1 #include <2geom/path-intersection.h>
3 #include <2geom/ord.h>
5 //for path_direction:
6 #include <2geom/sbasis-geometric.h>
7 #include <gsl/gsl_vector.h>
8 #include <gsl/gsl_multiroots.h>
10 namespace Geom {
12 /**
13 * This function computes the winding of the path, given a reference point.
14 * Positive values correspond to counter-clockwise in the mathematical coordinate system,
15 * and clockwise in screen coordinates. This particular implementation casts a ray in
16 * the positive x direction. It iterates the path, checking for intersection with the
17 * bounding boxes. If an intersection is found, the initial/final Y value of the curve is
18 * used to derive a delta on the winding value. If the point is within the bounding box,
19 * the curve specific winding function is called.
20 */
21 int winding(Path const &path, Point p) {
22 //start on a segment which is not a horizontal line with y = p[y]
23 Path::const_iterator start;
24 for(Path::const_iterator iter = path.begin(); ; ++iter) {
25 if(iter == path.end_closed()) { return 0; }
26 if(iter->initialPoint()[Y]!=p[Y]) { start = iter; break; }
27 if(iter->finalPoint()[Y]!=p[Y]) { start = iter; break; }
28 if(iter->boundsFast()->height()!=0.){ start = iter; break; }
29 }
30 int wind = 0;
31 unsigned cnt = 0;
32 bool starting = true;
33 for (Path::const_iterator iter = start; iter != start || starting
34 ; ++iter, iter = (iter == path.end_closed()) ? path.begin() : iter )
35 {
36 cnt++;
37 if(cnt > path.size()) return wind; //some bug makes this required
38 starting = false;
39 Rect bounds = *(iter->boundsFast());
40 Coord x = p[X], y = p[Y];
42 if(x > bounds.right() || !bounds[Y].contains(y)) continue; //ray doesn't intersect box
44 Point final = iter->finalPoint();
45 Point initial = iter->initialPoint();
46 Cmp final_to_ray = cmp(final[Y], y);
47 Cmp initial_to_ray = cmp(initial[Y], y);
49 // if y is included, these will have opposite values, giving order.
50 Cmp c = cmp(final_to_ray, initial_to_ray);
51 if(x < bounds.left()) {
52 // ray goes through bbox
53 // winding delta determined by position of endpoints
54 if(final_to_ray != EQUAL_TO) {
55 wind += int(c); // GT = counter-clockwise = 1; LT = clockwise = -1; EQ = not-included = 0
56 //std::cout << int(c) << " ";
57 goto cont;
58 }
59 } else {
60 //inside bbox, use custom per-curve winding thingie
61 int delt = iter->winding(p);
62 wind += delt;
63 //std::cout << "n" << delt << " ";
64 }
65 //Handling the special case of an endpoint on the ray:
66 if(final[Y] == y) {
67 //Traverse segments until it breaks away from y
68 //99.9% of the time this will happen the first go
69 Path::const_iterator next = iter;
70 next++;
71 for(; ; next++) {
72 if(next == path.end_closed()) next = path.begin();
73 Rect bnds = *(next->boundsFast());
74 //TODO: X considerations
75 if(bnds.height() > 0) {
76 //It has diverged
77 if(bnds.contains(p)) {
78 const double fudge = 0.01;
79 if(cmp(y, next->valueAt(fudge, Y)) == initial_to_ray) {
80 wind += int(c);
81 //std::cout << "!!!!!" << int(c) << " ";
82 }
83 iter = next; // No increment, as the rest of the thing hasn't been counted.
84 } else {
85 Coord ny = next->initialPoint()[Y];
86 if(cmp(y, ny) == initial_to_ray) {
87 //Is a continuation through the ray, so counts windingwise
88 wind += int(c);
89 //std::cout << "!!!!!" << int(c) << " ";
90 }
91 iter = ++next;
92 }
93 goto cont;
94 }
95 if(next==start) return wind;
96 }
97 //Looks like it looped, which means everything's flat
98 return 0;
99 }
101 cont:(void)0;
102 }
103 return wind;
104 }
106 /**
107 * This function should only be applied to simple paths (regions), as otherwise
108 * a boolean winding direction is undefined. It returns true for fill, false for
109 * hole. Defaults to using the sign of area when it reaches funny cases.
