705bdfb3de
Co-authored-by: Bart Louwers <bart@emeel.net> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Bart Louwers <bart.louwers@gmail.com>
120 lines
4.0 KiB
C++
120 lines
4.0 KiB
C++
/*
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* Copyright (C) 2008 Apple Inc. All Rights Reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
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* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
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* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#pragma once
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#include <cmath>
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#include <tuple>
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namespace mbgl {
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namespace util {
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struct UnitBezier {
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/// Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
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constexpr UnitBezier(double p1x, double p1y, double p2x, double p2y) noexcept
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: cx(3.0 * p1x),
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bx(3.0 * (p2x - p1x) - (3.0 * p1x)),
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ax(1.0 - (3.0 * p1x) - (3.0 * (p2x - p1x) - (3.0 * p1x))),
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cy(3.0 * p1y),
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by(3.0 * (p2y - p1y) - (3.0 * p1y)),
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ay(1.0 - (3.0 * p1y) - (3.0 * (p2y - p1y) - (3.0 * p1y))) {}
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std::pair<double, double> getP1() const noexcept { return {cx / 3.0, cy / 3.0}; }
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std::pair<double, double> getP2() const noexcept {
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return {
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(bx + (3.0 * cx / 3.0) + cx) / 3.0,
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(by + (3.0 * cy / 3.0) + cy) / 3.0,
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};
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}
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double sampleCurveX(double t) const noexcept {
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// `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
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return ((ax * t + bx) * t + cx) * t;
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}
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double sampleCurveY(double t) const noexcept { return ((ay * t + by) * t + cy) * t; }
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double sampleCurveDerivativeX(double t) const noexcept { return (3.0 * ax * t + 2.0 * bx) * t + cx; }
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/// Given an x value, find a parametric value it came from.
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double solveCurveX(double x, double epsilon) const noexcept {
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double t0;
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double t1;
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double t2;
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double x2;
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double d2;
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int i;
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// First try a few iterations of Newton's method -- normally very fast.
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for (t2 = x, i = 0; i < 8; ++i) {
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x2 = sampleCurveX(t2) - x;
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if (fabs(x2) < epsilon) return t2;
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d2 = sampleCurveDerivativeX(t2);
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if (fabs(d2) < 1e-6) break;
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t2 = t2 - x2 / d2;
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}
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// Fall back to the bisection method for reliability.
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t0 = 0.0;
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t1 = 1.0;
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t2 = x;
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if (t2 < t0) return t0;
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if (t2 > t1) return t1;
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while (t0 < t1) {
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x2 = sampleCurveX(t2);
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if (fabs(x2 - x) < epsilon) return t2;
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if (x > x2)
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t0 = t2;
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else
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t1 = t2;
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t2 = (t1 - t0) * .5 + t0;
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}
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// Failure.
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return t2;
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}
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double solve(double x, double epsilon) const noexcept { return sampleCurveY(solveCurveX(x, epsilon)); }
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bool operator==(const UnitBezier& rhs) const noexcept {
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return std::tie(cx, bx, ax, cy, by, ay) == std::tie(rhs.cx, rhs.bx, rhs.ax, rhs.cy, rhs.by, rhs.ay);
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}
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private:
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const double cx;
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const double bx;
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const double ax;
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const double cy;
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const double by;
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const double ay;
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};
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} // namespace util
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} // namespace mbgl
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