UI GFX Geometry: Make UnitBezier a wrapper for gfx::CubicBezier

third_party/WebKit/Source/platform/animation/UnitBezier.cpp

-// Copyright 2016 The Chromium Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style license that can be
-// found in the LICENSE file.
-
-#include "platform/animation/UnitBezier.h"
-
-namespace blink {
-
-const double UnitBezier::kBezierEpsilon = 1e-7;
-
-UnitBezier::UnitBezier(double p1x, double p1y, double p2x, double p2y)
-{
-    initCoefficients(p1x, p1y, p2x, p2y);
-    initGradients(p1x, p1y, p2x, p2y);
-    initRange(p1y, p2y);
-}
-
-void UnitBezier::initCoefficients(double p1x, double p1y, double p2x, double p2y)
-{
-    // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
-    cx = 3.0 * p1x;
-    bx = 3.0 * (p2x - p1x) - cx;
-    ax = 1.0 - cx -bx;
-
-    cy = 3.0 * p1y;
-    by = 3.0 * (p2y - p1y) - cy;
-    ay = 1.0 - cy - by;
-}
-
-void UnitBezier::initGradients(double p1x, double p1y, double p2x, double p2y)
-{
-    // End-point gradients are used to calculate timing function results
-    // outside the range [0, 1].
-    //
-    // There are three possibilities for the gradient at each end:
-    // (1) the closest control point is not horizontally coincident with regard to
-    //     (0, 0) or (1, 1). In this case the line between the end point and
-    //     the control point is tangent to the bezier at the end point.
-    // (2) the closest control point is coincident with the end point. In
-    //     this case the line between the end point and the far control
-    //     point is tangent to the bezier at the end point.
-    // (3) the closest control point is horizontally coincident with the end
-    //     point, but vertically distinct. In this case the gradient at the
-    //     end point is Infinite. However, this causes issues when
-    //     interpolating. As a result, we break down to a simple case of
-    //     0 gradient under these conditions.
-
-    if (p1x > 0)
-        m_startGradient = p1y / p1x;
-    else if (!p1y && p2x > 0)
-        m_startGradient = p2y / p2x;
-    else
-        m_startGradient = 0;
-
-    if (p2x < 1)
-        m_endGradient = (p2y - 1) / (p2x - 1);
-    else if (p2x == 1 && p1x < 1)
-        m_endGradient = (p1y - 1) / (p1x - 1);
-    else
-        m_endGradient = 0;
-}
-
-void UnitBezier::initRange(double p1y, double p2y)
-{
-    m_rangeMin = 0;
-    m_rangeMax = 1;
-    if (0 <= p1y && p1y < 1 && 0 <= p2y && p2y <= 1)
-        return;
-
-    // Represent the function's derivative in the form at^2 + bt + c
-    // as in sampleCurveDerivativeY.
-    // (Technically this is (dy/dt)*(1/3), which is suitable for finding zeros
-    // but does not actually give the slope of the curve.)
-    const double a = 3.0 * ay;
-    const double b = 2.0 * by;
-    const double c = cy;
-
-    // Check if the derivative is constant.
-    if (std::abs(a) < kBezierEpsilon && std::abs(b) < kBezierEpsilon)
-        return;
-
-    // Zeros of the function's derivative.
-    double t1 = 0;
-    double t2 = 0;
-
-    if (std::abs(a) < kBezierEpsilon) {
-        // The function's derivative is linear.
-        t1 = -c / b;
-    } else {
-        // The function's derivative is a quadratic. We find the zeros of this
-        // quadratic using the quadratic formula.
-        double discriminant = b * b - 4 * a * c;
-        if (discriminant < 0)
-            return;
-        double discriminantSqrt = sqrt(discriminant);
-        t1 = (-b + discriminantSqrt) / (2 * a);
-        t2 = (-b - discriminantSqrt) / (2 * a);
-    }
-
-    double sol1 = 0;
-    double sol2 = 0;
-
-    if (0 < t1 && t1 < 1)
-        sol1 = sampleCurveY(t1);
-
-    if (0 < t2 && t2 < 1)
-        sol2 = sampleCurveY(t2);
-
-    m_rangeMin = std::min(std::min(m_rangeMin, sol1), sol2);
-    m_rangeMax = std::max(std::max(m_rangeMax, sol1), sol2);
-}
-
-} // namespace blink