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1 /* | 1 /* |
2 * Copyright 2012 Google Inc. | 2 * Copyright 2012 Google Inc. |
3 * | 3 * |
4 * Use of this source code is governed by a BSD-style license that can be | 4 * Use of this source code is governed by a BSD-style license that can be |
5 * found in the LICENSE file. | 5 * found in the LICENSE file. |
6 */ | 6 */ |
7 #include "SkPathOpsCubic.h" | 7 #include "SkPathOpsCubic.h" |
8 #include "SkPathOpsLine.h" | 8 #include "SkPathOpsLine.h" |
9 #include "SkPathOpsQuad.h" | 9 #include "SkPathOpsQuad.h" |
10 | 10 |
11 // Sources | 11 // Sources |
12 // computer-aided design - volume 22 number 9 november 1990 pp 538 - 549 | 12 // computer-aided design - volume 22 number 9 november 1990 pp 538 - 549 |
13 // online at http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf | 13 // online at http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf |
14 | 14 |
15 // This turns a line segment into a parameterized line, of the form | 15 // This turns a line segment into a parameterized line, of the form |
16 // ax + by + c = 0 | 16 // ax + by + c = 0 |
17 // When a^2 + b^2 == 1, the line is normalized. | 17 // When a^2 + b^2 == 1, the line is normalized. |
18 // The distance to the line for (x, y) is d(x,y) = ax + by + c | 18 // The distance to the line for (x, y) is d(x,y) = ax + by + c |
19 // | 19 // |
20 // Note that the distances below are not necessarily normalized. To get the true | 20 // Note that the distances below are not necessarily normalized. To get the true |
21 // distance, it's necessary to either call normalize() after xxxEndPoints(), or | 21 // distance, it's necessary to either call normalize() after xxxEndPoints(), or |
22 // divide the result of xxxDistance() by sqrt(normalSquared()) | 22 // divide the result of xxxDistance() by sqrt(normalSquared()) |
23 | 23 |
24 class SkLineParameters { | 24 class SkLineParameters { |
25 public: | 25 public: |
26 | 26 |
27 void cubicEndPoints(const SkDCubic& pts) { | 27 bool cubicEndPoints(const SkDCubic& pts) { |
28 int endIndex = 1; | 28 int endIndex = 1; |
29 cubicEndPoints(pts, 0, endIndex); | 29 cubicEndPoints(pts, 0, endIndex); |
30 if (dy() != 0) { | 30 if (dy() != 0) { |
31 return; | 31 return true; |
32 } | 32 } |
33 if (dx() == 0) { | 33 if (dx() == 0) { |
34 cubicEndPoints(pts, 0, ++endIndex); | 34 cubicEndPoints(pts, 0, ++endIndex); |
35 SkASSERT(endIndex == 2); | 35 SkASSERT(endIndex == 2); |
36 if (dy() != 0) { | 36 if (dy() != 0) { |
37 return; | 37 return true; |
38 } | 38 } |
39 if (dx() == 0) { | 39 if (dx() == 0) { |
40 cubicEndPoints(pts, 0, ++endIndex); // line | 40 cubicEndPoints(pts, 0, ++endIndex); // line |
41 SkASSERT(endIndex == 3); | 41 SkASSERT(endIndex == 3); |
42 return; | 42 return false; |
43 } | 43 } |
44 } | 44 } |
| 45 // FIXME: after switching to round sort, remove bumping fA |
45 if (dx() < 0) { // only worry about y bias when breaking cw/ccw tie | 46 if (dx() < 0) { // only worry about y bias when breaking cw/ccw tie |
46 return; | 47 return true; |
47 } | 48 } |
48 // if cubic tangent is on x axis, look at next control point to break ti
e | 49 // if cubic tangent is on x axis, look at next control point to break ti
e |
49 // control point may be approximate, so it must move significantly to ac
count for error | 50 // control point may be approximate, so it must move significantly to ac