110 */
111 bool path_direction(Path const &p) {
112 if(p.empty()) return false;
113 //could probably be more efficient, but this is a quick job
114 double y = p.initialPoint()[Y];
115 double x = p.initialPoint()[X];
116 Cmp res = cmp(p[0].finalPoint()[Y], y);
117 goto doh;
118 for(unsigned i = 1; i <= p.size(); i++) {
119 Cmp final_to_ray = cmp(p[i].finalPoint()[Y], y);
120 Cmp initial_to_ray = cmp(p[i].initialPoint()[Y], y);
121 // if y is included, these will have opposite values, giving order.
122 Cmp c = cmp(final_to_ray, initial_to_ray);
123 if(c != EQUAL_TO) {
124 std::vector<double> rs = p[i].roots(y, Y);
125 for(unsigned j = 0; j < rs.size(); j++) {
126 double nx = p[i].valueAt(rs[j], X);
127 if(nx > x) {
128 x = nx;
129 res = c;
130 }
131 }
132 } else if(final_to_ray == EQUAL_TO) goto doh;
133 }
134 return res < 0;
136 doh:
137 //Otherwise fallback on area
139 Piecewise<D2<SBasis> > pw = p.toPwSb();
140 double area;
141 Point centre;
142 Geom::centroid(pw, centre, area);
143 return area > 0;
144 }
146 //pair intersect code based on njh's pair-intersect
148 /** A little sugar for appending a list to another */
149 template<typename T>
150 void append(T &a, T const &b) {
151 a.insert(a.end(), b.begin(), b.end());
152 }
154 /**
155 * Finds the intersection between the lines defined by A0 & A1, and B0 & B1.
156 * Returns through the last 3 parameters, returning the t-values on the lines
157 * and the cross-product of the deltas (a useful byproduct). The return value
158 * indicates if the time values are within their proper range on the line segments.
159 */
160 bool
161 linear_intersect(Point A0, Point A1, Point B0, Point B1,
162 double &tA, double &tB, double &det) {
163 // kramers rule as cross products
164 Point Ad = A1 - A0,
165 Bd = B1 - B0,
166 d = B0 - A0;
167 det = cross(Ad, Bd);
168 if( 1.0 + det == 1.0 )
169 return false;
170 else
171 {
172 double detinv = 1.0 / det;
173 tA = cross(d, Bd) * detinv;
174 tB = cross(d, Ad) * detinv;
175 return tA >= 0. && tA <= 1. && tB >= 0. && tB <= 1.;
176 }
177 }
180 #if 0
181 typedef union dbl_64{
182 long long i64;
183 double d64;
184 };
186 static double EpsilonOf(double value)
187 {
188 dbl_64 s;
189 s.d64 = value;
190 if(s.i64 == 0)
191 {
192 s.i64++;
193 return s.d64 - value;
194 }
195 else if(s.i64-- < 0)
196 return s.d64 - value;
197 else
198 return value - s.d64;
199 }
200 #endif
202 struct rparams {
203 Curve const &A;
204 Curve const &B;
205 };
207 static int
208 intersect_polish_f (const gsl_vector * x, void *params,
209 gsl_vector * f)
210 {
211 const double x0 = gsl_vector_get (x, 0);
212 const double x1 = gsl_vector_get (x, 1);
214 Geom::Point dx = ((struct rparams *) params)->A(x0) -
215 ((struct rparams *) params)->B(x1);
217 gsl_vector_set (f, 0, dx[0]);
218 gsl_vector_set (f, 1, dx[1]);
220 return GSL_SUCCESS;
221 }
223 static void
