1 /*
2 * vim: ts=4 sw=4 et tw=0 wm=0
3 *
4 * libavoid - Fast, Incremental, Object-avoiding Line Router
5 * Copyright (C) 2004-2006 Michael Wybrow <mjwybrow@users.sourceforge.net>
6 *
7 * --------------------------------------------------------------------
8 * Much of the code in this module is based on code published with
9 * and/or described in "Computational Geometry in C" (Second Edition),
10 * Copyright (C) 1998 Joseph O'Rourke <orourke@cs.smith.edu>
11 * --------------------------------------------------------------------
12 * The segmentIntersectPoint function is based on code published and
13 * described in Franklin Antonio, Faster Line Segment Intersection,
14 * Graphics Gems III, p. 199-202, code: p. 500-501.
15 * --------------------------------------------------------------------
16 *
17 * This library is free software; you can redistribute it and/or
18 * modify it under the terms of the GNU Lesser General Public
19 * License as published by the Free Software Foundation; either
20 * version 2.1 of the License, or (at your option) any later version.
21 *
22 * This library is distributed in the hope that it will be useful,
23 * but WITHOUT ANY WARRANTY; without even the implied warranty of
24 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
25 * Lesser General Public License for more details.
26 *
27 * You should have received a copy of the GNU Lesser General Public
28 * License along with this library; if not, write to the Free Software
29 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
30 *
31 */
33 #include "libavoid/graph.h"
34 #include "libavoid/geometry.h"
35 #include "libavoid/polyutil.h"
37 #include <math.h>
39 namespace Avoid {
42 Point::Point()
43 {
44 }
47 Point::Point(const double xv, const double yv)
48 : x(xv)
49 , y(yv)
50 {
51 }
54 bool Point::operator==(const Point& rhs) const
55 {
56 if ((x == rhs.x) && (y == rhs.y))
57 {
58 return true;
59 }
60 return false;
61 }
64 bool Point::operator!=(const Point& rhs) const
65 {
66 if ((x != rhs.x) || (y != rhs.y))
67 {
68 return true;
69 }
70 return false;
71 }
74 // Returns true iff the point c lies on the closed segment ab.
75 //
76 // Based on the code of 'Between'.
77 //
78 static const bool inBetween(const Point& a, const Point& b, const Point& c)
79 {
80 // We only call this when we know the points are collinear,
81 // otherwise we should be checking this here.
82 assert(vecDir(a, b, c) == 0);
84 if (a.x != b.x)
85 {
86 // not vertical
87 return (((a.x < c.x) && (c.x < b.x)) ||
88 ((b.x < c.x) && (c.x < a.x)));
89 }
90 else
91 {
92 return (((a.y < c.y) && (c.y < b.y)) ||
93 ((b.y < c.y) && (c.y < a.y)));
94 }
95 }
98 // Returns true if the segment cd intersects the segment ab, blocking
99 // visibility.
100 //
101 // Based on the code of 'IntersectProp' and 'Intersect'.
102 //
103 bool segmentIntersect(const Point& a, const Point& b, const Point& c,
104 const Point& d)
105 {
106 int ab_c = vecDir(a, b, c);
107 if ((ab_c == 0) && inBetween(a, b, c))
108 {
109 return true;
110 }
112 int ab_d = vecDir(a, b, d);
113 if ((ab_d == 0) && inBetween(a, b, d))
114 {
115 return true;
116 }
118 // It's ok for either of the points a or b to be on the line cd,
119 // so we don't have to check the other two cases.
121 int cd_a = vecDir(c, d, a);
122 int cd_b = vecDir(c, d, b);
124 // Is an intersection if a and b are on opposite sides of cd,
125 // and c and d are on opposite sides of the line ab.
126 //
127 // Note: this is safe even though the textbook warns about it
128 // since, unlike them, our vecDir is equivilent to 'AreaSign'
129 // rather than 'Area2'.
130 return (((ab_c * ab_d) < 0) && ((cd_a * cd_b) < 0));
131 }
134 // Returns true iff the point p in a valid region that can contain
135 // shortest paths. a0, a1, a2 are ordered vertices of a shape.
136 //
137 // Based on the code of 'InCone'.
