node_modules/@mapbox/unitbezier/index.js

/*
 * 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));
};