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00024 #ifndef WFMATH_INTERSECT_H
00025 #define WFMATH_INTERSECT_H
00026
00027 #include <wfmath/vector.h>
00028 #include <wfmath/point.h>
00029 #include <wfmath/const.h>
00030 #include <wfmath/intersect_decls.h>
00031 #include <wfmath/axisbox.h>
00032 #include <wfmath/ball.h>
00033 #include <wfmath/segment.h>
00034 #include <wfmath/rotbox.h>
00035
00036 namespace WFMath {
00037
00038
00039
00040 template<class S1, class S2>
00041 inline bool Intersect(const S1& s1, const S2& s2, bool proper)
00042 {
00043 return Intersect(s2, s1, proper);
00044 }
00045
00046
00047
00048 template<const int dim>
00049 inline bool Intersect(const Point<dim>& p1, const Point<dim>& p2, bool proper)
00050 {
00051 return !proper && p1 == p2;
00052 }
00053
00054 template<const int dim, class S>
00055 inline bool Contains(const S& s, const Point<dim>& p, bool proper)
00056 {
00057 return Intersect(p, s, proper);
00058 }
00059
00060 template<const int dim>
00061 inline bool Contains(const Point<dim>& p1, const Point<dim>& p2, bool proper)
00062 {
00063 return !proper && p1 == p2;
00064 }
00065
00066
00067
00068 template<const int dim>
00069 inline bool Intersect(const AxisBox<dim>& b, const Point<dim>& p, bool proper)
00070 {
00071 for(int i = 0; i < dim; ++i)
00072 if(_Greater(b.m_low[i], p[i], proper) || _Less(b.m_high[i], p[i], proper))
00073 return false;
00074
00075 return true;
00076 }
00077
00078 template<const int dim>
00079 inline bool Contains(const Point<dim>& p, const AxisBox<dim>& b, bool proper)
00080 {
00081 return !proper && p == b.m_low && p == b.m_high;
00082 }
00083
00084 template<const int dim>
00085 inline bool Intersect(const AxisBox<dim>& b1, const AxisBox<dim>& b2, bool proper)
00086 {
00087 for(int i = 0; i < dim; ++i)
00088 if(_Greater(b1.m_low[i], b2.m_high[i], proper)
00089 || _Less(b1.m_high[i], b2.m_low[i], proper))
00090 return false;
00091
00092 return true;
00093 }
00094
00095 template<const int dim>
00096 inline bool Contains(const AxisBox<dim>& outer, const AxisBox<dim>& inner, bool proper)
00097 {
00098 for(int i = 0; i < dim; ++i)
00099 if(_Less(inner.m_low[i], outer.m_low[i], proper)
00100 || _Greater(inner.m_high[i], outer.m_high[i], proper))
00101 return false;
00102
00103 return true;
00104 }
00105
00106
00107
00108 template<const int dim>
00109 inline bool Intersect(const Ball<dim>& b, const Point<dim>& p, bool proper)
00110 {
00111 return _LessEq(SquaredDistance(b.m_center, p), b.m_radius * b.m_radius
00112 * (1 + WFMATH_EPSILON), proper);
00113 }
00114
00115 template<const int dim>
00116 inline bool Contains(const Point<dim>& p, const Ball<dim>& b, bool proper)
00117 {
00118 return !proper && b.m_radius == 0 && p == b.m_center;
00119 }
00120
00121 template<const int dim>
00122 inline bool Intersect(const Ball<dim>& b, const AxisBox<dim>& a, bool proper)
00123 {
00124 CoordType dist = 0;
00125
00126 for(int i = 0; i < dim; ++i) {
00127 CoordType dist_i;
00128 if(b.m_center[i] < a.m_low[i])
00129 dist_i = b.m_center[i] - a.m_low[i];
00130 else if(b.m_center[i] > a.m_high[i])
00131 dist_i = b.m_center[i] - a.m_high[i];
00132 else
00133 continue;
00134 dist+= dist_i * dist_i;
00135 }
00136
00137 return _LessEq(dist, b.m_radius * b.m_radius, proper);
00138 }
00139
00140 template<const int dim>
00141 inline bool Contains(const Ball<dim>& b, const AxisBox<dim>& a, bool proper)
00142 {
00143 CoordType sqr_dist = 0;
00144
00145 for(int i = 0; i < dim; ++i) {
