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 {
firstSkDCubicPair15 const SkDCubic& first() const { return (const SkDCubic&) pts[0]; }
secondSkDCubicPair16 const SkDCubic& second() const { return (const SkDCubic&) pts[3]; }
17 SkDPoint pts[7];
18 };
19
20 struct SkDCubic {
21 static const int kPointCount = 4;
22 static const int kPointLast = kPointCount - 1;
23 static const int kMaxIntersections = 9;
24
25 enum SearchAxis {
26 kXAxis,
27 kYAxis
28 };
29
collapsedSkDCubic30 bool collapsed() const {
31 return fPts[0].approximatelyEqual(fPts[1]) && fPts[0].approximatelyEqual(fPts[2])
32 && fPts[0].approximatelyEqual(fPts[3]);
33 }
34
controlsInsideSkDCubic35 bool controlsInside() const {
36 SkDVector v01 = fPts[0] - fPts[1];
37 SkDVector v02 = fPts[0] - fPts[2];
38 SkDVector v03 = fPts[0] - fPts[3];
39 SkDVector v13 = fPts[1] - fPts[3];
40 SkDVector v23 = fPts[2] - fPts[3];
41 return v03.dot(v01) > 0 && v03.dot(v02) > 0 && v03.dot(v13) > 0 && v03.dot(v23) > 0;
42 }
43
IsConicSkDCubic44 static bool IsConic() { return false; }
45
46 const SkDPoint& operator[](int n) const { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }
47 SkDPoint& operator[](int n) { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }
48
49 void align(int endIndex, int ctrlIndex, SkDPoint* dstPt) const;
50 double binarySearch(double min, double max, double axisIntercept, SearchAxis xAxis) const;
51 double calcPrecision() const;
52 SkDCubicPair chopAt(double t) const;
53 static void Coefficients(const double* cubic, double* A, double* B, double* C, double* D);
54 static bool ComplexBreak(const SkPoint pts[4], SkScalar* t);
55 int convexHull(char order[kPointCount]) const;
56
debugInitSkDCubic57 void debugInit() {
58 sk_bzero(fPts, sizeof(fPts));
59 }
60
61 void dump() const; // callable from the debugger when the implementation code is linked in
62 void dumpID(int id) const;
63 void dumpInner() const;
64 SkDVector dxdyAtT(double t) const;
65 bool endsAreExtremaInXOrY() const;
66 static int FindExtrema(const double src[], double tValue[2]);
67 int findInflections(double tValues[2]) const;
68
FindInflectionsSkDCubic69 static int FindInflections(const SkPoint a[kPointCount], double tValues[2]) {
70 SkDCubic cubic;
71 return cubic.set(a).findInflections(tValues);
72 }
73
74 int findMaxCurvature(double tValues[]) const;
75 bool hullIntersects(const SkDCubic& c2, bool* isLinear) const;
76 bool hullIntersects(const SkDConic& c, bool* isLinear) const;
77 bool hullIntersects(const SkDQuad& c2, bool* isLinear) const;
78 bool hullIntersects(const SkDPoint* pts, int ptCount, bool* isLinear) const;
79 bool isLinear(int startIndex, int endIndex) const;
80 bool monotonicInX() const;
81 bool monotonicInY() const;
82 void otherPts(int index, const SkDPoint* o1Pts[kPointCount - 1]) const;
83 SkDPoint ptAtT(double t) const;
84 static int RootsReal(double A, double B, double C, double D, double t[3]);
85 static int RootsValidT(const double A, const double B, const double C, double D, double s[3]);
86
87 int searchRoots(double extremes[6], int extrema, double axisIntercept,
88 SearchAxis xAxis, double* validRoots) const;
89
90 /**
91 * Return the number of valid roots (0 < root < 1) for this cubic intersecting the
92 * specified horizontal line.
93 */
94 int horizontalIntersect(double yIntercept, double roots[3]) const;
95 /**
96 * Return the number of valid roots (0 < root < 1) for this cubic intersecting the
97 * specified vertical line.
98 */
99 int verticalIntersect(double xIntercept, double roots[3]) const;
100
setSkDCubic101 const SkDCubic& set(const SkPoint pts[kPointCount]) {
102 fPts[0] = pts[0];
103 fPts[1] = pts[1];
104 fPts[2] = pts[2];
105 fPts[3] = pts[3];
106 return *this;
107 }
108
109 SkDCubic subDivide(double t1, double t2) const;
110
SubDivideSkDCubic111 static SkDCubic SubDivide(const SkPoint a[kPointCount], double t1, double t2) {
112 SkDCubic cubic;
113 return cubic.set(a).subDivide(t1, t2);
114 }
115
116 void subDivide(const SkDPoint& a, const SkDPoint& d, double t1, double t2, SkDPoint p[2]) const;
117
SubDivideSkDCubic118 static void SubDivide(const SkPoint pts[kPointCount], const SkDPoint& a, const SkDPoint& d, double t1,
119 double t2, SkDPoint p[2]) {
120 SkDCubic cubic;
121 cubic.set(pts).subDivide(a, d, t1, t2, p);
122 }
123
124 double top(const SkDCubic& dCurve, double startT, double endT, SkDPoint*topPt) const;
125 SkDQuad toQuad() const;
126
127 static const int gPrecisionUnit;
128
129 SkDPoint fPts[kPointCount];
130 };
131
132 /* Given the set [0, 1, 2, 3], and two of the four members, compute an XOR mask
133 that computes the other two. Note that:
134
135 one ^ two == 3 for (0, 3), (1, 2)
136 one ^ two < 3 for (0, 1), (0, 2), (1, 3), (2, 3)
137 3 - (one ^ two) is either 0, 1, or 2
138 1 >> (3 - (one ^ two)) is either 0 or 1
139 thus:
140 returned == 2 for (0, 3), (1, 2)
141 returned == 3 for (0, 1), (0, 2), (1, 3), (2, 3)
142 given that:
143 (0, 3) ^ 2 -> (2, 1) (1, 2) ^ 2 -> (3, 0)
144 (0, 1) ^ 3 -> (3, 2) (0, 2) ^ 3 -> (3, 1) (1, 3) ^ 3 -> (2, 0) (2, 3) ^ 3 -> (1, 0)
145 */
other_two(int one,int two)146 inline int other_two(int one, int two) {
147 return 1 >> (3 - (one ^ two)) ^ 3;
148 }
149
150 #endif
151