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https://github.com/scratchfoundation/paper.js.git
synced 2025-01-06 04:42:15 -05:00
Further optimise getParameter() / getLength() code by reusing a integrand function and taking advantage of integral ranges.
This commit is contained in:
Jürg Lehni
parent
3447d11a6f
commit
0e8c346888
1 changed files with 90 additions and 88 deletions
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@ -151,8 +151,13 @@ var Curve = this.Curve = Base.extend({
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];
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},
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getLength: function() {
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return Curve.getLength.apply(Curve, this.getCurveValues());
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// TODO: Port back to Scriptographer, optionally suppporting from, to
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// TODO: Replaces getPartLength(fromParameter, toParameter)?
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getLength: function(from, to) {
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var values = this.getCurveValues();
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if (arguments.length > 0)
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values.push(from, to);
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return Curve.getLength.apply(Curve, values);
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},
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/**
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@ -190,7 +195,6 @@ var Curve = this.Curve = Base.extend({
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// TODO: divide
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// TODO: split
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// TODO: getPartLength(fromParameter, toParameter)
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clone: function() {
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return new Curve(this._segment1, this._segment2);
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@ -204,91 +208,6 @@ var Curve = this.Curve = Base.extend({
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? ', handle2: ' + this._segment2._handleIn : '')
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+ ', point2: ' + this._segment2._point
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+ ' }';
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},
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statics: {
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getLength: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
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if (p1x == c1x && p1y == c1y && p2x == c2x && p2y == c2y) {
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// Straight line
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var dx = p2x - p1x,
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dy = p2y - p1y;
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return Math.sqrt(dx * dx + dy * dy);
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}
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// Calculate the coefficients of a Bezier derivative.
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var ax = 9 * (c1x - c2x) + 3 * (p2x - p1x),
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bx = 6 * (p1x + c2x) - 12 * c1x,
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cx = 3 * (c1x - p1x),
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ay = 9 * (c1y - c2y) + 3 * (p2y - p1y),
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by = 6 * (p1y + c2y) - 12 * c1y,
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cy = 3 * (c1y - p1y);
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function ds(t) {
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// Calculate quadratic equations of derivatives for x and y
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var dx = (ax * t + bx) * t + cx,
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dy = (ay * t + by) * t + cy;
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return Math.sqrt(dx * dx + dy * dy);
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}
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return Numerical.gauss(ds, 0.0, 1.0, 8);
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},
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subdivide: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) {
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var u = 1 - t,
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// Interpolate from 4 to 3 points
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p3x = u * p1x + t * c1x,
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p3y = u * p1y + t * c1y,
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p4x = u * c1x + t * c2x,
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p4y = u * c1y + t * c2y,
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p5x = u * c2x + t * p2x,
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p5y = u * c2y + t * p2y,
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// Interpolate from 3 to 2 points
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p6x = u * p3x + t * p4x,
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p6y = u * p3y + t * p4y,
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p7x = u * p4x + t * p5x,
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p7y = u * p4y + t * p5y,
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// Interpolate from 2 points to 1 point
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p8x = u * p6x + t * p7x,
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p8y = u * p6y + t * p7y;
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// We now have all the values we need to build the subcurves
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return [
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[p1x, p1y, p3x, p3y, p6x, p6y, p8x, p8y], // left
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[p8x, p8y, p7x, p7y, p5x, p5y, p2x, p2y] // right
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];
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},
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getPartLength: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t, right) {
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if (t == 0)
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return 0;
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var part;
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if (t < 1) {
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part = Curve.subdivide(p1x, p1y, c1x, c1y, c2x, c2y,
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p2x, p2y, t)[right ? 1 : 0];
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} else {
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part = arguments;
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}
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return Curve.getLength.apply(Curve, part);
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},
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getParameter: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, length) {
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if (length <= 0)
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return 0;
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var bezierLength = Curve.getLength(
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p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
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if (length >= bezierLength)
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return 1;
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// Let's use the Van Wijngaarden–Dekker–Brent Method to find
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// solutions more reliably than with False Position Method.
