/* * Copyright (C) 2008 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. ``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 * 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. * * Ported from Webkit * http://svn.webkit.org/repository/webkit/trunk/Source/WebCore/platform/graphics/UnitBezier.h */ module.exports = UnitBezier; function UnitBezier(p1x, p1y, p2x, p2y) { // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1). this.cx = 3.0 * p1x; this.bx = 3.0 * (p2x - p1x) - this.cx; this.ax = 1.0 - this.cx - this.bx; this.cy = 3.0 * p1y; this.by = 3.0 * (p2y - p1y) - this.cy; this.ay = 1.0 - this.cy - this.by; this.p1x = p1x; this.p1y = p2y; this.p2x = p2x; this.p2y = p2y; } UnitBezier.prototype.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; }; UnitBezier.prototype.sampleCurveY = function(t) { return ((this.ay * t + this.by) * t + this.cy) * t; }; UnitBezier.prototype.sampleCurveDerivativeX = function(t) { return (3.0 * this.ax * t + 2.0 * this.bx) * t + this.cx; }; UnitBezier.prototype.solveCurveX = function(x, epsilon) { if (typeof epsilon === 'undefined') epsilon = 1e-6; var t0, t1, t2, x2, 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; var 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; }; UnitBezier.prototype.solve = function(x, epsilon) { return this.sampleCurveY(this.solveCurveX(x, epsilon)); };