1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
|
/*
* Copyright 2012 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "SkIntersections.h"
#include "SkPathOpsLine.h"
/* Determine the intersection point of two lines. This assumes the lines are not parallel,
and that that the lines are infinite.
From http://en.wikipedia.org/wiki/Line-line_intersection
*/
SkDPoint SkIntersections::Line(const SkDLine& a, const SkDLine& b) {
double axLen = a[1].fX - a[0].fX;
double ayLen = a[1].fY - a[0].fY;
double bxLen = b[1].fX - b[0].fX;
double byLen = b[1].fY - b[0].fY;
double denom = byLen * axLen - ayLen * bxLen;
SkASSERT(denom);
double term1 = a[1].fX * a[0].fY - a[1].fY * a[0].fX;
double term2 = b[1].fX * b[0].fY - b[1].fY * b[0].fX;
SkDPoint p;
p.fX = (term1 * bxLen - axLen * term2) / denom;
p.fY = (term1 * byLen - ayLen * term2) / denom;
return p;
}
int SkIntersections::computePoints(const SkDLine& line, int used) {
fPt[0] = line.xyAtT(fT[0][0]);
if ((fUsed = used) == 2) {
fPt[1] = line.xyAtT(fT[0][1]);
}
return fUsed;
}
/*
Determine the intersection point of two line segments
Return FALSE if the lines don't intersect
from: http://paulbourke.net/geometry/lineline2d/
*/
int SkIntersections::intersect(const SkDLine& a, const SkDLine& b) {
double axLen = a[1].fX - a[0].fX;
double ayLen = a[1].fY - a[0].fY;
double bxLen = b[1].fX - b[0].fX;
double byLen = b[1].fY - b[0].fY;
/* Slopes match when denom goes to zero:
axLen / ayLen == bxLen / byLen
(ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
byLen * axLen == ayLen * bxLen
byLen * axLen - ayLen * bxLen == 0 ( == denom )
*/
double denom = byLen * axLen - ayLen * bxLen;
double ab0y = a[0].fY - b[0].fY;
double ab0x = a[0].fX - b[0].fX;
double numerA = ab0y * bxLen - byLen * ab0x;
double numerB = ab0y * axLen - ayLen * ab0x;
bool mayNotOverlap = (numerA < 0 && denom > numerA) || (numerA > 0 && denom < numerA)
|| (numerB < 0 && denom > numerB) || (numerB > 0 && denom < numerB);
numerA /= denom;
numerB /= denom;
if ((!approximately_zero(denom) || (!approximately_zero_inverse(numerA)
&& !approximately_zero_inverse(numerB))) && !sk_double_isnan(numerA)
&& !sk_double_isnan(numerB)) {
if (mayNotOverlap) {
return fUsed = 0;
}
fT[0][0] = numerA;
fT[1][0] = numerB;
fPt[0] = a.xyAtT(numerA);
return computePoints(a, 1);
}
/* See if the axis intercepts match:
ay - ax * ayLen / axLen == by - bx * ayLen / axLen
axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen)
axLen * ay - ax * ayLen == axLen * by - bx * ayLen
*/
if (!AlmostEqualUlps(axLen * a[0].fY - ayLen * a[0].fX,
axLen * b[0].fY - ayLen * b[0].fX)) {
return fUsed = 0;
}
const double* aPtr;
const double* bPtr;
if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) {
aPtr = &a[0].fX;
bPtr = &b[0].fX;
} else {
aPtr = &a[0].fY;
bPtr = &b[0].fY;
}
double a0 = aPtr[0];
double a1 = aPtr[2];
double b0 = bPtr[0];
double b1 = bPtr[2];
// OPTIMIZATION: restructure to reject before the divide
// e.g., if ((a0 - b0) * (a0 - a1) < 0 || abs(a0 - b0) > abs(a0 - a1))
// (except efficient)
double aDenom = a0 - a1;
if (approximately_zero(aDenom)) {
if (!between(b0, a0, b1)) {
return fUsed = 0;
}
fT[0][0] = fT[0][1] = 0;
} else {
double at0 = (a0 - b0) / aDenom;
double at1 = (a0 - b1) / aDenom;
if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
return fUsed = 0;
}
fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
}
double bDenom = b0 - b1;
if (approximately_zero(bDenom)) {
fT[1][0] = fT[1][1] = 0;
} else {
int bIn = aDenom * bDenom < 0;
fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / bDenom, 1.0), 0.0);
fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / bDenom, 1.0), 0.0);
}
bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON;
SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second);
return computePoints(a, 1 + second);
}
int SkIntersections::horizontal(const SkDLine& line, double y) {
double min = line[0].fY;
double max = line[1].fY;
if (min > max) {
SkTSwap(min, max);
}
if (min > y || max < y) {
return fUsed = 0;
}
if (AlmostEqualUlps(min, max)) {
fT[0][0] = 0;
fT[0][1] = 1;
return fUsed = 2;
}
fT[0][0] = (y - line[0].fY) / (line[1].fY - line[0].fY);
return fUsed = 1;
}
// OPTIMIZATION Given: dy = line[1].fY - line[0].fY