count for error |
50 if (NotAlmostEqualUlps(pts[0].fY, pts[++endIndex].fY)) { | 51 if (NotAlmostEqualUlps(pts[0].fY, pts[++endIndex].fY)) { |
51 if (pts[0].fY > pts[endIndex].fY) { | 52 if (pts[0].fY > pts[endIndex].fY) { |
52 a = DBL_EPSILON; // push it from 0 to slightly negative (y() ret
urns -a) | 53 fA = DBL_EPSILON; // push it from 0 to slightly negative (y() re
turns -a) |
53 } | 54 } |
54 return; | 55 return true; |
55 } | 56 } |
56 if (endIndex == 3) { | 57 if (endIndex == 3) { |
57 return; | 58 return true; |
58 } | 59 } |
59 SkASSERT(endIndex == 2); | 60 SkASSERT(endIndex == 2); |
60 if (pts[0].fY > pts[3].fY) { | 61 if (pts[0].fY > pts[3].fY) { |
61 a = DBL_EPSILON; // push it from 0 to slightly negative (y() returns
-a) | 62 fA = DBL_EPSILON; // push it from 0 to slightly negative (y() return
s -a) |
62 } | 63 } |
| 64 return true; |
63 } | 65 } |
64 | 66 |
65 void cubicEndPoints(const SkDCubic& pts, int s, int e) { | 67 void cubicEndPoints(const SkDCubic& pts, int s, int e) { |
66 a = pts[s].fY - pts[e].fY; | 68 fA = pts[s].fY - pts[e].fY; |
67 b = pts[e].fX - pts[s].fX; | 69 fB = pts[e].fX - pts[s].fX; |
68 c = pts[s].fX * pts[e].fY - pts[e].fX * pts[s].fY; | 70 fC = pts[s].fX * pts[e].fY - pts[e].fX * pts[s].fY; |
69 } | 71 } |
70 | 72 |
71 double cubicPart(const SkDCubic& part) { | 73 double cubicPart(const SkDCubic& part) { |
72 cubicEndPoints(part); | 74 cubicEndPoints(part); |
73 if (part[0] == part[1] || ((const SkDLine& ) part[0]).nearRay(part[2]))
{ | 75 if (part[0] == part[1] || ((const SkDLine& ) part[0]).nearRay(part[2]))
{ |
74 return pointDistance(part[3]); | 76 return pointDistance(part[3]); |
75 } | 77 } |
76 return pointDistance(part[2]); | 78 return pointDistance(part[2]); |
77 } | 79 } |
78 | 80 |
79 void lineEndPoints(const SkDLine& pts) { | 81 void lineEndPoints(const SkDLine& pts) { |
80 a = pts[0].fY - pts[1].fY; | 82 fA = pts[0].fY - pts[1].fY; |
81 b = pts[1].fX - pts[0].fX; | 83 fB = pts[1].fX - pts[0].fX; |
82 c = pts[0].fX * pts[1].fY - pts[1].fX * pts[0].fY; | 84 fC = pts[0].fX * pts[1].fY - pts[1].fX * pts[0].fY; |
83 } | 85 } |
84 | 86 |
85 void quadEndPoints(const SkDQuad& pts) { | 87 bool quadEndPoints(const SkDQuad& pts) { |
86 quadEndPoints(pts, 0, 1); | 88 quadEndPoints(pts, 0, 1); |
87 if (dy() != 0) { | 89 if (dy() != 0) { |
88 return; | 90 return true; |
89 } | 91 } |
90 if (dx() == 0) { | 92 if (dx() == 0) { |
91 quadEndPoints(pts, 0, 2); | 93 quadEndPoints(pts, 0, 2); |
92 return; | 94 return false; |
93 } | 95 } |
94 if (dx() < 0) { // only worry about y bias when breaking cw/ccw tie | 96 if (dx() < 0) { // only worry about y bias when breaking cw/ccw tie |
95 return; | 97 return true; |
96 } | 98 } |
| 99 // FIXME: after switching to round sort, remove this |
97 if (pts[0].fY > pts[2].fY) { | 100 if (pts[0].fY > pts[2].fY) { |
98 a = DBL_EPSILON; | 101 fA = DBL_EPSILON; |
99 } | 102 } |
| 103 return true; |
100 } | 104 } |
101 | 105 |
102 void quadEndPoints(const SkDQuad& pts, int s, int e) { | 106 void quadEndPoints(const SkDQuad& pts, int s, int e) { |
103 a = pts[s].fY - pts[e].fY; | 107 fA = pts[s].fY - pts[e].fY; |
104 b = pts[e].fX - pts[s].fX; | 108 fB = pts[e].fX - pts[s].fX; |
105 c = pts[s].fX * pts[e].fY - pts[e].fX * pts[s].fY; | 109 fC = pts[s].fX * pts[e].fY - pts[e].fX * pts[s].fY; |
106 } | 110 } |
107 | 111 |
108 double quadPart(const SkDQuad& part) { | 112 double quadPart(const SkDQuad& part) { |
