1/*
2 * Copyright 2012 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
8#ifndef SkPathOpsCubic_DEFINED
9#define SkPathOpsCubic_DEFINED
10
11#include "include/core/SkPath.h"
12#include "src/core/SkArenaAlloc.h"
13#include "src/pathops/SkPathOpsTCurve.h"
14
15struct SkDCubicPair;
16
17struct SkDCubic {
18 static const int kPointCount = 4;
19 static const int kPointLast = kPointCount - 1;
20 static const int kMaxIntersections = 9;
21
22 enum SearchAxis {
23 kXAxis,
24 kYAxis
25 };
26
27 bool collapsed() const {
28 return fPts[0].approximatelyEqual(fPts[1]) && fPts[0].approximatelyEqual(fPts[2])
29 && fPts[0].approximatelyEqual(fPts[3]);
30 }
31
32 bool controlsInside() const {
33 SkDVector v01 = fPts[0] - fPts[1];
34 SkDVector v02 = fPts[0] - fPts[2];
35 SkDVector v03 = fPts[0] - fPts[3];
36 SkDVector v13 = fPts[1] - fPts[3];
37 SkDVector v23 = fPts[2] - fPts[3];
38 return v03.dot(v01) > 0 && v03.dot(v02) > 0 && v03.dot(v13) > 0 && v03.dot(v23) > 0;
39 }
40
41 static bool IsConic() { return false; }
42
43 const SkDPoint& operator[](int n) const { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }
44 SkDPoint& operator[](int n) { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }
45
46 void align(int endIndex, int ctrlIndex, SkDPoint* dstPt) const;
47 double binarySearch(double min, double max, double axisIntercept, SearchAxis xAxis) const;
48 double calcPrecision() const;
49 SkDCubicPair chopAt(double t) const;
50 static void Coefficients(const double* cubic, double* A, double* B, double* C, double* D);
51 static int ComplexBreak(const SkPoint pts[4], SkScalar* t);
52 int convexHull(char order[kPointCount]) const;
53
54 void debugInit() {
55 sk_bzero(fPts, sizeof(fPts));
56 }
57
58 void debugSet(const SkDPoint* pts);
59
60 void dump() const; // callable from the debugger when the implementation code is linked in
61 void dumpID(int id) const;
62 void dumpInner() const;
63 SkDVector dxdyAtT(double t) const;
64 bool endsAreExtremaInXOrY() const;
65 static int FindExtrema(const double src[], double tValue[2]);
66 int findInflections(double tValues[2]) const;
67
68 static int FindInflections(const SkPoint a[kPointCount], double tValues[2]) {
69 SkDCubic cubic;
70 return cubic.set(a).findInflections(tValues);
71 }
72
73 int findMaxCurvature(double tValues[]) const;
74
75#ifdef SK_DEBUG
76 SkOpGlobalState* globalState() const { return fDebugGlobalState; }
77#endif
78
79 bool hullIntersects(const SkDCubic& c2, bool* isLinear) const;
80 bool hullIntersects(const SkDConic& c, bool* isLinear) const;
81 bool hullIntersects(const SkDQuad& c2, bool* isLinear) const;
82 bool hullIntersects(const SkDPoint* pts, int ptCount, bool* isLinear) const;
83 bool isLinear(int startIndex, int endIndex) const;
84 static int maxIntersections() { return kMaxIntersections; }
85 bool monotonicInX() const;
86 bool monotonicInY() const;
87 void otherPts(int index, const SkDPoint* o1Pts[kPointCount - 1]) const;
88 static int pointCount() { return kPointCount; }
89 static int pointLast() { return kPointLast; }
90 SkDPoint ptAtT(double t) const;
91 static int RootsReal(double A, double B, double C, double D, double t[3]);
92 static int RootsValidT(const double A, const double B, const double C, double D, double s[3]);
93
94 int searchRoots(double extremes[6], int extrema, double axisIntercept,
95 SearchAxis xAxis, double* validRoots) const;
96
97 bool toFloatPoints(SkPoint* ) const;
98 /**
99 * Return the number of valid roots (0 < root < 1) for this cubic intersecting the
100 * specified horizontal line.
101 */
102 int horizontalIntersect(double yIntercept, double roots[3]) const;
103 /**
104 * Return the number of valid roots (0 < root < 1) for this cubic intersecting the
105 * specified vertical line.
