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
conic_deriv_coeff(const double src[],SkScalar w,double coeff[3])14 static 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
conic_eval_tan(const double coord[],SkScalar w,double t)25 static 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
FindExtrema(const double src[],SkScalar w,double t[1])31 int 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
dxdyAtT(double t) const46 SkDVector 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 if (result.fX == 0 && result.fY == 0) {
52 if (zero_or_one(t)) {
53 result = fPts[2] - fPts[0];
54 } else {
55 // incomplete
56 SkDebugf("!k");
57 }
58 }
59 return result;
60 }
61
conic_eval_numerator(const double src[],SkScalar w,double t)62 static double conic_eval_numerator(const double src[], SkScalar w, double t) {
63 SkASSERT(src);
64 SkASSERT(t >= 0 && t <= 1);
65 double src2w = src[2] * w;
66 double C = src[0];
67 double A = src[4] - 2 * src2w + C;
68 double B = 2 * (src2w - C);
69 return (A * t + B) * t + C;
70 }
71
72
conic_eval_denominator(SkScalar w,double t)73 static double conic_eval_denominator(SkScalar w, double t) {
74 double B = 2 * (w - 1);
75 double C = 1;
76 double A = -B;
77 return (A * t + B) * t + C;
78 }
79
hullIntersects(const SkDCubic & cubic,bool * isLinear) const80 bool SkDConic::hullIntersects(const SkDCubic& cubic, bool* isLinear) const {
81 return cubic.hullIntersects(*this, isLinear);
82 }
83
ptAtT(double t) const84 SkDPoint SkDConic::ptAtT(double t) const {
85 if (t == 0) {
86 return fPts[0];
87 }
88 if (t == 1) {
89 return fPts[2];
90 }
91 double denominator = conic_eval_denominator(fWeight, t);
92 SkDPoint result = {
93 conic_eval_numerator(&fPts[0].fX, fWeight, t) / denominator,
94 conic_eval_numerator(&fPts[0].fY, fWeight, t) / denominator
95 };
96 return result;
97 }
98
99 /* see quad subdivide for point rationale */
100 /* w rationale : the mid point between t1 and t2 could be determined from the computed a/b/c
101 values if the computed w was known. Since we know the mid point at (t1+t2)/2, we'll assume
102 that it is the same as the point on the new curve t==(0+1)/2.
103
104 d / dz == conic_poly(dst, unknownW, .5) / conic_weight(unknownW, .5);
105
106 conic_poly(dst, unknownW, .5)
107 = a / 4 + (b * unknownW) / 2 + c / 4
108 = (a + c) / 4 + (bx * unknownW) / 2
109
110 conic_weight(unknownW, .5)
111 = unknownW / 2 + 1 / 2
112
113 d / dz == ((a + c) / 2 + b * unknownW) / (unknownW + 1)
114 d / dz * (unknownW + 1) == (a + c) / 2 + b * unknownW
115 unknownW = ((a + c) / 2 - d / dz) / (d / dz - b)
116
117 Thus, w is the ratio of the distance from the mid of end points to the on-curve point, and the
118 distance of the on-curve point to the control point.
119 */
subDivide(double t1,double t2) const120 SkDConic SkDConic::subDivide(double t1, double t2) const {
121 double ax, ay, az;
122 if (t1 == 0) {
123 ax = fPts[0].fX;
124 ay = fPts[0].fY;
125 az = 1;
126 } else if (t1 != 1) {
127 ax = conic_eval_numerator(&fPts[0].fX, fWeight, t1);
128 ay = conic_eval_numerator(&fPts[0].fY, fWeight, t1);
129 az = conic_eval_denominator(fWeight, t1);
130 } else {
131 ax = fPts[2].fX;
132 ay = fPts[2].fY;
133 az = 1;
134 }
135 double midT = (t1 + t2) / 2;
136 double dx = conic_eval_numerator(&fPts[0].fX, fWeight, midT);
137 double dy = conic_eval_numerator(&fPts[0].fY, fWeight, midT);
138 double dz = conic_eval_denominator(fWeight, midT);
139 double cx, cy, cz;
140 if (t2 == 1) {
141 cx = fPts[2].fX;
142 cy = fPts[2].fY;
143 cz = 1;
144 } else if (t2 != 0) {
145 cx = conic_eval_numerator(&fPts[0].fX, fWeight, t2);
146 cy = conic_eval_numerator(&fPts[0].fY, fWeight, t2);
147 cz = conic_eval_denominator(fWeight, t2);
148 } else {
149 cx = fPts[0].fX;
150 cy = fPts[0].fY;
151 cz = 1;
152 }
153 double bx = 2 * dx - (ax + cx) / 2;
154 double by = 2 * dy - (ay + cy) / 2;
155 double bz = 2 * dz - (az + cz) / 2;
156 SkDConic dst = {{{{ax / az, ay / az}, {bx / bz, by / bz}, {cx / cz, cy / cz}}},
157 SkDoubleToScalar(bz / sqrt(az * cz)) };
158 return dst;
159 }
160
subDivide(const SkDPoint & a,const SkDPoint & c,double t1,double t2,SkScalar * weight) const161 SkDPoint SkDConic::subDivide(const SkDPoint& a, const SkDPoint& c, double t1, double t2,
162 SkScalar* weight) const {
163 SkDConic chopped = this->subDivide(t1, t2);
164 *weight = chopped.fWeight;
165 return chopped[1];
166 }
167