224 intersect_polish_root (Curve const &A, double &s,
225 Curve const &B, double &t) {
226 int status;
227 size_t iter = 0;
229 const size_t n = 2;
230 struct rparams p = {A, B};
231 gsl_multiroot_function f = {&intersect_polish_f, n, &p};
233 double x_init[2] = {s, t};
234 gsl_vector *x = gsl_vector_alloc (n);
236 gsl_vector_set (x, 0, x_init[0]);
237 gsl_vector_set (x, 1, x_init[1]);
239 const gsl_multiroot_fsolver_type *T = gsl_multiroot_fsolver_hybrids;
240 gsl_multiroot_fsolver *sol = gsl_multiroot_fsolver_alloc (T, 2);
241 gsl_multiroot_fsolver_set (sol, &f, x);
243 do
244 {
245 iter++;
246 status = gsl_multiroot_fsolver_iterate (sol);
248 if (status) /* check if solver is stuck */
249 break;
251 status =
252 gsl_multiroot_test_residual (sol->f, 1e-12);
253 }
254 while (status == GSL_CONTINUE && iter < 1000);
256 s = gsl_vector_get (sol->x, 0);
257 t = gsl_vector_get (sol->x, 1);
259 gsl_multiroot_fsolver_free (sol);
260 gsl_vector_free (x);
261 }
263 /**
264 * This uses the local bounds functions of curves to generically intersect two.
265 * It passes in the curves, time intervals, and keeps track of depth, while
266 * returning the results through the Crossings parameter.
267 */
268 void pair_intersect(Curve const & A, double Al, double Ah,
269 Curve const & B, double Bl, double Bh,
270 Crossings &ret, unsigned depth=0) {
271 // std::cout << depth << "(" << Al << ", " << Ah << ")\n";
272 OptRect Ar = A.boundsLocal(Interval(Al, Ah));
273 if (!Ar) return;
275 OptRect Br = B.boundsLocal(Interval(Bl, Bh));
276 if (!Br) return;
278 if(! Ar->intersects(*Br)) return;
280 //Checks the general linearity of the function
281 if((depth > 12)) { // || (A.boundsLocal(Interval(Al, Ah), 1).maxExtent() < 0.1
282 //&& B.boundsLocal(Interval(Bl, Bh), 1).maxExtent() < 0.1)) {
283 double tA, tB, c;
284 if(linear_intersect(A.pointAt(Al), A.pointAt(Ah),
285 B.pointAt(Bl), B.pointAt(Bh),
286 tA, tB, c)) {
287 tA = tA * (Ah - Al) + Al;
288 tB = tB * (Bh - Bl) + Bl;
289 intersect_polish_root(A, tA,
290 B, tB);
291 if(depth % 2)
292 ret.push_back(Crossing(tB, tA, c < 0));
293 else
294 ret.push_back(Crossing(tA, tB, c > 0));
295 return;
296 }
297 }
298 if(depth > 12) return;
299 double mid = (Bl + Bh)/2;
300 pair_intersect(B, Bl, mid,
301 A, Al, Ah,
302 ret, depth+1);
303 pair_intersect(B, mid, Bh,
304 A, Al, Ah,
305 ret, depth+1);
306 }
308 /** A simple wrapper around pair_intersect */
309 Crossings SimpleCrosser::crossings(Curve const &a, Curve const &b) {
310 Crossings ret;
311 pair_intersect(a, 0, 1, b, 0, 1, ret);
312 return ret;
313 }
315 /**
316 * Takes two paths and time ranges on them, with the invariant that the
317 * paths are monotonic on the range. Splits A when the linear intersection
318 * doesn't exist or is inaccurate. Uses the fact that it is monotonic to
319 * do very fast local bounds.