106 */
107 int verticalIntersect(double xIntercept, double roots[3]) const;
108
109// add debug only global pointer so asserts can be skipped by fuzzers
110 const SkDCubic& set(const SkPoint pts[kPointCount]
111 SkDEBUGPARAMS(SkOpGlobalState* state = nullptr)) {
112 fPts[0] = pts[0];
113 fPts[1] = pts[1];
114 fPts[2] = pts[2];
115 fPts[3] = pts[3];
116 SkDEBUGCODE(fDebugGlobalState = state);
117 return *this;
118 }
119
120 SkDCubic subDivide(double t1, double t2) const;
121 void subDivide(double t1, double t2, SkDCubic* c) const { *c = this->subDivide(t1, t2); }
122
123 static SkDCubic SubDivide(const SkPoint a[kPointCount], double t1, double t2) {
124 SkDCubic cubic;
125 return cubic.set(a).subDivide(t1, t2);
126 }
127
128 void subDivide(const SkDPoint& a, const SkDPoint& d, double t1, double t2, SkDPoint p[2]) const;
129
130 static void SubDivide(const SkPoint pts[kPointCount], const SkDPoint& a, const SkDPoint& d, double t1,
131 double t2, SkDPoint p[2]) {
132 SkDCubic cubic;
133 cubic.set(pts).subDivide(a, d, t1, t2, p);
134 }
135
136 double top(const SkDCubic& dCurve, double startT, double endT, SkDPoint*topPt) const;
137 SkDQuad toQuad() const;
138
139 static const int gPrecisionUnit;
140 SkDPoint fPts[kPointCount];
141 SkDEBUGCODE(SkOpGlobalState* fDebugGlobalState);
142};
143
144/* Given the set [0, 1, 2, 3], and two of the four members, compute an XOR mask
145 that computes the other two. Note that:
146
147 one ^ two == 3 for (0, 3), (1, 2)
148 one ^ two < 3 for (0, 1), (0, 2), (1, 3), (2, 3)
149 3 - (one ^ two) is either 0, 1, or 2
150 1 >> (3 - (one ^ two)) is either 0 or 1
151thus:
152 returned == 2 for (0, 3), (1, 2)
153 returned == 3 for (0, 1), (0, 2), (1, 3), (2, 3)
154given that:
155 (0, 3) ^ 2 -> (2, 1) (1, 2) ^ 2 -> (3, 0)
156 (0, 1) ^ 3 -> (3, 2) (0, 2) ^ 3 -> (3, 1) (1, 3) ^ 3 -> (2, 0) (2, 3) ^ 3 -> (1, 0)
157*/
158inline int other_two(int one, int two) {
159 return 1 >> (3 - (one ^ two)) ^ 3;
160}
161
162struct SkDCubicPair {
163 SkDCubic first() const {
164#ifdef SK_DEBUG
165 SkDCubic result;
166 result.debugSet(&pts[0]);
167 return result;
168#else
169 return (const SkDCubic&) pts[0];
170#endif
171 }
172 SkDCubic second() const {
173#ifdef SK_DEBUG
174 SkDCubic result;
175 result.debugSet(&pts[3]);
176 return result;
177#else
178 return (const SkDCubic&) pts[3];
179#endif
180 }
181 SkDPoint pts[7];
182};
183
184class SkTCubic : public SkTCurve {
185public:
186 SkDCubic fCubic;
187
188 SkTCubic() {}
189
190 SkTCubic(const SkDCubic& c)
191 : fCubic(c) {
192 }
193
194 ~SkTCubic() override {}
195
196 const SkDPoint& operator[](int n) const override { return fCubic[n]; }
197 SkDPoint& operator[](int n) override { return fCubic[n]; }
198
199 bool collapsed() const override { return fCubic.collapsed(); }
200 bool controlsInside() const override { return fCubic.controlsInside(); }
201 void debugInit() override { return fCubic.debugInit(); }
202#if DEBUG_T_SECT
203 void dumpID(int id) const override { return fCubic.dumpID(id); }
204#endif
205 SkDVector dxdyAtT(double t) const override { return fCubic.dxdyAtT(t); }
206#ifdef SK_DEBUG
207 SkOpGlobalState* globalState() const override { return fCubic.globalState(); }
208#endif
209 bool hullIntersects(const SkDQuad& quad, bool* isLinear) const override;
210 bool hullIntersects(const SkDConic& conic, bool* isLinear) const override;
211
212 bool hullIntersects(const SkDCubic& cubic, bool* isLinear) const override {
213 return cubic.hullIntersects(fCubic, isLinear);
214 }
215
216 bool hullIntersects(const SkTCurve& curve, bool* isLinear) const override {
217 return curve.hullIntersects(fCubic, isLinear);
218 }
219
220 int intersectRay(SkIntersections* i, const SkDLine& line) const override;
221 bool IsConic() const override { return false; }
222 SkTCurve* make(SkArenaAlloc& heap) const override { return heap.make<SkTCubic>(); }
223
224 int maxIntersections() const override { return SkDCubic::kMaxIntersections; }
225
226 void otherPts(int oddMan, const SkDPoint* endPt[2]) const override {
227 fCubic.otherPts(oddMan, endPt);
228 }
229
230 int pointCount() const override { return SkDCubic::kPointCount; }
231 int pointLast() const override { return SkDCubic::kPointLast; }
232 SkDPoint ptAtT(double t) const override { return fCubic.ptAtT(t); }
233 void setBounds(SkDRect* ) const override;
234
235 void subDivide(double t1, double t2, SkTCurve* curve) const override {
236 ((SkTCubic*) curve)->fCubic = fCubic.subDivide(t1, t2);
237 }
238};
239
240#endif
241