1 // intersect.h (Shape intersection functions)
2 //
3 // The WorldForge Project
4 // Copyright (C) 2002 The WorldForge Project
5 //
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7 // it under the terms of the GNU General Public License as published by
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10 //
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15 //
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22 //
23
24 #ifndef WFMATH_INTERSECT_H
25 #define WFMATH_INTERSECT_H
26
27 #include <wfmath/vector.h>
28 #include <wfmath/point.h>
29 #include <wfmath/const.h>
30 #include <wfmath/intersect_decls.h>
31 #include <wfmath/axisbox.h>
32 #include <wfmath/ball.h>
33 #include <wfmath/segment.h>
34 #include <wfmath/rotbox.h>
35
36 #include <cmath>
37
38 namespace WFMath {
39
40 // Get the reversed order intersect functions (is this safe? FIXME)
41 // No it's not. In the case of an unknown intersection we end up in
42 // a stack crash loop.
43
44 template<class S1, class S2>
Intersect(const S1 & s1,const S2 & s2,bool proper)45 inline bool Intersect(const S1& s1, const S2& s2, bool proper)
46 {
47 return Intersect(s2, s1, proper);
48 }
49
50 // Point<>
51
52 template<int dim>
Intersect(const Point<dim> & p1,const Point<dim> & p2,bool proper)53 inline bool Intersect(const Point<dim>& p1, const Point<dim>& p2, bool proper)
54 {
55 return !proper && p1 == p2;
56 }
57
58 template<int dim, class S>
Contains(const S & s,const Point<dim> & p,bool proper)59 inline bool Contains(const S& s, const Point<dim>& p, bool proper)
60 {
61 return Intersect(p, s, proper);
62 }
63
64 template<int dim>
Contains(const Point<dim> & p1,const Point<dim> & p2,bool proper)65 inline bool Contains(const Point<dim>& p1, const Point<dim>& p2, bool proper)
66 {
67 return !proper && p1 == p2;
68 }
69
70 // AxisBox<>
71
72 template<int dim>
Intersect(const AxisBox<dim> & b,const Point<dim> & p,bool proper)73 inline bool Intersect(const AxisBox<dim>& b, const Point<dim>& p, bool proper)
74 {
75 for(int i = 0; i < dim; ++i)
76 if(_Greater(b.m_low[i], p[i], proper) || _Less(b.m_high[i], p[i], proper))
77 return false;
78
79 return true;
80 }
81
82 template<int dim>
Contains(const Point<dim> & p,const AxisBox<dim> & b,bool proper)83 inline bool Contains(const Point<dim>& p, const AxisBox<dim>& b, bool proper)
84 {
85 return !proper && p == b.m_low && p == b.m_high;
86 }
87
88 template<int dim>
Intersect(const AxisBox<dim> & b1,const AxisBox<dim> & b2,bool proper)89 inline bool Intersect(const AxisBox<dim>& b1, const AxisBox<dim>& b2, bool proper)
90 {
91 for(int i = 0; i < dim; ++i)
92 if(_Greater(b1.m_low[i], b2.m_high[i], proper)
93 || _Less(b1.m_high[i], b2.m_low[i], proper))
94 return false;
95
96 return true;
97 }
98
99 template<int dim>
Contains(const AxisBox<dim> & outer,const AxisBox<dim> & inner,bool proper)100 inline bool Contains(const AxisBox<dim>& outer, const AxisBox<dim>& inner, bool proper)
101 {
102 for(int i = 0; i < dim; ++i)
103 if(_Less(inner.m_low[i], outer.m_low[i], proper)
104 || _Greater(inner.m_high[i], outer.m_high[i], proper))
105 return false;
106
107 return true;
108 }
109
110 // Ball<>
111
112 template<int dim>
Intersect(const Ball<dim> & b,const Point<dim> & p,bool proper)113 inline bool Intersect(const Ball<dim>& b, const Point<dim>& p, bool proper)
114 {
115 return _LessEq(SquaredDistance(b.m_center, p), b.m_radius * b.m_radius
116 * (1 + numeric_constants<CoordType>::epsilon()), proper);
117 }
118
119 template<int dim>
Contains(const Point<dim> & p,const Ball<dim> & b,bool proper)120 inline bool Contains(const Point<dim>& p, const Ball<dim>& b, bool proper)
121 {
