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 "SkPath.h"
12 #include "SkPathOpsPoint.h"
13
14 struct SkDCubicPair;
15
16 struct SkDCubic {
17 static const int kPointCount = 4;
18 static const int kPointLast = kPointCount - 1;
19 static const int kMaxIntersections = 9;
20
21 enum SearchAxis {
22 kXAxis,
23 kYAxis
24 };
25
collapsedSkDCubic26 bool collapsed() const {
27 return fPts[0].approximatelyEqual(fPts[1]) && fPts[0].approximatelyEqual(fPts[2])
28 && fPts[0].approximatelyEqual(fPts[3]);
29 }
30
controlsInsideSkDCubic31 bool controlsInside() const {
32 SkDVector v01 = fPts[0] - fPts[1];
33 SkDVector v02 = fPts[0] - fPts[2];
34 SkDVector v03 = fPts[0] - fPts[3];
35 SkDVector v13 = fPts[1] - fPts[3];
36 SkDVector v23 = fPts[2] - fPts[3];
37 return v03.dot(v01) > 0 && v03.dot(v02) > 0 && v03.dot(v13) > 0 && v03.dot(v23) > 0;
38 }
39
IsConicSkDCubic40 static bool IsConic() { return false; }
41
42 const SkDPoint& operator[](int n) const { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }
43 SkDPoint& operator[](int n) { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }
44
45 void align(int endIndex, int ctrlIndex, SkDPoint* dstPt) const;
46 double binarySearch(double min, double max, double axisIntercept, SearchAxis xAxis) const;
47 double calcPrecision() const;
48 SkDCubicPair chopAt(double t) const;
49 static void Coefficients(const double* cubic, double* A, double* B, double* C, double* D);
50 static int ComplexBreak(const SkPoint pts[4], SkScalar* t);
51 int convexHull(char order[kPointCount]) const;
52
debugInitSkDCubic53 void debugInit() {
54 sk_bzero(fPts, sizeof(fPts));
55 }
56
57 void debugSet(const SkDPoint* pts);
58
59 void dump() const; // callable from the debugger when the implementation code is linked in
60 void dumpID(int id) const;
61 void dumpInner() const;
62 SkDVector dxdyAtT(double t) const;
63 bool endsAreExtremaInXOrY() const;
64 static int FindExtrema(const double src[], double tValue[2]);
65 int findInflections(double tValues[2]) const;
66
FindInflectionsSkDCubic67 static int FindInflections(const SkPoint a[kPointCount], double tValues[2]) {
68 SkDCubic cubic;
69 return cubic.set(a).findInflections(tValues);
70 }
71
72 int findMaxCurvature(double tValues[]) const;
73
74 #ifdef SK_DEBUG
globalStateSkDCubic75 SkOpGlobalState* globalState() const { return fDebugGlobalState; }
76 #endif
77
78 bool hullIntersects(const SkDCubic& c2, bool* isLinear) const;
79 bool hullIntersects(const SkDConic& c, bool* isLinear) const;
80 bool hullIntersects(const SkDQuad& c2, bool* isLinear) const;
81 bool hullIntersects(const SkDPoint* pts, int ptCount, bool* isLinear) const;
82 bool isLinear(int startIndex, int endIndex) const;
83 bool monotonicInX() const;
84 bool monotonicInY() const;
85 void otherPts(int index, const SkDPoint* o1Pts[kPointCount - 1]) const;
86 SkDPoint ptAtT(double t) const;
87 static int RootsReal(double A, double B, double C, double D, double t[3]);
88 static int RootsValidT(const double A, const double B, const double C, double D, double s[3]);
89
90 int searchRoots(double extremes[6], int extrema, double axisIntercept,
91 SearchAxis xAxis, double* validRoots) const;
92
93 bool toFloatPoints(SkPoint* ) const;
94 /**
95 * Return the number of valid roots (0 < root < 1) for this cubic intersecting the
96 * specified horizontal line.
97 */
98 int horizontalIntersect(double yIntercept, double roots[3]) const;
99 /**
100 * Return the number of valid roots (0 < root < 1) for this cubic intersecting the
101 * specified vertical line.
102 */
103 int verticalIntersect(double xIntercept, double roots[3]) const;
104
105 // add debug only global pointer so asserts can be skipped by fuzzers
setSkDCubic106 const SkDCubic& set(const SkPoint pts[kPointCount]
107 SkDEBUGPARAMS(SkOpGlobalState* state = nullptr)) {
108 fPts[0] = pts[0];
109 fPts[1] = pts[1];
110 fPts[2] = pts[2];
111 fPts[3] = pts[3];
112 SkDEBUGCODE(fDebugGlobalState = state);
113 return *this;
114 }
115
116 SkDCubic subDivide(double t1, double t2) const;
117
SubDivideSkDCubic118 static SkDCubic SubDivide(const SkPoint a[kPointCount], double t1, double t2) {
119 SkDCubic cubic;
120 return cubic.set(a).subDivide(t1, t2);
121 }
122
123 void subDivide(const SkDPoint& a, const SkDPoint& d, double t1, double t2, SkDPoint p[2]) const;
124
SubDivideSkDCubic125 static void SubDivide(const SkPoint pts[kPointCount], const SkDPoint& a, const SkDPoint& d, double t1,
126 double t2, SkDPoint p[2]) {
127 SkDCubic cubic;
128 cubic.set(pts).subDivide(a, d, t1, t2, p);
129 }
130
131 double top(const SkDCubic& dCurve, double startT, double endT, SkDPoint*topPt) const;
132 SkDQuad toQuad() const;
133
134 static const int gPrecisionUnit;
135 SkDPoint fPts[kPointCount];
136 SkDEBUGCODE(SkOpGlobalState* fDebugGlobalState);
137 };
138
139 /* Given the set [0, 1, 2, 3], and two of the four members, compute an XOR mask
140 that computes the other two. Note that:
141
142 one ^ two == 3 for (0, 3), (1, 2)
143 one ^ two < 3 for (0, 1), (0, 2), (1, 3), (2, 3)
144 3 - (one ^ two) is either 0, 1, or 2
145 1 >> (3 - (one ^ two)) is either 0 or 1
146 thus:
147 returned == 2 for (0, 3), (1, 2)
148 returned == 3 for (0, 1), (0, 2), (1, 3), (2, 3)
149 given that:
150 (0, 3) ^ 2 -> (2, 1) (1, 2) ^ 2 -> (3, 0)
151 (0, 1) ^ 3 -> (3, 2) (0, 2) ^ 3 -> (3, 1) (1, 3) ^ 3 -> (2, 0) (2, 3) ^ 3 -> (1, 0)
152 */
other_two(int one,int two)153 inline int other_two(int one, int two) {
154 return 1 >> (3 - (one ^ two)) ^ 3;
155 }
156
157 struct SkDCubicPair {
firstSkDCubicPair158 const SkDCubic first() const {
159 #ifdef SK_DEBUG
160 SkDCubic result;
161 result.debugSet(&pts[0]);
162 return result;
163 #else
164 return (const SkDCubic&) pts[0];
165 #endif
166 }
secondSkDCubicPair167 const SkDCubic second() const {
168 #ifdef SK_DEBUG
169 SkDCubic result;
170 result.debugSet(&pts[3]);
171 return result;
172 #else
173 return (const SkDCubic&) pts[3];
174 #endif
175 }
176 SkDPoint pts[7];
177 };
178
179 #endif
180