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Implement new Curve.isFlatEnough().
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@ -579,6 +579,21 @@ var Curve = this.Curve = Base.extend(/** @lends Curve# */{
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},
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isFlatEnough: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
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// Code from Nearest Point-on-Curve Problem and by Philip J.
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// Schneider from "Graphics Gems", Academic Press, 1990, adapted
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// and optimised for cubic bezier curves.
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// Derive the implicit equation for line connecting first and last
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// control points
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var a = p1y - p2y,
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b = p2x - p1x,
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c = p1x * p2y - p2x * p1y,
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// Find the largest distance
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// Compute distance from each of the points to that line
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v1 = a * c1x + b * c1y + c,
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v2 = a * c2x + b * c2y + c;
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// Compute intercepts of bounding box
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return Math.abs((v1 * v1 + v2 * v2) / (a * (a * a + b * b))) < 0.005;
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/*
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// Inspired by Skia, but to be tested:
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// Calculate 1/3 (m1) and 2/3 (m2) along the line between start (p1)
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// and end (p2), measure distance from there the control points and
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@ -595,6 +610,7 @@ var Curve = this.Curve = Base.extend(/** @lends Curve# */{
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return Math.max(
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Math.abs(m1x - c1x), Math.abs(m1y - c1y),
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Math.abs(m2x - c1x), Math.abs(m1y - c1y)) < 1 / 2;
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*/
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/*
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// Thanks to Kaspar Fischer for the following:
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// http://www.inf.ethz.ch/personal/fischerk/pubs/bez.pdf
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