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