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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 "IntersectionUtilities.h" | |
9 #include "QuadraticUtilities.h" | |
10 | |
11 /* | |
12 Given a quadratic q, t1, and t2, find a small quadratic segment. | |
13 | |
14 The new quadratic is defined by A, B, and C, where | |
15 A = c[0]*(1 - t1)*(1 - t1) + 2*c[1]*t1*(1 - t1) + c[2]*t1*t1 | |
16 C = c[3]*(1 - t1)*(1 - t1) + 2*c[2]*t1*(1 - t1) + c[1]*t1*t1 | |
17 | |
18 To find B, compute the point halfway between t1 and t2: | |
19 | |
20 q(at (t1 + t2)/2) == D | |
21 | |
22 Next, compute where D must be if we know the value of B: | |
23 | |
24 _12 = A/2 + B/2 | |
25 12_ = B/2 + C/2 | |
26 123 = A/4 + B/2 + C/4 | |
27 = D | |
28 | |
29 Group the known values on one side: | |
30 | |
31 B = D*2 - A/2 - C/2 | |
32 */ | |
33 | |
34 static double interp_quad_coords(const double* src, double t) | |
35 { | |
36 double ab = interp(src[0], src[2], t); | |
37 double bc = interp(src[2], src[4], t); | |
38 double abc = interp(ab, bc, t); | |
39 return abc; | |
40 } | |
41 | |
42 void sub_divide(const Quadratic& src, double t1, double t2, Quadratic& dst) { | |
43 double ax = dst[0].x = interp_quad_coords(&src[0].x, t1); | |
44 double ay = dst[0].y = interp_quad_coords(&src[0].y, t1); | |
45 double dx = interp_quad_coords(&src[0].x, (t1 + t2) / 2); | |
46 double dy = interp_quad_coords(&src[0].y, (t1 + t2) / 2); | |
47 double cx = dst[2].x = interp_quad_coords(&src[0].x, t2); | |
48 double cy = dst[2].y = interp_quad_coords(&src[0].y, t2); | |
49 /* bx = */ dst[1].x = 2*dx - (ax + cx)/2; | |
50 /* by = */ dst[1].y = 2*dy - (ay + cy)/2; | |
51 } | |
52 | |
53 _Point sub_divide(const Quadratic& src, const _Point& a, const _Point& c, double
t1, double t2) { | |
54 _Point b; | |
55 double dx = interp_quad_coords(&src[0].x, (t1 + t2) / 2); | |
56 double dy = interp_quad_coords(&src[0].y, (t1 + t2) / 2); | |
57 b.x = 2 * dx - (a.x + c.x) / 2; | |
58 b.y = 2 * dy - (a.y + c.y) / 2; | |
59 return b; | |
60 } | |
61 | |
62 /* classic one t subdivision */ | |
63 static void interp_quad_coords(const double* src, double* dst, double t) | |
64 { | |
65 double ab = interp(src[0], src[2], t); | |
66 double bc = interp(src[2], src[4], t); | |
67 | |
68 dst[0] = src[0]; | |
69 dst[2] = ab; | |
70 dst[4] = interp(ab, bc, t); | |
71 dst[6] = bc; | |
72 dst[8] = src[4]; | |
73 } | |
74 | |
75 void chop_at(const Quadratic& src, QuadraticPair& dst, double t) | |
76 { | |
77 interp_quad_coords(&src[0].x, &dst.pts[0].x, t); | |
78 interp_quad_coords(&src[0].y, &dst.pts[0].y, t); | |
79 } | |
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