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/*
* Copyright (C) 2013 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.
*/
WI.CubicBezierTimingFunction = class CubicBezierTimingFunction
{
constructor(x1, y1, x2, y2)
{
this._inPoint = new WI.Point(x1, y1);
this._outPoint = new WI.Point(x2, y2);
// Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
this._curveInfo = {
x: {c: 3.0 * x1},
y: {c: 3.0 * y1}
};
this._curveInfo.x.b = 3.0 * (x2 - x1) - this._curveInfo.x.c;
this._curveInfo.x.a = 1.0 - this._curveInfo.x.c - this._curveInfo.x.b;
this._curveInfo.y.b = 3.0 * (y2 - y1) - this._curveInfo.y.c;
this._curveInfo.y.a = 1.0 - this._curveInfo.y.c - this._curveInfo.y.b;
}
// Static
static fromCoordinates(coordinates)
{
if (!coordinates || coordinates.length < 4)
return null;
coordinates = coordinates.map(Number);
if (coordinates.includes(NaN))
return null;
return new WI.CubicBezierTimingFunction(coordinates[0], coordinates[1], coordinates[2], coordinates[3]);
}
static fromString(text)
{
if (!text || !text.length)
return null;
var trimmedText = text.toLowerCase().replace(/\s/g, "");
if (!trimmedText.length)
return null;
if (Object.keys(WI.CubicBezierTimingFunction.keywordValues).includes(trimmedText))
return WI.CubicBezierTimingFunction.fromCoordinates(WI.CubicBezierTimingFunction.keywordValues[trimmedText]);
var matches = trimmedText.match(/^cubic-bezier\(([-\d.]+),([-\d.]+),([-\d.]+),([-\d.]+)\)$/);
if (!matches)
return null;
matches.splice(0, 1);
return WI.CubicBezierTimingFunction.fromCoordinates(matches);
}
// Public
get inPoint()
{
return this._inPoint;
}
get outPoint()
{
return this._outPoint;
}
copy()
{
return new WI.CubicBezierTimingFunction(this._inPoint.x, this._inPoint.y, this._outPoint.x, this._outPoint.y);
}
toString()
{
var values = [this._inPoint.x, this._inPoint.y, this._outPoint.x, this._outPoint.y];
for (var key in WI.CubicBezierTimingFunction.keywordValues) {
if (Array.shallowEqual(WI.CubicBezierTimingFunction.keywordValues[key], values))
return key;
}
return "cubic-bezier(" + values.join(", ") + ")";
}
solve(x, epsilon)
{
return this._sampleCurveY(this._solveCurveX(x, epsilon));
}
// Private
_sampleCurveX(t)
{
// `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
return ((this._curveInfo.x.a * t + this._curveInfo.x.b) * t + this._curveInfo.x.c) * t;
}
_sampleCurveY(t)
{
return ((this._curveInfo.y.a * t + this._curveInfo.y.b) * t + this._curveInfo.y.c) * t;
}
_sampleCurveDerivativeX(t)
{
return (3.0 * this._curveInfo.x.a * t + 2.0 * this._curveInfo.x.b) * t + this._curveInfo.x.c;
}
// Given an x value, find a parametric value it came from.
_solveCurveX(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;
}
};
WI.CubicBezierTimingFunction.keywordValues = {
"ease": [0.25, 0.1, 0.25, 1],
"ease-in": [0.42, 0, 1, 1],
"ease-out": [0, 0, 0.58, 1],
"ease-in-out": [0.42, 0, 0.58, 1],
"linear": [0, 0, 1, 1]
};
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