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 #include "src/pathops/SkPathOpsCubic.h"
8
rotate(const SkDCubic & cubic,int zero,int index,SkDCubic & rotPath)9 static bool rotate(const SkDCubic& cubic, int zero, int index, SkDCubic& rotPath) {
10 double dy = cubic[index].fY - cubic[zero].fY;
11 double dx = cubic[index].fX - cubic[zero].fX;
12 if (approximately_zero(dy)) {
13 if (approximately_zero(dx)) {
14 return false;
15 }
16 rotPath = cubic;
17 if (dy) {
18 rotPath[index].fY = cubic[zero].fY;
19 int mask = other_two(index, zero);
20 int side1 = index ^ mask;
21 int side2 = zero ^ mask;
22 if (approximately_equal(cubic[side1].fY, cubic[zero].fY)) {
23 rotPath[side1].fY = cubic[zero].fY;
24 }
25 if (approximately_equal(cubic[side2].fY, cubic[zero].fY)) {
26 rotPath[side2].fY = cubic[zero].fY;
27 }
28 }
29 return true;
30 }
31 for (int index = 0; index < 4; ++index) {
32 rotPath[index].fX = cubic[index].fX * dx + cubic[index].fY * dy;
33 rotPath[index].fY = cubic[index].fY * dx - cubic[index].fX * dy;
34 }
35 return true;
36 }
37
38
39 // Returns 0 if negative, 1 if zero, 2 if positive
side(double x)40 static int side(double x) {
41 return (x > 0) + (x >= 0);
42 }
43
44 /* Given a cubic, find the convex hull described by the end and control points.
45 The hull may have 3 or 4 points. Cubics that degenerate into a point or line
46 are not considered.
47
48 The hull is computed by assuming that three points, if unique and non-linear,
49 form a triangle. The fourth point may replace one of the first three, may be
50 discarded if in the triangle or on an edge, or may be inserted between any of
51 the three to form a convex quadralateral.
52
53 The indices returned in order describe the convex hull.
54 */
convexHull(char order[4]) const55 int SkDCubic::convexHull(char order[4]) const {
56 size_t index;
57 // find top point
58 size_t yMin = 0;
59 for (index = 1; index < 4; ++index) {
60 if (fPts[yMin].fY > fPts[index].fY || (fPts[yMin].fY == fPts[index].fY
61 && fPts[yMin].fX > fPts[index].fX)) {
62 yMin = index;
63 }
64 }
65 order[0] = yMin;
66 int midX = -1;
67 int backupYMin = -1;
68 for (int pass = 0; pass < 2; ++pass) {
69 for (index = 0; index < 4; ++index) {
70 if (index == yMin) {
71 continue;
72 }
73 // rotate line from (yMin, index) to axis
74 // see if remaining two points are both above or below
75 // use this to find mid
76 int mask = other_two(yMin, index);
77 int side1 = yMin ^ mask;
78 int side2 = index ^ mask;
79 SkDCubic rotPath;
80 if (!rotate(*this, yMin, index, rotPath)) { // ! if cbc[yMin]==cbc[idx]
81 order[1] = side1;
82 order[2] = side2;
83 return 3;
84 }
85 int sides = side(rotPath[side1].fY - rotPath[yMin].fY);
86 sides ^= side(rotPath[side2].fY - rotPath[yMin].fY);
87 if (sides == 2) { // '2' means one remaining point <0, one >0
88 if (midX >= 0) {
89 // one of the control points is equal to an end point
90 order[0] = 0;
91 order[1] = 3;
92 if (fPts[1] == fPts[0] || fPts[1] == fPts[3]) {
93 order[2] = 2;
94 return 3;
95 }
96 if (fPts[2] == fPts[0] || fPts[2] == fPts[3]) {
97 order[2] = 1;
98 return 3;
99 }
100 // one of the control points may be very nearly but not exactly equal --
101 double dist1_0 = fPts[1].distanceSquared(fPts[0]);
102 double dist1_3 = fPts[1].distanceSquared(fPts[3]);
103 double dist2_0 = fPts[2].distanceSquared(fPts[0]);
104 double dist2_3 = fPts[2].distanceSquared(fPts[3]);
105 double smallest1distSq = std::min(dist1_0, dist1_3);
106 double smallest2distSq = std::min(dist2_0, dist2_3);
107 if (approximately_zero(std::min(smallest1distSq, smallest2distSq))) {
108 order[2] = smallest1distSq < smallest2distSq ? 2 : 1;
109 return 3;
110 }
111 }
112 midX = index;
113 } else if (sides == 0) { // '0' means both to one side or the other
114 backupYMin = index;
115 }
116 }
117 if (midX >= 0) {
118 break;
119 }
120 if (backupYMin < 0) {
121 break;
122 }
123 yMin = backupYMin;
124 backupYMin = -1;
125 }
126 if (midX < 0) {
127 midX = yMin ^ 3; // choose any other point
128 }
129 int mask = other_two(yMin, midX);
130 int least = yMin ^ mask;
131 int most = midX ^ mask;
132 order[0] = yMin;
133 order[1] = least;
134
135 // see if mid value is on same side of line (least, most) as yMin
136 SkDCubic midPath;
137 if (!rotate(*this, least, most, midPath)) { // ! if cbc[least]==cbc[most]
138 order[2] = midX;
139 return 3;
140 }
141 int midSides = side(midPath[yMin].fY - midPath[least].fY);
142 midSides ^= side(midPath[midX].fY - midPath[least].fY);
143 if (midSides != 2) { // if mid point is not between
144 order[2] = most;
145 return 3; // result is a triangle
146 }
147 order[2] = midX;
148 order[3] = most;
149 return 4; // result is a quadralateral
150 }
151