122 return !proper && b.m_radius == 0 && p == b.m_center;
123 }
124
125 template<int dim>
Intersect(const Ball<dim> & b,const AxisBox<dim> & a,bool proper)126 inline bool Intersect(const Ball<dim>& b, const AxisBox<dim>& a, bool proper)
127 {
128 CoordType dist = 0;
129
130 for(int i = 0; i < dim; ++i) {
131 CoordType dist_i;
132 if(b.m_center[i] < a.m_low[i])
133 dist_i = b.m_center[i] - a.m_low[i];
134 else if(b.m_center[i] > a.m_high[i])
135 dist_i = b.m_center[i] - a.m_high[i];
136 else
137 continue;
138 dist+= dist_i * dist_i;
139 }
140
141 return _LessEq(dist, b.m_radius * b.m_radius, proper);
142 }
143
144 template<int dim>
Contains(const Ball<dim> & b,const AxisBox<dim> & a,bool proper)145 inline bool Contains(const Ball<dim>& b, const AxisBox<dim>& a, bool proper)
146 {
147 CoordType sqr_dist = 0;
148
149 for(int i = 0; i < dim; ++i) {
150 CoordType furthest = FloatMax(std::fabs(b.m_center[i] - a.m_low[i]),
151 std::fabs(b.m_center[i] - a.m_high[i]));
152 sqr_dist += furthest * furthest;
153 }
154
155 return _LessEq(sqr_dist, b.m_radius * b.m_radius * (1 + numeric_constants<CoordType>::epsilon()), proper);
156 }
157
158 template<int dim>
Contains(const AxisBox<dim> & a,const Ball<dim> & b,bool proper)159 inline bool Contains(const AxisBox<dim>& a, const Ball<dim>& b, bool proper)
160 {
161 for(int i = 0; i < dim; ++i)
162 if(_Less(b.m_center[i] - b.m_radius, a.lowerBound(i), proper)
163 || _Greater(b.m_center[i] + b.m_radius, a.upperBound(i), proper))
164 return false;
165
166 return true;
167 }
168
169 template<int dim>
Intersect(const Ball<dim> & b1,const Ball<dim> & b2,bool proper)170 inline bool Intersect(const Ball<dim>& b1, const Ball<dim>& b2, bool proper)
171 {
172 CoordType sqr_dist = SquaredDistance(b1.m_center, b2.m_center);
173 CoordType rad_sum = b1.m_radius + b2.m_radius;
174
175 return _LessEq(sqr_dist, rad_sum * rad_sum, proper);
176 }
177
178 template<int dim>
Contains(const Ball<dim> & outer,const Ball<dim> & inner,bool proper)179 inline bool Contains(const Ball<dim>& outer, const Ball<dim>& inner, bool proper)
180 {
181 CoordType rad_diff = outer.m_radius - inner.m_radius;
182
183 if(_Less(rad_diff, 0, proper))
184 return false;
185
186 CoordType sqr_dist = SquaredDistance(outer.m_center, inner.m_center);
187
188 return _LessEq(sqr_dist, rad_diff * rad_diff, proper);
189 }
190
191 // Segment<>
192
193 template<int dim>
Intersect(const Segment<dim> & s,const Point<dim> & p,bool proper)194 inline bool Intersect(const Segment<dim>& s, const Point<dim>& p, bool proper)
195 {
196 // This is only true if p lies on the line between m_p1 and m_p2
197
198 Vector<dim> v1 = s.m_p1 - p, v2 = s.m_p2 - p;
199
200 CoordType proj = Dot(v1, v2);
201
202 if(_Greater(proj, 0, proper)) // p is on the same side of both ends, not between them
203 return false;
204
205 // Check for colinearity
206 return Equal(proj * proj, v1.sqrMag() * v2.sqrMag());
207 }
208
209 template<int dim>
Contains(const Point<dim> & p,const Segment<dim> & s,bool proper)210 inline bool Contains(const Point<dim>& p, const Segment<dim>& s, bool proper)
211 {
212 return !proper && p == s.m_p1 && p == s.m_p2;
213 }
214
215 template<int dim>
Intersect(const Segment<dim> & s,const AxisBox<dim> & b,bool proper)216 bool Intersect(const Segment<dim>& s, const AxisBox<dim>& b, bool proper)
217 {
218 // Use parametric coordinates on the line, where 0 is the location
219 // of m_p1 and 1 is the location of m_p2
220
221 // Find the parametric coordinates of the portion of the line
222 // which lies betweens b.lowerBound(i) and b.upperBound(i) for
223 // each i. Find the intersection of those segments and the
224 // segment (0, 1), and check if it's nonzero.