138 //
139 bool inValidRegion(bool IgnoreRegions, const Point& a0, const Point& a1,
140 const Point& a2, const Point& b)
141 {
142 // r is a0--a1
143 // s is a1--a2
145 int rSide = vecDir(b, a0, a1);
146 int sSide = vecDir(b, a1, a2);
148 bool rOutOn = (rSide <= 0);
149 bool sOutOn = (sSide <= 0);
151 bool rOut = (rSide < 0);
152 bool sOut = (sSide < 0);
154 if (vecDir(a0, a1, a2) > 0)
155 {
156 // Convex at a1:
157 //
158 // !rO rO
159 // sO sO
160 //
161 // ---s---+
162 // |
163 // !rO r rO
164 // !sO | !sO
165 //
166 //
167 if (IgnoreRegions)
168 {
169 return (rOutOn && !sOut) || (!rOut && sOutOn);
170 }
171 return (rOutOn || sOutOn);
172 }
173 else
174 {
175 // Concave at a1:
176 //
177 // !rO rO
178 // !sO !sO
179 //
180 // +---s---
181 // |
182 // !rO r rO
183 // sO | sO
184 //
185 //
186 return (IgnoreRegions ? false : (rOutOn && sOutOn));
187 }
188 }
191 // Gives the side of a corner that a point lies on:
192 // 1 anticlockwise
193 // -1 clockwise
194 // e.g. /|s2
195 // /s3 -1 / |
196 // / / |
197 // 1 |s2 -1 / 1 | -1
198 // | / |
199 // |s1 s3/ |s1
200 //
201 int cornerSide(const Point &c1, const Point &c2, const Point &c3,
202 const Point& p)
203 {
204 int s123 = vecDir(c1, c2, c3);
205 int s12p = vecDir(c1, c2, p);
206 int s23p = vecDir(c2, c3, p);
208 if (s12p == 0)
209 {
210 // Case of p being somewhere on c1-c2.
211 return s23p;
212 }
213 if (s23p == 0)
214 {
215 // Case of p being somewhere on c2-c3.
216 return s12p;
217 }
219 if (s123 == 1)
220 {
221 if ((s12p == 1) && (s23p == 1))
222 {
223 return 1;
224 }
225 return -1;
226 }
227 else if (s123 == -1)
228 {
229 if ((s12p == -1) && (s23p == -1))
230 {
231 return -1;
232 }
233 return 1;
234 }
235 // Case of c3 being somewhere on c1-c2.
236 return s12p;
237 }
240 // Returns the distance between points a and b.
241 //
242 double dist(const Point& a, const Point& b)
243 {
244 double xdiff = a.x - b.x;
245 double ydiff = a.y - b.y;
247 return sqrt((xdiff * xdiff) + (ydiff * ydiff));
248 }
250 // Returns the total length of all line segments in the polygon
251 double totalLength(const Polygn& poly)
252 {
253 double l = 0;
254 for (int i = 0; i < poly.pn-1; ++i) {
255 l += dist(poly.ps[i], poly.ps[i+1]);
256 }
257 return l;
258 }
260 // Uses the dot-product rule to find the angle (radians) between ab and bc
261 double angle(const Point& a, const Point& b, const Point& c)
262 {
263 double ux = b.x - a.x,
264 uy = b.y - a.y,
265 vx = c.x - b.x,
266 vy = c.y - b.y,
267 lu = sqrt(ux*ux+uy*uy),
268 lv = sqrt(vx*vx+vy*vy),
269 udotv = ux * vx + uy * vy,
270 costheta = udotv / (lu * lv);
271 return acos(costheta);
272 }
274 // Returns true iff the point q is inside (or on the edge of) the
275 // polygon argpoly.
276 //
277 // This is a fast version that only works for convex shapes. The
278 // other version (inPolyGen) is more general.
279 //
280 bool inPoly(const Polygn& poly, const Point& q)
281 {
282 int n = poly.pn;
283 Point *P = poly.ps;
284 for (int i = 0; i < n; i++)
285 {
286 // point index; i1 = i-1 mod n
287 int prev = (i + n - 1) % n;
288 if (vecDir(P[prev], P[i], q) == -1)
289 {
290 return false;
291 }
292 }
293 return true;
294 }
297 // Returns true iff the point q is inside (or on the edge of) the
298 // polygon argpoly.
299 //
300 // Based on the code of 'InPoly'.
301 //
302 bool inPolyGen(const Polygn& argpoly, const Point& q)
303 {
304 // Numbers of right and left edge/ray crossings.
305 int Rcross = 0;
306 int Lcross = 0;
308 // Copy the argument polygon
309 Polygn poly = copyPoly(argpoly);
310 Point *P = poly.ps;
311 int n = poly.pn;
313 // Shift so that q is the origin. This is done for pedogical clarity.
314 for (int i = 0; i < n; ++i)
315 {
316 P[i].x = P[i].x - q.x;
317 P[i].y = P[i].y - q.y;
318 }
320 // For each edge e=(i-1,i), see if crosses ray.
321 for (int i = 0; i < n; ++i)
322 {
323 // First see if q=(0,0) is a vertex.
324 if ((P[i].x == 0) && (P[i].y == 0))
325 {
326 // We count a vertex as inside.
327 freePoly(poly);
328 return true;
329 }
331 // point index; i1 = i-1 mod n
332 int i1 = ( i + n - 1 ) % n;
334 // if e "straddles" the x-axis...