109 quadEndPoints(part); | 113 quadEndPoints(part); |
110 return pointDistance(part[2]); | 114 return pointDistance(part[2]); |
111 } | 115 } |
112 | 116 |
113 double normalSquared() const { | 117 double normalSquared() const { |
114 return a * a + b * b; | 118 return fA * fA + fB * fB; |
115 } | 119 } |
116 | 120 |
117 bool normalize() { | 121 bool normalize() { |
118 double normal = sqrt(normalSquared()); | 122 double normal = sqrt(normalSquared()); |
119 if (approximately_zero(normal)) { | 123 if (approximately_zero(normal)) { |
120 a = b = c = 0; | 124 fA = fB = fC = 0; |
121 return false; | 125 return false; |
122 } | 126 } |
123 double reciprocal = 1 / normal; | 127 double reciprocal = 1 / normal; |
124 a *= reciprocal; | 128 fA *= reciprocal; |
125 b *= reciprocal; | 129 fB *= reciprocal; |
126 c *= reciprocal; | 130 fC *= reciprocal; |
127 return true; | 131 return true; |
128 } | 132 } |
129 | 133 |
130 void cubicDistanceY(const SkDCubic& pts, SkDCubic& distance) const { | 134 void cubicDistanceY(const SkDCubic& pts, SkDCubic& distance) const { |
131 double oneThird = 1 / 3.0; | 135 double oneThird = 1 / 3.0; |
132 for (int index = 0; index < 4; ++index) { | 136 for (int index = 0; index < 4; ++index) { |
133 distance[index].fX = index * oneThird; | 137 distance[index].fX = index * oneThird; |
134 distance[index].fY = a * pts[index].fX + b * pts[index].fY + c; | 138 distance[index].fY = fA * pts[index].fX + fB * pts[index].fY + fC; |
135 } | 139 } |
136 } | 140 } |
137 | 141 |
138 void quadDistanceY(const SkDQuad& pts, SkDQuad& distance) const { | 142 void quadDistanceY(const SkDQuad& pts, SkDQuad& distance) const { |
139 double oneHalf = 1 / 2.0; | 143 double oneHalf = 1 / 2.0; |
140 for (int index = 0; index < 3; ++index) { | 144 for (int index = 0; index < 3; ++index) { |
141 distance[index].fX = index * oneHalf; | 145 distance[index].fX = index * oneHalf; |
142 distance[index].fY = a * pts[index].fX + b * pts[index].fY + c; | 146 distance[index].fY = fA * pts[index].fX + fB * pts[index].fY + fC; |
143 } | 147 } |
144 } | 148 } |
145 | 149 |
146 double controlPtDistance(const SkDCubic& pts, int index) const { | 150 double controlPtDistance(const SkDCubic& pts, int index) const { |
147 SkASSERT(index == 1 || index == 2); | 151 SkASSERT(index == 1 || index == 2); |
148 return a * pts[index].fX + b * pts[index].fY + c; | 152 return fA * pts[index].fX + fB * pts[index].fY + fC; |
149 } | 153 } |
150 | 154 |
151 double controlPtDistance(const SkDQuad& pts) const { | 155 double controlPtDistance(const SkDQuad& pts) const { |
152 return a * pts[1].fX + b * pts[1].fY + c; | 156 return fA * pts[1].fX + fB * pts[1].fY + fC; |
153 } | 157 } |
154 | 158 |
155 double pointDistance(const SkDPoint& pt) const { | 159 double pointDistance(const SkDPoint& pt) const { |
156 return a * pt.fX + b * pt.fY + c; | 160 return fA * pt.fX + fB * pt.fY + fC; |
157 } | 161 } |
158 | 162 |
159 double dx() const { | 163 double dx() const { |
160 return b; | 164 return fB; |
161 } | 165 } |
162 | 166 |
163 double dy() const { | 167 double dy() const { |
164 return -a; | 168 return -fA; |
165 } | 169 } |
166 | 170 |
167 private: | 171 private: |
168 double a; | 172 double fA; |
169 double b; | 173 double fB; |
170 double c; | 174 double fC; |
171 }; | 175 }; |
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