320 */
321 void mono_pair(Path const &A, double Al, double Ah,
322 Path const &B, double Bl, double Bh,
323 Crossings &ret, double /*tol*/, unsigned depth = 0) {
324 if( Al >= Ah || Bl >= Bh) return;
325 std::cout << " " << depth << "[" << Al << ", " << Ah << "]" << "[" << Bl << ", " << Bh << "]";
327 Point A0 = A.pointAt(Al), A1 = A.pointAt(Ah),
328 B0 = B.pointAt(Bl), B1 = B.pointAt(Bh);
329 //inline code that this implies? (without rect/interval construction)
330 if(!Rect(A0, A1).intersects(Rect(B0, B1)) || A0 == A1 || B0 == B1) return;
332 //Checks the general linearity of the function
333 //if((depth > 12) || (A.boundsLocal(Interval(Al, Ah), 1).maxExtent() < 0.1
334 // && B.boundsLocal(Interval(Bl, Bh), 1).maxExtent() < 0.1)) {
335 double tA, tB, c;
336 if(linear_intersect(A0, A1, B0, B1,
337 tA, tB, c)) {
338 tA = tA * (Ah - Al) + Al;
339 tB = tB * (Bh - Bl) + Bl;
340 if(depth % 2)
341 ret.push_back(Crossing(tB, tA, c < 0));
342 else
343 ret.push_back(Crossing(tA, tB, c > 0));
344 return;
345 }
346 //}
347 if(depth > 12) return;
348 double mid = (Bl + Bh)/2;
349 mono_pair(B, Bl, mid,
350 A, Al, Ah,
351 ret, depth+1);
352 mono_pair(B, mid, Bh,
353 A, Al, Ah,
354 ret, depth+1);
355 }
357 /** This returns the times when the x or y derivative is 0 in the curve. */
358 std::vector<double> curve_mono_splits(Curve const &d) {
359 std::vector<double> rs = d.roots(0, X);
360 append(rs, d.roots(0, Y));
361 std::sort(rs.begin(), rs.end());
362 return rs;
363 }
365 /** Convenience function to add a value to each entry in a vector of doubles. */
366 std::vector<double> offset_doubles(std::vector<double> const &x, double offs) {
367 std::vector<double> ret;
368 for(unsigned i = 0; i < x.size(); i++) {
369 ret.push_back(x[i] + offs);
370 }
371 return ret;
372 }
374 /**
375 * Finds all the monotonic splits for a path. Only includes the split between
376 * curves if they switch derivative directions at that point.
377 */
378 std::vector<double> path_mono_splits(Path const &p) {
379 std::vector<double> ret;
380 if(p.empty()) return ret;
381 ret.push_back(0);
383 Curve* deriv = p[0].derivative();
384 append(ret, curve_mono_splits(*deriv));
385 delete deriv;
387 bool pdx=2, pdy=2; //Previous derivative direction
388 for(unsigned i = 0; i <= p.size(); i++) {
389 deriv = p[i].derivative();
390 std::vector<double> spl = offset_doubles(curve_mono_splits(*deriv), i);
391 delete deriv;
392 bool dx = p[i].initialPoint()[X] > (spl.empty()? p[i].finalPoint()[X] :
393 p.valueAt(spl.front(), X));
394 bool dy = p[i].initialPoint()[Y] > (spl.empty()? p[i].finalPoint()[Y] :
395 p.valueAt(spl.front(), Y));
396 //The direction changed, include the split time
397 if(dx != pdx || dy != pdy) {
398 ret.push_back(i);
399 pdx = dx; pdy = dy;
400 }
401 append(ret, spl);
402 }
403 return ret;
404 }
406 /**
407 * Applies path_mono_splits to multiple paths, and returns the results such that
408 * time-set i corresponds to Path i.
409 */
410 std::vector<std::vector<double> > paths_mono_splits(std::vector<Path> const &ps) {
411 std::vector<std::vector<double> > ret;
412 for(unsigned i = 0; i < ps.size(); i++)
413 ret.push_back(path_mono_splits(ps[i]));
414 return ret;
415 }
417 /**
418 * Processes the bounds for a list of paths and a list of splits on them, yielding a list of rects for each.
419 * Each entry i corresponds to path i of the input. The number of rects in each entry is guaranteed to be the
420 * number of splits for that path, subtracted by one.
