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 const SkDCubic& first() const { return (const SkDCubic&) pts[0]; } 16 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 30 bool collapsed() const { 31 return fPts[0].approximatelyEqual(fPts[1]) && fPts[0].approximatelyEqual(fPts[2]) 32 && fPts[0].approximatelyEqual(fPts[3]); 33 } 34 35 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 44 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 57 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 69 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; 100 101 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; 110 111 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; 117 118 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 */ 146 inline int other_two(int one, int two) { 147 return 1 >> (3 - (one ^ two)) ^ 3; 148 } 149 150 #endif 151