00146 CoordType furthest = FloatMax(fabs(b.m_center[i] - a.m_low[i]),
00147 fabs(b.m_center[i] - a.m_high[i]));
00148 sqr_dist += furthest * furthest;
00149 }
00150
00151 return _LessEq(sqr_dist, b.m_radius * b.m_radius * (1 + WFMATH_EPSILON), proper);
00152 }
00153
00154 template<const int dim>
00155 inline bool Contains(const AxisBox<dim>& a, const Ball<dim>& b, bool proper)
00156 {
00157 for(int i = 0; i < dim; ++i)
00158 if(_Less(b.m_center[i] - b.m_radius, a.lowerBound(i), proper)
00159 || _Greater(b.m_center[i] + b.m_radius, a.upperBound(i), proper))
00160 return false;
00161
00162 return true;
00163 }
00164
00165 template<const int dim>
00166 inline bool Intersect(const Ball<dim>& b1, const Ball<dim>& b2, bool proper)
00167 {
00168 CoordType sqr_dist = SquaredDistance(b1.m_center, b2.m_center);
00169 CoordType rad_sum = b1.m_radius + b2.m_radius;
00170
00171 return _LessEq(sqr_dist, rad_sum * rad_sum, proper);
00172 }
00173
00174 template<const int dim>
00175 inline bool Contains(const Ball<dim>& outer, const Ball<dim>& inner, bool proper)
00176 {
00177 CoordType rad_diff = outer.m_radius - inner.m_radius;
00178
00179 if(_Less(rad_diff, 0, proper))
00180 return false;
00181
00182 CoordType sqr_dist = SquaredDistance(outer.m_center, inner.m_center);
00183
00184 return _LessEq(sqr_dist, rad_diff * rad_diff, proper);
00185 }
00186
00187
00188
00189 template<const int dim>
00190 inline bool Intersect(const Segment<dim>& s, const Point<dim>& p, bool proper)
00191 {
00192
00193
00194 Vector<dim> v1 = s.m_p1 - p, v2 = s.m_p2 - p;
00195
00196 CoordType proj = Dot(v1, v2);
00197
00198 if(_Greater(proj, 0, proper))
00199 return false;
00200
00201
00202 return Equal(proj * proj, v1.sqrMag() * v2.sqrMag());
00203 }
00204
00205 template<const int dim>
00206 inline bool Contains(const Point<dim>& p, const Segment<dim>& s, bool proper)
00207 {
00208 return !proper && p == s.m_p1 && p == s.m_p2;
00209 }
00210
00211 template<const int dim>
00212 bool Intersect(const Segment<dim>& s, const AxisBox<dim>& b, bool proper)
00213 {
00214
00215
00216
00217
00218
00219
00220
00221
00222 CoordType min = 0, max = 1;
00223
00224 for(int i = 0; i < dim; ++i) {
00225 CoordType dist = s.m_p2[i] - s.m_p1[i];
00226 if(dist == 0) {
00227 if(_Less(s.m_p1[i], b.m_low[i], proper)
00228 || _Greater(s.m_p1[i], b.m_high[i], proper))
00229 return false;
00230 }
00231 else {
00232 CoordType low = (b.m_low[i] - s.m_p1[i]) / dist;
00233 CoordType high = (b.m_high[i] - s.m_p1[i]) / dist;
00234 if(low > high) {
00235 CoordType tmp = high;
00236 high = low;
00237 low = tmp;
00238 }
00239 if(low > min)
00240 min = low;
00241 if(high < max)
00242 max = high;
00243 }
00244 }
00245
00246 return _LessEq(min, max, proper);
00247 }
00248
00249 template<const int dim>
00250 inline bool Contains(const Segment<dim>& s, const AxisBox<dim>& b, bool proper)
00251 {
00252
00253
00254
00255 bool got_difference = false;
00256
00257 for(int i = 0; i < dim; ++i) {
00258 if(b.m_low[i] == b.m_high[i])
00259 continue;
00260 if(got_difference)
00261 return false;
00262 else
00263 got_difference = true;
00264 }
00265
00266 return Contains(s, b.m_low, proper) &&
00267 (got_difference ? Contains(s, b.m_high, proper) : true);
00268 }
00269
00270 template<const int dim>
00271 inline bool Contains(const AxisBox<dim>& b, const Segment<dim>& s, bool proper)
00272 {
00273 return Contains(b, s.m_p1, proper) && Contains(b, s.m_p2, proper);
00274 }
00275
00276 template<const int dim>
00277 bool Intersect(const Segment<dim>& s, const Ball<dim>& b, bool proper)