421 */
422 std::vector<std::vector<Rect> > split_bounds(std::vector<Path> const &p, std::vector<std::vector<double> > splits) {
423 std::vector<std::vector<Rect> > ret;
424 for(unsigned i = 0; i < p.size(); i++) {
425 std::vector<Rect> res;
426 for(unsigned j = 1; j < splits[i].size(); j++)
427 res.push_back(Rect(p[i].pointAt(splits[i][j-1]), p[i].pointAt(splits[i][j])));
428 ret.push_back(res);
429 }
430 return ret;
431 }
433 /**
434 * This is the main routine of "MonoCrosser", and implements a monotonic strategy on multiple curves.
435 * Finds crossings between two sets of paths, yielding a CrossingSet. [0, a.size()) of the return correspond
436 * to the sorted crossings of a with paths of b. The rest of the return, [a.size(), a.size() + b.size()],
437 * corresponds to the sorted crossings of b with paths of a.
438 *
439 * This function does two sweeps, one on the bounds of each path, and after that cull, one on the curves within.
440 * This leads to a certain amount of code complexity, however, most of that is factored into the above functions
441 */
442 CrossingSet MonoCrosser::crossings(std::vector<Path> const &a, std::vector<Path> const &b) {
443 if(b.empty()) return CrossingSet(a.size(), Crossings());
444 CrossingSet results(a.size() + b.size(), Crossings());
445 if(a.empty()) return results;
447 std::vector<std::vector<double> > splits_a = paths_mono_splits(a), splits_b = paths_mono_splits(b);
448 std::vector<std::vector<Rect> > bounds_a = split_bounds(a, splits_a), bounds_b = split_bounds(b, splits_b);
450 std::vector<Rect> bounds_a_union, bounds_b_union;
451 for(unsigned i = 0; i < bounds_a.size(); i++) bounds_a_union.push_back(union_list(bounds_a[i]));
452 for(unsigned i = 0; i < bounds_b.size(); i++) bounds_b_union.push_back(union_list(bounds_b[i]));
454 std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds_a_union, bounds_b_union);
455 Crossings n;
456 for(unsigned i = 0; i < cull.size(); i++) {
457 for(unsigned jx = 0; jx < cull[i].size(); jx++) {
458 unsigned j = cull[i][jx];
459 unsigned jc = j + a.size();
460 Crossings res;
462 //Sweep of the monotonic portions
463 std::vector<std::vector<unsigned> > cull2 = sweep_bounds(bounds_a[i], bounds_b[j]);
464 for(unsigned k = 0; k < cull2.size(); k++) {
465 for(unsigned lx = 0; lx < cull2[k].size(); lx++) {
466 unsigned l = cull2[k][lx];
467 mono_pair(a[i], splits_a[i][k-1], splits_a[i][k],
468 b[j], splits_b[j][l-1], splits_b[j][l],
469 res, .1);
470 }
471 }
473 for(unsigned k = 0; k < res.size(); k++) { res[k].a = i; res[k].b = jc; }
475 merge_crossings(results[i], res, i);
476 merge_crossings(results[i], res, jc);
477 }
478 }
480 return results;
481 }
483 /* This function is similar codewise to the MonoCrosser, the main difference is that it deals with
484 * only one set of paths and includes self intersection
485 CrossingSet crossings_among(std::vector<Path> const &p) {
486 CrossingSet results(p.size(), Crossings());
487 if(p.empty()) return results;
489 std::vector<std::vector<double> > splits = paths_mono_splits(p);
490 std::vector<std::vector<Rect> > prs = split_bounds(p, splits);
491 std::vector<Rect> rs;
492 for(unsigned i = 0; i < prs.size(); i++) rs.push_back(union_list(prs[i]));
494 std::vector<std::vector<unsigned> > cull = sweep_bounds(rs);
