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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 "IntersectionUtilities.h" | |
10 | |
11 /* Given a cubic, find the convex hull described by the end and control points. | |
12 The hull may have 3 or 4 points. Cubics that degenerate into a point or line | |
13 are not considered. | |
14 | |
15 The hull is computed by assuming that three points, if unique and non-linear, | |
16 form a triangle. The fourth point may replace one of the first three, may be | |
17 discarded if in the triangle or on an edge, or may be inserted between any of | |
18 the three to form a convex quadralateral. | |
19 | |
20 The indices returned in order describe the convex hull. | |
21 */ | |
22 int convex_hull(const Cubic& cubic, char order[4]) { | |
23 size_t index; | |
24 // find top point | |
25 size_t yMin = 0; | |
26 for (index = 1; index < 4; ++index) { | |
27 if (cubic[yMin].y > cubic[index].y || (cubic[yMin].y == cubic[index].y | |
28 && cubic[yMin].x > cubic[index].x)) { | |
29 yMin = index; | |
30 } | |
31 } | |
32 order[0] = yMin; | |
33 int midX = -1; | |
34 int backupYMin = -1; | |
35 for (int pass = 0; pass < 2; ++pass) { | |
36 for (index = 0; index < 4; ++index) { | |
37 if (index == yMin) { | |
38 continue; | |
39 } | |
40 // rotate line from (yMin, index) to axis | |
41 // see if remaining two points are both above or below | |
42 // use this to find mid | |
43 int mask = other_two(yMin, index); | |
44 int side1 = yMin ^ mask; | |
45 int side2 = index ^ mask; | |
46 Cubic rotPath; | |
47 if (!rotate(cubic, yMin, index, rotPath)) { // ! if cbc[yMin]==cbc[i
dx] | |
48 order[1] = side1; | |
49 order[2] = side2; | |
50 return 3; | |
51 } | |
52 int sides = side(rotPath[side1].y - rotPath[yMin].y); | |
53 sides ^= side(rotPath[side2].y - rotPath[yMin].y); | |
54 if (sides == 2) { // '2' means one remaining point <0, one >0 | |
55 if (midX >= 0) { | |
56 printf("%s unexpected mid\n", __FUNCTION__); // there can be
only one mid | |
57 } | |
58 midX = index; | |
59 } else if (sides == 0) { // '0' means both to one side or the other | |
60 backupYMin = index; | |
61 } | |
62 } | |
63 if (midX >= 0) { | |
64 break; | |
65 } | |
66 if (backupYMin < 0) { | |
67 break; | |
68 } | |
69 yMin = backupYMin; | |
70 backupYMin = -1; | |
71 } | |
72 if (midX < 0) { | |
73 midX = yMin ^ 3; // choose any other point | |
74 } | |
75 int mask = other_two(yMin, midX); | |
76 int least = yMin ^ mask; | |
77 int most = midX ^ mask; | |
78 order[0] = yMin; | |
79 order[1] = least; | |
80 | |
81 // see if mid value is on same side of line (least, most) as yMin | |
82 Cubic midPath; | |
83 if (!rotate(cubic, least, most, midPath)) { // ! if cbc[least]==cbc[most] | |
84 order[2] = midX; | |
85 return 3; | |
86 } | |
87 int midSides = side(midPath[yMin].y - midPath[least].y); | |
88 midSides ^= side(midPath[midX].y - midPath[least].y); | |
89 if (midSides != 2) { // if mid point is not between | |
90 order[2] = most; | |
91 return 3; // result is a triangle | |
92 } | |
93 order[2] = midX; | |
94 order[3] = most; | |
95 return 4; // result is a quadralateral | |
96 } | |
97 | |
98 /* Find the convex hull for cubics with the x-axis interval regularly spaced. | |
99 Cubics computed as distance functions are formed this way. | |
100 | |
101 connectTo0[0], connectTo0[1] are the point indices that cubic[0] connects to. | |
102 connectTo3[0], connectTo3[1] are the point indices that cubic[3] connects to. | |
103 | |
104 Returns true if cubic[1] to cubic[2] also forms part of the hull. | |
105 */ | |
106 bool convex_x_hull(const Cubic& cubic, char connectTo0[2], char connectTo3[2]) { | |
107 double projectedY[4]; | |
108 projectedY[0] = 0; | |
109 int index; | |
110 for (index = 1; index < 4; ++index) { | |
111 projectedY[index] = (cubic[index].y - cubic[0].y) * (3.0 / index); | |
112 } | |
113 int lower0Index = 1; | |
114 int upper0Index = 1; | |
115 for (index = 2; index < 4; ++index) { | |
116 if (approximately_greater_or_equal(projectedY[lower0Index], projectedY[i
ndex])) { | |
117 lower0Index = index; | |
118 } | |
119 if (approximately_lesser_or_equal(projectedY[upper0Index], projectedY[in
dex])) { | |
120 upper0Index = index; | |
121 } | |
122 } | |
123 connectTo0[0] = lower0Index; | |
124 connectTo0[1] = upper0Index; | |
125 for (index = 0; index < 3; ++index) { | |
126 projectedY[index] = (cubic[3].y - cubic[index].y) * (3.0 / (3 - index)); | |
127 } | |
128 projectedY[3] = 0; | |
129 int lower3Index = 2; | |
130 int upper3Index = 2; | |
131 for (index = 1; index > -1; --index) { | |
132 if (approximately_greater_or_equal(projectedY[lower3Index], projectedY[i
ndex])) { | |
133 lower3Index = index; | |
134 } | |
135 if (approximately_lesser_or_equal(projectedY[upper3Index], projectedY[in
dex])) { | |
136 upper3Index = index; | |
137 } | |
138 } | |
139 connectTo3[0] = lower3Index; | |
140 connectTo3[1] = upper3Index; | |
141 return (1 << lower0Index | 1 << upper0Index | |
142 | 1 << lower3Index | 1 << upper3Index) == 0x0F; | |
143 } | |
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