335 // The commented-out statement is logically equivalent to the one
336 // following.
337 // if( ((P[i].y > 0) && (P[i1].y <= 0)) ||
338 // ((P[i1].y > 0) && (P[i].y <= 0)) )
340 if ((P[i].y > 0) != (P[i1].y > 0))
341 {
342 // e straddles ray, so compute intersection with ray.
343 double x = (P[i].x * P[i1].y - P[i1].x * P[i].y)
344 / (P[i1].y - P[i].y);
346 // crosses ray if strictly positive intersection.
347 if (x > 0)
348 {
349 Rcross++;
350 }
351 }
353 // if e straddles the x-axis when reversed...
354 // if( ((P[i].y < 0) && (P[i1].y >= 0)) ||
355 // ((P[i1].y < 0) && (P[i].y >= 0)) )
357 if ((P[i].y < 0) != (P[i1].y < 0))
358 {
359 // e straddles ray, so compute intersection with ray.
360 double x = (P[i].x * P[i1].y - P[i1].x * P[i].y)
361 / (P[i1].y - P[i].y);
363 // crosses ray if strictly positive intersection.
364 if (x < 0)
365 {
366 Lcross++;
367 }
368 }
369 }
370 freePoly(poly);
372 // q on the edge if left and right cross are not the same parity.
373 if ( (Rcross % 2) != (Lcross % 2) )
374 {
375 // We count the edge as inside.
376 return true;
377 }
379 // Inside iff an odd number of crossings.
380 if ((Rcross % 2) == 1)
381 {
382 return true;
383 }
385 // Outside.
386 return false;
387 }
391 // Line Segment Intersection
392 // Original code by Franklin Antonio
393 //
394 // The SAME_SIGNS macro assumes arithmetic where the exclusive-or
395 // operation will work on sign bits. This works for twos-complement,
396 // and most other machine arithmetic.
397 #define SAME_SIGNS( a, b ) \
398 (((long) ((unsigned long) a ^ (unsigned long) b)) >= 0 )
399 //
400 int segmentIntersectPoint(const Point& a1, const Point& a2,
401 const Point& b1, const Point& b2, double *x, double *y)
402 {
404 double Ax,Bx,Cx,Ay,By,Cy,d,e,f,num,offset;
405 double x1lo,x1hi,y1lo,y1hi;
407 Ax = a2.x - a1.x;
408 Bx = b1.x - b2.x;
410 // X bound box test:
411 if (Ax < 0)
412 {
413 x1lo = a2.x;
414 x1hi = a1.x;
415 }
416 else
417 {
418 x1hi = a2.x;
419 x1lo = a1.x;
420 }
421 if (Bx > 0)
422 {
423 if (x1hi < b2.x || b1.x < x1lo) return DONT_INTERSECT;
424 }
425 else
426 {
427 if (x1hi < b1.x || b2.x < x1lo) return DONT_INTERSECT;
428 }
430 Ay = a2.y - a1.y;
431 By = b1.y - b2.y;
433 // Y bound box test:
434 if (Ay < 0)
435 {
436 y1lo = a2.y;
437 y1hi = a1.y;
438 }
439 else
440 {
441 y1hi = a2.y;
442 y1lo = a1.y;
443 }
444 if (By > 0)
445 {
446 if (y1hi < b2.y || b1.y < y1lo) return DONT_INTERSECT;
447 }
448 else
449 {
450 if (y1hi < b1.y || b2.y < y1lo) return DONT_INTERSECT;
451 }
454 Cx = a1.x - b1.x;
455 Cy = a1.y - b1.y;
456 // alpha numerator:
457 d = By*Cx - Bx*Cy;
458 // Both denominator:
459 f = Ay*Bx - Ax*By;
460 // aplha tests:
461 if (f > 0)
462 {
463 if (d < 0 || d > f) return DONT_INTERSECT;
464 }
465 else
466 {
467 if (d > 0 || d < f) return DONT_INTERSECT;
468 }
470 // beta numerator:
471 e = Ax*Cy - Ay*Cx;
472 // beta tests:
473 if (f > 0)
474 {
475 if (e < 0 || e > f) return DONT_INTERSECT;
476 }
477 else
478 {
479 if (e > 0 || e < f) return DONT_INTERSECT;
480 }
482 // compute intersection coordinates:
484 if (f == 0) return PARALLEL;
486 // Numerator:
487 num = d*Ax;
488 // Round direction:
489 offset = SAME_SIGNS(num,f) ? f/2 : -f/2;
490 // Intersection X:
491 *x = a1.x + (num+offset) / f;
493 num = d*Ay;
494 offset = SAME_SIGNS(num,f) ? f/2 : -f/2;
495 // Intersection Y:
496 *y = a1.y + (num+offset) / f;
498 return DO_INTERSECT;
499 }
502 }