496 //we actually want to do the self-intersections, so add em in:
497 for(unsigned i = 0; i < cull.size(); i++) cull[i].push_back(i);
499 for(unsigned i = 0; i < cull.size(); i++) {
500 for(unsigned jx = 0; jx < cull[i].size(); jx++) {
501 unsigned j = cull[i][jx];
502 Crossings res;
504 //Sweep of the monotonic portions
505 std::vector<std::vector<unsigned> > cull2 = sweep_bounds(prs[i], prs[j]);
506 for(unsigned k = 0; k < cull2.size(); k++) {
507 for(unsigned lx = 0; lx < cull2[k].size(); lx++) {
508 unsigned l = cull2[k][lx];
509 mono_pair(p[i], splits[i][k-1], splits[i][k],
510 p[j], splits[j][l-1], splits[j][l],
511 res, .1);
512 }
513 }
515 for(unsigned k = 0; k < res.size(); k++) { res[k].a = i; res[k].b = j; }
517 merge_crossings(results[i], res, i);
518 merge_crossings(results[j], res, j);
519 }
520 }
522 return results;
523 }
524 */
527 Crossings curve_self_crossings(Curve const &a) {
528 Crossings res;
529 std::vector<double> spl;
530 spl.push_back(0);
531 append(spl, curve_mono_splits(a));
532 spl.push_back(1);
533 for(unsigned i = 1; i < spl.size(); i++)
534 for(unsigned j = i+1; j < spl.size(); j++)
535 pair_intersect(a, spl[i-1], spl[i], a, spl[j-1], spl[j], res);
536 return res;
537 }
539 /*
540 void mono_curve_intersect(Curve const & A, double Al, double Ah,
541 Curve const & B, double Bl, double Bh,
542 Crossings &ret, unsigned depth=0) {
543 // std::cout << depth << "(" << Al << ", " << Ah << ")\n";
544 Point A0 = A.pointAt(Al), A1 = A.pointAt(Ah),
545 B0 = B.pointAt(Bl), B1 = B.pointAt(Bh);
546 //inline code that this implies? (without rect/interval construction)
547 if(!Rect(A0, A1).intersects(Rect(B0, B1)) || A0 == A1 || B0 == B1) return;
549 //Checks the general linearity of the function
550 if((depth > 12) || (A.boundsLocal(Interval(Al, Ah), 1).maxExtent() < 0.1
551 && B.boundsLocal(Interval(Bl, Bh), 1).maxExtent() < 0.1)) {
552 double tA, tB, c;
553 if(linear_intersect(A0, A1, B0, B1, tA, tB, c)) {
554 tA = tA * (Ah - Al) + Al;
555 tB = tB * (Bh - Bl) + Bl;
556 if(depth % 2)
557 ret.push_back(Crossing(tB, tA, c < 0));
558 else
559 ret.push_back(Crossing(tA, tB, c > 0));
560 return;
561 }
562 }
563 if(depth > 12) return;
564 double mid = (Bl + Bh)/2;
565 mono_curve_intersect(B, Bl, mid,
566 A, Al, Ah,
567 ret, depth+1);
568 mono_curve_intersect(B, mid, Bh,
569 A, Al, Ah,
570 ret, depth+1);
571 }
573 std::vector<std::vector<double> > curves_mono_splits(Path const &p) {
574 std::vector<std::vector<double> > ret;
575 for(unsigned i = 0; i <= p.size(); i++) {
576 std::vector<double> spl;
577 spl.push_back(0);
578 append(spl, curve_mono_splits(p[i]));
579 spl.push_back(1);
580 ret.push_back(spl);
581 }
582 }
584 std::vector<std::vector<Rect> > curves_split_bounds(Path const &p, std::vector<std::vector<double> > splits) {
585 std::vector<std::vector<Rect> > ret;
586 for(unsigned i = 0; i < splits.size(); i++) {
587 std::vector<Rect> res;
588 for(unsigned j = 1; j < splits[i].size(); j++)
589 res.push_back(Rect(p.pointAt(splits[i][j-1]+i), p.pointAt(splits[i][j]+i)));
590 ret.push_back(res);
591 }
592 return ret;
593 }
595 Crossings path_self_crossings(Path const &p) {
596 Crossings ret;
597 std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds(p));