225
226 CoordType min = 0, max = 1;
227
228 for(int i = 0; i < dim; ++i) {
229 CoordType dist = s.m_p2[i] - s.m_p1[i];
230 if(dist == 0) {
231 if(_Less(s.m_p1[i], b.m_low[i], proper)
232 || _Greater(s.m_p1[i], b.m_high[i], proper))
233 return false;
234 }
235 else {
236 CoordType low = (b.m_low[i] - s.m_p1[i]) / dist;
237 CoordType high = (b.m_high[i] - s.m_p1[i]) / dist;
238 if(low > high) {
239 CoordType tmp = high;
240 high = low;
241 low = tmp;
242 }
243 if(low > min)
244 min = low;
245 if(high < max)
246 max = high;
247 }
248 }
249
250 return _LessEq(min, max, proper);
251 }
252
253 template<int dim>
Contains(const Segment<dim> & s,const AxisBox<dim> & b,bool proper)254 inline bool Contains(const Segment<dim>& s, const AxisBox<dim>& b, bool proper)
255 {
256 // This is only possible for zero width or zero height box,
257 // in which case we check for containment of the endpoints.
258
259 bool got_difference = false;
260
261 for(int i = 0; i < dim; ++i) {
262 if(b.m_low[i] == b.m_high[i])
263 continue;
264 if(got_difference)
265 return false;
266 else // It's okay to be different on one axis
267 got_difference = true;
268 }
269
270 return Contains(s, b.m_low, proper) &&
271 (got_difference ? Contains(s, b.m_high, proper) : true);
272 }
273
274 template<int dim>
Contains(const AxisBox<dim> & b,const Segment<dim> & s,bool proper)275 inline bool Contains(const AxisBox<dim>& b, const Segment<dim>& s, bool proper)
276 {
277 return Contains(b, s.m_p1, proper) && Contains(b, s.m_p2, proper);
278 }
279
280 template<int dim>
Intersect(const Segment<dim> & s,const Ball<dim> & b,bool proper)281 bool Intersect(const Segment<dim>& s, const Ball<dim>& b, bool proper)
282 {
283 Vector<dim> line = s.m_p2 - s.m_p1, offset = b.m_center - s.m_p1;
284
285 // First, see if the closest point on the line to the center of
286 // the ball lies inside the segment
287
288 CoordType proj = Dot(line, offset);
289
290 // If the nearest point on the line is outside the segment,
291 // intersection reduces to checking the nearest endpoint.
292
293 if(proj <= 0)
294 return Intersect(b, s.m_p1, proper);
295
296 CoordType lineSqrMag = line.sqrMag();
297
298 if (proj >= lineSqrMag)
299 return Intersect(b, s.m_p2, proper);
300
301 Vector<dim> perp_part = offset - line * (proj / lineSqrMag);
302
303 return _LessEq(perp_part.sqrMag(), b.m_radius * b.m_radius, proper);
304 }
305
306 template<int dim>
Contains(const Ball<dim> & b,const Segment<dim> & s,bool proper)307 inline bool Contains(const Ball<dim>& b, const Segment<dim>& s, bool proper)
308 {
309 return Contains(b, s.m_p1, proper) && Contains(b, s.m_p2, proper);
310 }
311
312 template<int dim>
Contains(const Segment<dim> & s,const Ball<dim> & b,bool proper)313 inline bool Contains(const Segment<dim>& s, const Ball<dim>& b, bool proper)
314 {
315 return b.m_radius == 0 && Contains(s, b.m_center, proper);
316 }
317
318 template<int dim>
Intersect(const Segment<dim> & s1,const Segment<dim> & s2,bool proper)319 bool Intersect(const Segment<dim>& s1, const Segment<dim>& s2, bool proper)
320 {
321 // Check that the lines that contain the segments intersect, and then check
322 // that the intersection point lies within the segments
323
324 Vector<dim> v1 = s1.m_p2 - s1.m_p1, v2 = s2.m_p2 - s2.m_p1,
325 deltav = s2.m_p1 - s1.m_p1;
326
327 CoordType v1sqr = v1.sqrMag(), v2sqr = v2.sqrMag();
328 CoordType proj12 = Dot(v1, v2), proj1delta = Dot(v1, deltav),
329 proj2delta = Dot(v2, deltav);
330
331 CoordType denom = v1sqr * v2sqr - proj12 * proj12;
332
333 if(dim > 2 && !Equal(v2sqr * proj1delta * proj1delta +
334 v1sqr * proj2delta * proj2delta,
335 2 * proj12 * proj1delta * proj2delta +
336 deltav.sqrMag() * denom))
337 return false; // Skew lines; don't intersect
338
339 if(denom > 0) {
340 // Find the location of the intersection point in parametric coordinates,
341 // where one end of the segment is at zero and the other at one
342
343 CoordType coord1 = (v2sqr * proj1delta - proj12 * proj2delta) / denom;
344 CoordType coord2 = -(v1sqr * proj2delta - proj12 * proj1delta) / denom;
345
346 return _LessEq(coord1, 0, proper) && _LessEq(coord1, 1, proper)
347 && _GreaterEq(coord2, 0, proper) && _GreaterEq(coord2, 1, proper);
348 }
349 else {
350 // Parallel segments, see if one contains an endpoint of the other
351 return Contains(s1, s2.m_p1, proper) || Contains(s1, s2.m_p2, proper)
352 || Contains(s2, s1.m_p1, proper) || Contains(s2, s1.m_p2, proper)
353 // Degenerate case (identical segments), nonzero length
354 || ((proper && s1.m_p1 != s1.m_p2)
355 && ((s1.m_p1 == s2.m_p1 && s1.m_p2 == s2.m_p2)
356 || (s1.m_p1 == s2.m_p2 && s1.m_p2 == s2.m_p1)));
357 }
358 }
359
360 template<int dim>
Contains(const Segment<dim> & s1,const Segment<dim> & s2,bool proper)361 inline bool Contains(const Segment<dim>& s1, const Segment<dim>& s2, bool proper)
362 {
363 return Contains(s1, s2.m_p1, proper) && Contains(s1, s2.m_p2, proper);
364 }
365
366 // RotBox<>
367
368 template<int dim>
Intersect(const RotBox<dim> & r,const Point<dim> & p,bool proper)369 inline bool Intersect(const RotBox<dim>& r, const Point<dim>& p, bool proper)
370 {
371 // Rotate the point into the internal coordinate system of the box
372
373 Vector<dim> shift = ProdInv(p - r.m_corner0, r.m_orient);
374
375 for(int i = 0; i < dim; ++i) {
376 if(r.m_size[i] < 0) {
377 if(_Less(shift[i], r.m_size[i], proper) || _Greater(shift[i], 0, proper))
378 return false;
379 }
380 else {
381 if(_Greater(shift[i], r.m_size[i], proper) || _Less(shift[i], 0, proper))
382 return false;
383 }
384 }
385
386 return true;
387 }
388
389 template<int dim>
Contains(const Point<dim> & p,const RotBox<dim> & r,bool proper)390 inline bool Contains(const Point<dim>& p, const RotBox<dim>& r, bool proper)
391 {
392 if(proper)
393 return false;
394
395 for(int i = 0; i < dim; ++i)
396 if(r.m_size[i] != 0)
397 return false;
398
399 return p == r.m_corner0;
400 }
401
402 template<int dim>
