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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 "DataTypes.h" | |
8 | |
9 // Sources | |
10 // computer-aided design - volume 22 number 9 november 1990 pp 538 - 549 | |
11 // online at http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf | |
12 | |
13 // This turns a line segment into a parameterized line, of the form | |
14 // ax + by + c = 0 | |
15 // When a^2 + b^2 == 1, the line is normalized. | |
16 // The distance to the line for (x, y) is d(x,y) = ax + by + c | |
17 // | |
18 // Note that the distances below are not necessarily normalized. To get the true | |
19 // distance, it's necessary to either call normalize() after xxxEndPoints(), or | |
20 // divide the result of xxxDistance() by sqrt(normalSquared()) | |
21 | |
22 class LineParameters { | |
23 public: | |
24 void cubicEndPoints(const Cubic& pts) { | |
25 cubicEndPoints(pts, 0, 3); | |
26 } | |
27 | |
28 void cubicEndPoints(const Cubic& pts, int s, int e) { | |
29 a = approximately_pin(pts[s].y - pts[e].y); | |
30 b = approximately_pin(pts[e].x - pts[s].x); | |
31 c = pts[s].x * pts[e].y - pts[e].x * pts[s].y; | |
32 } | |
33 | |
34 void lineEndPoints(const _Line& pts) { | |
35 a = approximately_pin(pts[0].y - pts[1].y); | |
36 b = approximately_pin(pts[1].x - pts[0].x); | |
37 c = pts[0].x * pts[1].y - pts[1].x * pts[0].y; | |
38 } | |
39 | |
40 void quadEndPoints(const Quadratic& pts) { | |
41 quadEndPoints(pts, 0, 2); | |
42 } | |
43 | |
44 void quadEndPoints(const Quadratic& pts, int s, int e) { | |
45 a = approximately_pin(pts[s].y - pts[e].y); | |
46 b = approximately_pin(pts[e].x - pts[s].x); | |
47 c = pts[s].x * pts[e].y - pts[e].x * pts[s].y; | |
48 } | |
49 | |
50 double normalSquared() const { | |
51 return a * a + b * b; | |
52 } | |
53 | |
54 bool normalize() { | |
55 double normal = sqrt(normalSquared()); | |
56 if (approximately_zero(normal)) { | |
57 a = b = c = 0; | |
58 return false; | |
59 } | |
60 double reciprocal = 1 / normal; | |
61 a *= reciprocal; | |
62 b *= reciprocal; | |
63 c *= reciprocal; | |
64 return true; | |
65 } | |
66 | |
67 void cubicDistanceY(const Cubic& pts, Cubic& distance) const { | |
68 double oneThird = 1 / 3.0; | |
69 for (int index = 0; index < 4; ++index) { | |
70 distance[index].x = index * oneThird; | |
71 distance[index].y = a * pts[index].x + b * pts[index].y + c; | |
72 } | |
73 } | |
74 | |
75 void quadDistanceY(const Quadratic& pts, Quadratic& distance) const { | |
76 double oneHalf = 1 / 2.0; | |
77 for (int index = 0; index < 3; ++index) { | |
78 distance[index].x = index * oneHalf; | |
79 distance[index].y = a * pts[index].x + b * pts[index].y + c; | |
80 } | |
81 } | |
82 | |
83 double controlPtDistance(const Cubic& pts, int index) const { | |
84 SkASSERT(index == 1 || index == 2); | |
85 return a * pts[index].x + b * pts[index].y + c; | |
86 } | |
87 | |
88 double controlPtDistance(const Quadratic& pts) const { | |
89 return a * pts[1].x + b * pts[1].y + c; | |
90 } | |
91 | |
92 double pointDistance(const _Point& pt) const { | |
93 return a * pt.x + b * pt.y + c; | |
94 } | |
95 | |
96 double dx() const { | |
97 return b; | |
98 } | |
99 | |
100 double dy() const { | |
101 return -a; | |
102 } | |
103 | |
104 private: | |
105 double a; | |
106 double b; | |
107 double c; | |
108 }; | |
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