598 std::vector<std::vector<double> > spl = curves_mono_splits(p);
599 std::vector<std::vector<Rect> > bnds = curves_split_bounds(p, spl);
600 for(unsigned i = 0; i < cull.size(); i++) {
601 Crossings res;
602 for(unsigned k = 1; k < spl[i].size(); k++)
603 for(unsigned l = k+1; l < spl[i].size(); l++)
604 mono_curve_intersect(p[i], spl[i][k-1], spl[i][k], p[i], spl[i][l-1], spl[i][l], res);
605 offset_crossings(res, i, i);
606 append(ret, res);
607 for(unsigned jx = 0; jx < cull[i].size(); jx++) {
608 unsigned j = cull[i][jx];
609 res.clear();
611 std::vector<std::vector<unsigned> > cull2 = sweep_bounds(bnds[i], bnds[j]);
612 for(unsigned k = 0; k < cull2.size(); k++) {
613 for(unsigned lx = 0; lx < cull2[k].size(); lx++) {
614 unsigned l = cull2[k][lx];
615 mono_curve_intersect(p[i], spl[i][k-1], spl[i][k], p[j], spl[j][l-1], spl[j][l], res);
616 }
617 }
619 //if(fabs(int(i)-j) == 1 || fabs(int(i)-j) == p.size()-1) {
620 Crossings res2;
621 for(unsigned k = 0; k < res.size(); k++) {
622 if(res[k].ta != 0 && res[k].ta != 1 && res[k].tb != 0 && res[k].tb != 1) {
623 res.push_back(res[k]);
624 }
625 }
626 res = res2;
627 //}
628 offset_crossings(res, i, j);
629 append(ret, res);
630 }
631 }
632 return ret;
633 }
634 */
636 Crossings self_crossings(Path const &p) {
637 Crossings ret;
638 std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds(p));
639 for(unsigned i = 0; i < cull.size(); i++) {
640 Crossings res = curve_self_crossings(p[i]);
641 offset_crossings(res, i, i);
642 append(ret, res);
643 for(unsigned jx = 0; jx < cull[i].size(); jx++) {
644 unsigned j = cull[i][jx];
645 res.clear();
646 pair_intersect(p[i], 0, 1, p[j], 0, 1, res);
648 //if(fabs(int(i)-j) == 1 || fabs(int(i)-j) == p.size()-1) {
649 Crossings res2;
650 for(unsigned k = 0; k < res.size(); k++) {
651 if(res[k].ta != 0 && res[k].ta != 1 && res[k].tb != 0 && res[k].tb != 1) {
652 res2.push_back(res[k]);
653 }
654 }
655 res = res2;
656 //}
657 offset_crossings(res, i, j);
658 append(ret, res);
659 }
660 }
661 return ret;
662 }
664 void flip_crossings(Crossings &crs) {
665 for(unsigned i = 0; i < crs.size(); i++)
666 crs[i] = Crossing(crs[i].tb, crs[i].ta, crs[i].b, crs[i].a, !crs[i].dir);
667 }
669 CrossingSet crossings_among(std::vector<Path> const &p) {
670 CrossingSet results(p.size(), Crossings());
671 if(p.empty()) return results;
673 SimpleCrosser cc;
675 std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds(p));
676 for(unsigned i = 0; i < cull.size(); i++) {
677 Crossings res = self_crossings(p[i]);
678 for(unsigned k = 0; k < res.size(); k++) { res[k].a = res[k].b = i; }
679 merge_crossings(results[i], res, i);
680 flip_crossings(res);
681 merge_crossings(results[i], res, i);
682 for(unsigned jx = 0; jx < cull[i].size(); jx++) {
683 unsigned j = cull[i][jx];
685 Crossings res = cc.crossings(p[i], p[j]);
686 for(unsigned k = 0; k < res.size(); k++) { res[k].a = i; res[k].b = j; }
687 merge_crossings(results[i], res, i);
688 merge_crossings(results[j], res, j);
689 }
690 }
691 return results;
692 }
694 }
696 /*
697 Local Variables:
698 mode:c++
699 c-file-style:"stroustrup"
700 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
701 indent-tabs-mode:nil
702 fill-column:99
703 End:
704 */
705 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :