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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 "CurveIntersection.h" | |
8 #include "CurveUtilities.h" | |
9 #include "LineParameters.h" | |
10 | |
11 #define DEBUG_BEZIER_CLIP 1 | |
12 | |
13 // return false if unable to clip (e.g., unable to create implicit line) | |
14 // caller should subdivide, or create degenerate if the values are too small | |
15 bool bezier_clip(const Quadratic& q1, const Quadratic& q2, double& minT, double&
maxT) { | |
16 minT = 1; | |
17 maxT = 0; | |
18 // determine normalized implicit line equation for pt[0] to pt[3] | |
19 // of the form ax + by + c = 0, where a*a + b*b == 1 | |
20 | |
21 // find the implicit line equation parameters | |
22 LineParameters endLine; | |
23 endLine.quadEndPoints(q1); | |
24 if (!endLine.normalize()) { | |
25 printf("line cannot be normalized: need more code here\n"); | |
26 SkASSERT(0); | |
27 return false; | |
28 } | |
29 | |
30 double distance = endLine.controlPtDistance(q1); | |
31 | |
32 // find fat line | |
33 double top = 0; | |
34 double bottom = distance / 2; // http://students.cs.byu.edu/~tom/557/text/ci
c.pdf (7.6) | |
35 if (top > bottom) { | |
36 SkTSwap(top, bottom); | |
37 } | |
38 | |
39 // compute intersecting candidate distance | |
40 Quadratic distance2y; // points with X of (0, 1/2, 1) | |
41 endLine.quadDistanceY(q2, distance2y); | |
42 | |
43 int flags = 0; | |
44 if (approximately_lesser_or_equal(distance2y[0].y, top)) { | |
45 flags |= kFindTopMin; | |
46 } else if (approximately_greater_or_equal(distance2y[0].y, bottom)) { | |
47 flags |= kFindBottomMin; | |
48 } else { | |
49 minT = 0; | |
50 } | |
51 | |
52 if (approximately_lesser_or_equal(distance2y[2].y, top)) { | |
53 flags |= kFindTopMax; | |
54 } else if (approximately_greater_or_equal(distance2y[2].y, bottom)) { | |
55 flags |= kFindBottomMax; | |
56 } else { | |
57 maxT = 1; | |
58 } | |
59 // Find the intersection of distance convex hull and fat line. | |
60 int idx = 0; | |
61 do { | |
62 int next = idx + 1; | |
63 if (next == 3) { | |
64 next = 0; | |
65 } | |
66 x_at(distance2y[idx], distance2y[next], top, bottom, flags, minT, maxT); | |
67 idx = next; | |
68 } while (idx); | |
69 #if DEBUG_BEZIER_CLIP | |
70 _Rect r1, r2; | |
71 r1.setBounds(q1); | |
72 r2.setBounds(q2); | |
73 _Point testPt = {0.487, 0.337}; | |
74 if (r1.contains(testPt) && r2.contains(testPt)) { | |
75 printf("%s q1=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)" | |
76 " q2=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) minT=%1.9g maxT=%1.9g
\n", | |
77 __FUNCTION__, q1[0].x, q1[0].y, q1[1].x, q1[1].y, q1[2].x, q1[2]
.y, | |
78 q2[0].x, q2[0].y, q2[1].x, q2[1].y, q2[2].x, q2[2].y, minT, maxT
); | |
79 } | |
80 #endif | |
81 return minT < maxT; // returns false if distance shows no intersection | |
82 } | |
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