unitbezier.hpp

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#pragma once
 
#include <cmath>
#include <tuple>
 
namespace mbgl {
namespace util {
 
struct UnitBezier {
    constexpr UnitBezier(double p1x, double p1y, double p2x, double p2y)
        : cx(3.0 * p1x)
        , bx(3.0 * (p2x - p1x) - (3.0 * p1x))
        , ax(1.0 - (3.0 * p1x) - (3.0 * (p2x - p1x) - (3.0 * p1x)))
        , cy(3.0 * p1y)
        , by(3.0 * (p2y - p1y) - (3.0 * p1y))
        , ay(1.0 - (3.0 * p1y) - (3.0 * (p2y - p1y) - (3.0 * p1y))) {
    }
 
    std::pair<double, double> getP1() const {
        return { cx / 3.0, cy / 3.0 };
    }
 
    std::pair<double, double> getP2() const {
        return {
            (bx + (3.0 * cx / 3.0) + cx) / 3.0,
            (by + (3.0 * cy / 3.0) + cy) / 3.0,
        };
    }
 
    double sampleCurveX(double t) const {
        // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
        return ((ax * t + bx) * t + cx) * t;
    }
 
    double sampleCurveY(double t) const {
        return ((ay * t + by) * t + cy) * t;
    }
 
    double sampleCurveDerivativeX(double t) const {
        return (3.0 * ax * t + 2.0 * bx) * t + cx;
    }
 
    double solveCurveX(double x, double epsilon) const {
        double t0;
        double t1;
        double t2;
        double x2;
        double d2;
        int i;
 
        // First try a few iterations of Newton's method -- normally very fast.
        for (t2 = x, i = 0; i < 8; ++i) {
            x2 = sampleCurveX(t2) - x;
            if (fabs (x2) < epsilon)
                return t2;
            d2 = sampleCurveDerivativeX(t2);
            if (fabs(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 = sampleCurveX(t2);
            if (fabs(x2 - x) < epsilon)
                return t2;
            if (x > x2)
                t0 = t2;
            else
                t1 = t2;
            t2 = (t1 - t0) * .5 + t0;
        }
 
        // Failure.
        return t2;
    }
 
    double solve(double x, double epsilon) const {
        return sampleCurveY(solveCurveX(x, epsilon));
    }
    
    bool operator==(const UnitBezier& rhs) const {
        return std::tie(cx, bx, ax, cy, by, ay) ==
            std::tie(rhs.cx, rhs.bx, rhs.ax, rhs.cy, rhs.by, rhs.ay);
    }
 
private:
    const double cx;
    const double bx;
    const double ax;
 
    const double cy;
    const double by;
    const double ay;
};
 
} // namespace util
} // namespace mbgl