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 
26     bool collapsed() const {
27         return fPts[0].approximatelyEqual(fPts[1]) && fPts[0].approximatelyEqual(fPts[2])
28                 && fPts[0].approximatelyEqual(fPts[3]);
29     }
30 
31     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 
40     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 
53     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 
67     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
75     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
106     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 
118     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 
125     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 */
153 inline int other_two(int one, int two) {
154     return 1 >> (3 - (one ^ two)) ^ 3;
155 }
156 
157 struct SkDCubicPair {
158     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     }
167     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