// and: xIntercept / (y - line[0].fY) == (line[1].fX - line[0].fX) / dy
// then: xIntercept * dy == (line[1].fX - line[0].fX) * (y - line[0].fY)
// Assuming that dy is always > 0, the line segment intercepts if:
// left * dy <= xIntercept * dy <= right * dy
// thus: left * dy <= (line[1].fX - line[0].fX) * (y - line[0].fY) <= right * dy
// (clever as this is, it does not give us the t value, so may be useful only
// as a quick reject -- and maybe not then; it takes 3 muls, 3 adds, 2 cmps)
int SkIntersections::horizontal(const SkDLine& line, double left, double right, double y) {
int result = horizontal(line, y);
if (result != 1) {
SkASSERT(0);
return result;
}
double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX);
if (!precisely_between(left, xIntercept, right)) {
return fUsed = 0;
}
return result;
}
int SkIntersections::horizontal(const SkDLine& line, double left, double right,
double y, bool flipped) {
int result = horizontal(line, y);
switch (result) {
case 0:
break;
case 1: {
double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX);
if (!precisely_between(left, xIntercept, right)) {
return fUsed = 0;
}
fT[1][0] = (xIntercept - left) / (right - left);
break;
}
case 2:
double a0 = line[0].fX;
double a1 = line[1].fX;
double b0 = flipped ? right : left;
double b1 = flipped ? left : right;
// FIXME: share common code below
double at0 = (a0 - b0) / (a0 - a1);
double at1 = (a0 - b1) / (a0 - a1);
if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
return fUsed = 0;
}
fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
int bIn = (a0 - a1) * (b0 - b1) < 0;
fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), 1.0), 0.0);
fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), 1.0), 0.0);
bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON;
SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second);
return computePoints(line, 1 + second);
}
if (flipped) {
// OPTIMIZATION: instead of swapping, pass original line, use [1].fX - [0].fX
for (int index = 0; index < result; ++index) {
fT[1][index] = 1 - fT[1][index];
}
}
return computePoints(line, result);
}
int SkIntersections::vertical(const SkDLine& line, double x) {
double min = line[0].fX;
double max = line[1].fX;
if (min > max) {
SkTSwap(min, max);
}
if (!precisely_between(min, x, max)) {
return fUsed = 0;
}
if (AlmostEqualUlps(min, max)) {
fT[0][0] = 0;
fT[0][1] = 1;
return fUsed = 2;
}
fT[0][0] = (x - line[0].fX) / (line[1].fX - line[0].fX);
return fUsed = 1;
}
int SkIntersections::vertical(const SkDLine& line, double top, double bottom,
double x, bool flipped) {
int result = vertical(line, x);
switch (result) {
case 0:
break;
case 1: {
double yIntercept = line[0].fY + fT[0][0] * (line[1].fY - line[0].fY);
if (!precisely_between(top, yIntercept, bottom)) {
return fUsed = 0;
}
fT[1][0] = (yIntercept - top) / (bottom - top);
break;
}
case 2:
double a0 = line[0].fY;
double a1 = line[1].fY;
double b0 = flipped ? bottom : top;
double b1 = flipped ? top : bottom;
// FIXME: share common code above
double at0 = (a0 - b0) / (a0 - a1);
double at1 = (a0 - b1) / (a0 - a1);
if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
return fUsed = 0;
}
fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
int bIn = (a0 - a1) * (b0 - b1) < 0;
fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), 1.0), 0.0);
fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), 1.0), 0.0);
bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON;
SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second);
return computePoints(line, 1 + second);
}
if (flipped) {
// OPTIMIZATION: instead of swapping, pass original line, use [1].fY - [0].fY
for (int index = 0; index < result; ++index) {
fT[1][index] = 1 - fT[1][index];
}
}
return computePoints(line, result);
}
// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py
// 4 subs, 2 muls, 1 cmp
static bool ccw(const SkDPoint& A, const SkDPoint& B, const SkDPoint& C) {
return (C.fY - A.fY) * (B.fX - A.fX) > (B.fY - A.fY) * (C.fX - A.fX);
}
// 16 subs, 8 muls, 6 cmps
bool SkIntersections::Test(const SkDLine& a, const SkDLine& b) {
return ccw(a[0], b[0], b[1]) != ccw(a[1], b[0], b[1])
&& ccw(a[0], a[1], b[0]) != ccw(a[0], a[1], b[1]);
}
|