00278 {
00279 Vector<dim> line = s.m_p2 - s.m_p1, offset = b.m_center - s.m_p1;
00280
00281
00282
00283
00284 CoordType proj = Dot(line, offset);
00285
00286
00287
00288
00289 if(proj <= 0)
00290 return Intersect(b, s.m_p1, proper);
00291
00292 CoordType lineSqrMag = line.sqrMag();
00293
00294 if (proj >= lineSqrMag)
00295 return Intersect(b, s.m_p2, proper);
00296
00297 Vector<dim> perp_part = offset - line * (proj / lineSqrMag);
00298
00299 return _LessEq(perp_part.sqrMag(), b.m_radius * b.m_radius, proper);
00300 }
00301
00302 template<const int dim>
00303 inline bool Contains(const Ball<dim>& b, const Segment<dim>& s, bool proper)
00304 {
00305 return Contains(b, s.m_p1, proper) && Contains(b, s.m_p2, proper);
00306 }
00307
00308 template<const int dim>
00309 inline bool Contains(const Segment<dim>& s, const Ball<dim>& b, bool proper)
00310 {
00311 return b.m_radius == 0 && Contains(s, b.m_center, proper);
00312 }
00313
00314 template<const int dim>
00315 bool Intersect(const Segment<dim>& s1, const Segment<dim>& s2, bool proper)
00316 {
00317
00318
00319
00320 Vector<dim> v1 = s1.m_p2 - s1.m_p1, v2 = s2.m_p2 - s2.m_p1,
00321 deltav = s2.m_p1 - s1.m_p1;
00322
00323 CoordType v1sqr = v1.sqrMag(), v2sqr = v2.sqrMag();
00324 CoordType proj12 = Dot(v1, v2), proj1delta = Dot(v1, deltav),
00325 proj2delta = Dot(v2, deltav);
00326
00327 CoordType denom = v1sqr * v2sqr - proj12 * proj12;
00328
00329 if(dim > 2 && !Equal(v2sqr * proj1delta * proj1delta +
00330 v1sqr * proj2delta * proj2delta,
00331 2 * proj12 * proj1delta * proj2delta +
00332 deltav.sqrMag() * denom))
00333 return false;
00334
00335 if(denom > 0) {
00336
00337
00338
00339 CoordType coord1 = (v2sqr * proj1delta - proj12 * proj2delta) / denom;
00340 CoordType coord2 = -(v1sqr * proj2delta - proj12 * proj1delta) / denom;
00341
00342 return _LessEq(coord1, 0, proper) && _LessEq(coord1, 1, proper)
00343 && _GreaterEq(coord2, 0, proper) && _GreaterEq(coord2, 1, proper);
00344 }
00345 else {
00346
00347 return Contains(s1, s2.m_p1, proper) || Contains(s1, s2.m_p2, proper)
00348 || Contains(s2, s1.m_p1, proper) || Contains(s2, s1.m_p2, proper)
00349
00350 || proper && (s1.m_p1 != s1.m_p2)
00351 && ((s1.m_p1 == s2.m_p1 && s1.m_p2 == s2.m_p2)
00352 || (s1.m_p1 == s2.m_p2 && s1.m_p2 == s2.m_p1));
00353 }
00354 }
00355
00356 template<const int dim>
00357 inline bool Contains(const Segment<dim>& s1, const Segment<dim>& s2, bool proper)
00358 {
00359 return Contains(s1, s2.m_p1, proper) && Contains(s1, s2.m_p2, proper);
00360 }
00361
00362
00363
00364 template<const int dim>
00365 inline bool Intersect(const RotBox<dim>& r, const Point<dim>& p, bool proper)
00366 {
00367
00368
00369 Vector<dim> shift = ProdInv(p - r.m_corner0, r.m_orient);
00370
00371 for(int i = 0; i < dim; ++i) {
00372 if(r.m_size[i] < 0) {
00373 if(_Less(shift[i], r.m_size[i], proper) || _Greater(shift[i], 0, proper))
00374 return false;
00375 }
00376 else {
00377 if(_Greater(shift[i], r.m_size[i], proper) || _Less(shift[i], 0, proper))
00378 return false;
00379 }
00380 }
00381
00382 return true;
00383 }
00384
00385 template<const int dim>
00386 inline bool Contains(const Point<dim>& p, const RotBox<dim>& r, bool proper)
00387 {
00388 if(proper)
00389 return false;
00390
00391 for(int i = 0; i < dim; ++i)
00392 if(r.m_size[i] != 0)
00393 return false;
00394
00395 return p == r.m_corner0;
00396 }
00397
00398 template<const int dim>
00399 bool Intersect(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper);
00400
