1/*
2 * Copyright 2015 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7#include "SkIntersections.h"
8#include "SkLineParameters.h"
9#include "SkPathOpsConic.h"
10#include "SkPathOpsCubic.h"
11#include "SkPathOpsQuad.h"
12
13// cribbed from the float version in SkGeometry.cpp
14static void conic_deriv_coeff(const double src[],
15                              SkScalar w,
16                              double coeff[3]) {
17    const double P20 = src[4] - src[0];
18    const double P10 = src[2] - src[0];
19    const double wP10 = w * P10;
20    coeff[0] = w * P20 - P20;
21    coeff[1] = P20 - 2 * wP10;
22    coeff[2] = wP10;
23}
24
25static double conic_eval_tan(const double coord[], SkScalar w, double t) {
26    double coeff[3];
27    conic_deriv_coeff(coord, w, coeff);
28    return t * (t * coeff[0] + coeff[1]) + coeff[2];
29}
30
31int SkDConic::FindExtrema(const double src[], SkScalar w, double t[1]) {
32    double coeff[3];
33    conic_deriv_coeff(src, w, coeff);
34
35    double tValues[2];
36    int roots = SkDQuad::RootsValidT(coeff[0], coeff[1], coeff[2], tValues);
37    SkASSERT(0 == roots || 1 == roots);
38
39    if (1 == roots) {
40        t[0] = tValues[0];
41        return 1;
42    }
43    return 0;
44}
45
46SkDVector SkDConic::dxdyAtT(double t) const {
47    SkDVector result = {
48        conic_eval_tan(&fPts[0].fX, fWeight, t),
49        conic_eval_tan(&fPts[0].fY, fWeight, t)
50    };
51    return result;
52}
53
54static double conic_eval_numerator(const double src[], SkScalar w, double t) {
55    SkASSERT(src);
56    SkASSERT(t >= 0 && t <= 1);
57    double src2w = src[2] * w;
58    double C = src[0];
59    double A = src[4] - 2 * src2w + C;
60    double B = 2 * (src2w - C);
61    return (A * t + B) * t + C;
62}
63
64
65static double conic_eval_denominator(SkScalar w, double t) {
66    double B = 2 * (w - 1);
67    double C = 1;
68    double A = -B;
69    return (A * t + B) * t + C;
70}
71
72bool SkDConic::hullIntersects(const SkDCubic& cubic, bool* isLinear) const {
73    return cubic.hullIntersects(*this, isLinear);
74}
75
76SkDPoint SkDConic::ptAtT(double t) const {
77    double denominator = conic_eval_denominator(fWeight, t);
78    SkDPoint result = {
79        conic_eval_numerator(&fPts[0].fX, fWeight, t) / denominator,
80        conic_eval_numerator(&fPts[0].fY, fWeight, t) / denominator
81    };
82    return result;
83}
84
85/* see quad subdivide for rationale */
86SkDConic SkDConic::subDivide(double t1, double t2) const {
87    double ax = conic_eval_numerator(&fPts[0].fX, fWeight, t1);
88    double ay = conic_eval_numerator(&fPts[0].fY, fWeight, t1);
89    double az = conic_eval_denominator(fWeight, t1);
90    double midT = (t1 + t2) / 2;
91    double dx = conic_eval_numerator(&fPts[0].fX, fWeight, midT);
92    double dy = conic_eval_numerator(&fPts[0].fY, fWeight, midT);
93    double dz = conic_eval_denominator(fWeight, midT);
94    double cx = conic_eval_numerator(&fPts[0].fX, fWeight, t2);
95    double cy = conic_eval_numerator(&fPts[0].fY, fWeight, t2);
96    double cz = conic_eval_denominator(fWeight, t2);
97    double bx = 2 * dx - (ax + cx) / 2;
98    double by = 2 * dy - (ay + cy) / 2;
99    double bz = 2 * dz - (az + cz) / 2;
100    double dt = t2 - t1;
101    double dt_1 = 1 - dt;
102    SkScalar w = SkDoubleToScalar((1 + dt * (fWeight - 1))
103            / sqrt(dt * dt + 2 * dt * dt_1 * fWeight + dt_1 * dt_1));
104    SkDConic dst = {{{{ax / az, ay / az}, {bx / bz, by / bz}, {cx / cz, cy / cz}}}, w };
105    return dst;
106}
107
108SkDPoint SkDConic::subDivide(const SkDPoint& a, const SkDPoint& c, double t1, double t2,
109        SkScalar* weight) const {
110    SkDConic chopped = this->subDivide(t1, t2);
111    *weight = chopped.fWeight;
112    return chopped[1];
113}
114