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function f(t) {
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return length - Curve.getPartLength(
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p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t);
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}
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// Use length / bezierLength for an initial guess for b, to bring
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// us closer:
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return Numerical.brent(f, 0, length / bezierLength,
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Numerical.TOLERANCE);
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}
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}
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}, new function() {
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function evaluate(that, t, type) {
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@ -356,6 +275,24 @@ var Curve = this.Curve = Base.extend({
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return type == 2 ? new Point(y, -x) : new Point(x, y);
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}
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function getLengthIntegrand(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
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// Calculate the coefficients of a Bezier derivative.
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var ax = 9 * (c1x - c2x) + 3 * (p2x - p1x),
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bx = 6 * (p1x + c2x) - 12 * c1x,
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cx = 3 * (c1x - p1x),
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ay = 9 * (c1y - c2y) + 3 * (p2y - p1y),
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by = 6 * (p1y + c2y) - 12 * c1y,
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cy = 3 * (c1y - p1y);
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return function(t) {
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// Calculate quadratic equations of derivatives for x and y
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var dx = (ax * t + bx) * t + cx,
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dy = (ay * t + by) * t + cy;
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return Math.sqrt(dx * dx + dy * dy);
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}
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}
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return {
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getPoint: function(parameter) {
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return evaluate(this, parameter, 0);
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@ -367,6 +304,71 @@ var Curve = this.Curve = Base.extend({
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getNormal: function(parameter) {
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return evaluate(this, parameter, 2);
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},
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statics: {
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getLength: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, a, b) {
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if (a == undefined)
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a = 0;
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if (b == undefined)
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b = 1;
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if (p1x == c1x && p1y == c1y && p2x == c2x && p2y == c2y) {
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// Straight line
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var mul = (b - a),
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dx = (p2x - p1x) * mul,
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dy = (p2y - p1y) * mul;
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return Math.sqrt(dx * dx + dy * dy);
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}
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var ds = getLengthIntegrand(
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p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
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return Numerical.gauss(ds, a, b, 8);
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},
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getParameter: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y,
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length) {
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if (length <= 0)
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return 0;
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// TODO: Optimise for straight lines
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var bezierLength = Curve.getLength(
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p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, 0, 1);
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if (length >= bezierLength)
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return 1;
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// Let's use the Van Wijngaarden–Dekker–Brent Method to find
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// solutions more reliably than with False Position Method.
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var ds = getLengthIntegrand(
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p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
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function f(t) {
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return length - Numerical.gauss(ds, 0, t, 5);
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}
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// Use length / bezierLength for an initial guess for b, to
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// bring us closer:
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return Numerical.brent(f, 0, length / bezierLength,
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Numerical.TOLERANCE);
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},
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subdivide: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) {
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var u = 1 - t,
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// Interpolate from 4 to 3 points
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p3x = u * p1x + t * c1x,
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p3y = u * p1y + t * c1y,
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p4x = u * c1x + t * c2x,
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p4y = u * c1y + t * c2y,
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p5x = u * c2x + t * p2x,
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p5y = u * c2y + t * p2y,
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// Interpolate from 3 to 2 points
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p6x = u * p3x + t * p4x,
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p6y = u * p3y + t * p4y,
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p7x = u * p4x + t * p5x,
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p7y = u * p4y + t * p5y,
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// Interpolate from 2 points to 1 point
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p8x = u * p6x + t * p7x,
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p8y = u * p6y + t * p7y;
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// We now have all the values we need to build the subcurves
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return [
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[p1x, p1y, p3x, p3y, p6x, p6y, p8x, p8y], // left
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[p8x, p8y, p7x, p7y, p5x, p5y, p2x, p2y] // right
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];
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}
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}
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};
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});
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