureAt(' + entry[0] + ', true);');
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}
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});
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test('Curve#getCurvatureAt()', function() {
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var curve = new Path.Line({
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from: [100, 100],
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to: [200, 200],
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}).getFirstCurve();
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var curvatures = [
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[0, 0],
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[0.25, 0],
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[0.5, 0],
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[0.75, 0],
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[1, 0]
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];
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for (var i = 0; i < curvatures.length; i++) {
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var entry = curvatures[i];
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compareNumbers(curve.getCurvatureAt(entry[0], true), entry[1],
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'curve.getCurvatureAt(' + entry[0] + ', true);');
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}
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});
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