00401
00402
00403 template<>
00404 bool Intersect<2>(const RotBox<2>& r, const AxisBox<2>& b, bool proper);
00405 template<>
00406 bool Intersect<3>(const RotBox<3>& r, const AxisBox<3>& b, bool proper);
00407
00408 template<const int dim>
00409 inline bool Contains(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper)
00410 {
00411 RotMatrix<dim> m = r.m_orient.inverse();
00412
00413 return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
00414 RotBox<dim>(Point<dim>(b.m_low).rotate(m, r.m_corner0),
00415 b.m_high - b.m_low, m), proper);
00416 }
00417
00418 template<const int dim>
00419 inline bool Contains(const AxisBox<dim>& b, const RotBox<dim>& r, bool proper)
00420 {
00421 return Contains(b, r.boundingBox(), proper);
00422 }
00423
00424 template<const int dim>
00425 inline bool Intersect(const RotBox<dim>& r, const Ball<dim>& b, bool proper)
00426 {
00427 return Intersect(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
00428 Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
00429 r.m_orient), b.m_radius), proper);
00430 }
00431
00432 template<const int dim>
00433 inline bool Contains(const RotBox<dim>& r, const Ball<dim>& b, bool proper)
00434 {
00435 return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
00436 Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
00437 r.m_orient), b.m_radius), proper);
00438 }
00439
00440 template<const int dim>
00441 inline bool Contains(const Ball<dim>& b, const RotBox<dim>& r, bool proper)
00442 {
00443 return Contains(Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
00444 r.m_orient), b.m_radius),
00445 AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size), proper);
00446 }
00447
00448 template<const int dim>
00449 inline bool Intersect(const RotBox<dim>& r, const Segment<dim>& s, bool proper)
00450 {
00451 Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
00452 Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);
00453
00454 return Intersect(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
00455 Segment<dim>(p1, p2), proper);
00456 }
00457
00458 template<const int dim>
00459 inline bool Contains(const RotBox<dim>& r, const Segment<dim>& s, bool proper)
00460 {
00461 Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
00462 Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);
00463
00464 return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
00465 Segment<dim>(p1, p2), proper);
00466 }
00467
00468 template<const int dim>
00469 inline bool Contains(const Segment<dim>& s, const RotBox<dim>& r, bool proper)
00470 {
00471 Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
00472 Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);
00473
00474 return Contains(Segment<dim>(p1, p2),
00475 AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size), proper);
00476 }
00477
00478 template<const int dim>
00479 inline bool Intersect(const RotBox<dim>& r1, const RotBox<dim>& r2, bool proper)
00480 {
00481 return Intersect(RotBox<dim>(r1).rotatePoint(r2.m_orient.inverse(),
00482 r2.m_corner0),
00483 AxisBox<dim>(r2.m_corner0, r2.m_corner0 + r2.m_size), proper);
00484 }
00485
00486 template<const int dim>
00487 inline bool Contains(const RotBox<dim>& outer, const RotBox<dim>& inner, bool proper)
00488 {
00489 return Contains(AxisBox<dim>(outer.m_corner0, outer.m_corner0 + outer.m_size),
00490 RotBox<dim>(inner).rotatePoint(outer.m_orient.inverse(),
00491 outer.m_corner0), proper);
00492 }
00493
00494
00495
00496
00497 }
00498
00499 #endif // WFMATH_INTERSECT_H