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/*
* Copyright (C) 2014 Apple Inc. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. AND ITS CONTRIBUTORS ``AS IS''
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR ITS CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
WebInspector.UnitBezier = function(x1, y1, x2, y2)
{
WebInspector.Object.call(this);
// Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
this._cx = 3.0 * x1;
this._bx = 3.0 * (x2 - x1) - this._cx;
this._ax = 1.0 - this._cx - this._bx;
this._cy = 3.0 * y1;
this._by = 3.0 * (y2 - y1) - this._cy;
this._ay = 1.0 - this._cy - this._by;
};
WebInspector.UnitBezier.prototype = {
constructor: WebInspector.UnitBezier,
// Public
solve: function(x, epsilon)
{
return this._sampleCurveY(this._solveCurveX(x, epsilon));
},
// Private
_sampleCurveX: function(t)
{
// `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
return ((this._ax * t + this._bx) * t + this._cx) * t;
},
_sampleCurveY: function(t)
{
return ((this._ay * t + this._by) * t + this._cy) * t;
},
_sampleCurveDerivativeX: function(t)
{
return (3.0 * this._ax * t + 2.0 * this._bx) * t + this._cx;
},
// Given an x value, find a parametric value it came from.
_solveCurveX: function(x, epsilon)
{
var t0, t1, t2, x2, d2, i;
// First try a few iterations of Newton's method -- normally very fast.
for (t2 = x, i = 0; i < 8; i++) {
x2 = this._sampleCurveX(t2) - x;
if (Math.abs(x2) < epsilon)
return t2;
d2 = this._sampleCurveDerivativeX(t2);
if (Math.abs(d2) < 1e-6)
break;
t2 = t2 - x2 / d2;
}
// Fall back to the bisection method for reliability.
t0 = 0.0;
t1 = 1.0;
t2 = x;
if (t2 < t0)
return t0;
if (t2 > t1)
return t1;
while (t0 < t1) {
x2 = this._sampleCurveX(t2);
if (Math.abs(x2 - x) < epsilon)
return t2;
if (x > x2)
t0 = t2;
else
t1 = t2;
t2 = (t1 - t0) * 0.5 + t0;
}
// Failure.
return t2;
}
};
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