403 bool Intersect(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper);
404
405 template<int dim>
Contains(const RotBox<dim> & r,const AxisBox<dim> & b,bool proper)406 inline bool Contains(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper)
407 {
408 RotMatrix<dim> m = r.m_orient.inverse();
409
410 return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
411 RotBox<dim>(Point<dim>(b.m_low).rotate(m, r.m_corner0),
412 b.m_high - b.m_low, m), proper);
413 }
414
415 template<int dim>
Contains(const AxisBox<dim> & b,const RotBox<dim> & r,bool proper)416 inline bool Contains(const AxisBox<dim>& b, const RotBox<dim>& r, bool proper)
417 {
418 return Contains(b, r.boundingBox(), proper);
419 }
420
421 template<int dim>
Intersect(const RotBox<dim> & r,const Ball<dim> & b,bool proper)422 inline bool Intersect(const RotBox<dim>& r, const Ball<dim>& b, bool proper)
423 {
424 return Intersect(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
425 Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
426 r.m_orient), b.m_radius), proper);
427 }
428
429 template<int dim>
Contains(const RotBox<dim> & r,const Ball<dim> & b,bool proper)430 inline bool Contains(const RotBox<dim>& r, const Ball<dim>& b, bool proper)
431 {
432 return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
433 Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
434 r.m_orient), b.m_radius), proper);
435 }
436
437 template<int dim>
Contains(const Ball<dim> & b,const RotBox<dim> & r,bool proper)438 inline bool Contains(const Ball<dim>& b, const RotBox<dim>& r, bool proper)
439 {
440 return Contains(Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
441 r.m_orient), b.m_radius),
442 AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size), proper);
443 }
444
445 template<int dim>
Intersect(const RotBox<dim> & r,const Segment<dim> & s,bool proper)446 inline bool Intersect(const RotBox<dim>& r, const Segment<dim>& s, bool proper)
447 {
448 Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
449 Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);
450
451 return Intersect(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
452 Segment<dim>(p1, p2), proper);
453 }
454
455 template<int dim>
Contains(const RotBox<dim> & r,const Segment<dim> & s,bool proper)456 inline bool Contains(const RotBox<dim>& r, const Segment<dim>& s, bool proper)
457 {
458 Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
459 Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);
460
461 return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
462 Segment<dim>(p1, p2), proper);
463 }
464
465 template<int dim>
Contains(const Segment<dim> & s,const RotBox<dim> & r,bool proper)466 inline bool Contains(const Segment<dim>& s, const RotBox<dim>& r, bool proper)
467 {
468 Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
469 Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);
470
471 return Contains(Segment<dim>(p1, p2),
472 AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size), proper);
473 }
474
475 template<int dim>
Intersect(const RotBox<dim> & r1,const RotBox<dim> & r2,bool proper)476 inline bool Intersect(const RotBox<dim>& r1, const RotBox<dim>& r2, bool proper)
477 {
478 return Intersect(RotBox<dim>(r1).rotatePoint(r2.m_orient.inverse(),
479 r2.m_corner0),
480 AxisBox<dim>(r2.m_corner0, r2.m_corner0 + r2.m_size), proper);
481 }
482
483 template<int dim>
Contains(const RotBox<dim> & outer,const RotBox<dim> & inner,bool proper)484 inline bool Contains(const RotBox<dim>& outer, const RotBox<dim>& inner, bool proper)
485 {
486 return Contains(AxisBox<dim>(outer.m_corner0, outer.m_corner0 + outer.m_size),
487 RotBox<dim>(inner).rotatePoint(outer.m_orient.inverse(),
488 outer.m_corner0), proper);
489 }
490
491 // Polygon<> intersection functions are in polygon_funcs.h, to avoid
492 // unnecessary inclusion of <vector>
493
494 } // namespace WFMath
495
496 #endif // WFMATH_INTERSECT_H
497