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b32b8144 FG |
1 | // Boost.Geometry |
2 | ||
11fdf7f2 TL |
3 | // Copyright (c) 2017 Adam Wulkiewicz, Lodz, Poland. |
4 | ||
1e59de90 | 5 | // Copyright (c) 2016-2021, Oracle and/or its affiliates. |
b32b8144 FG |
6 | // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle |
7 | ||
8 | // Use, modification and distribution is subject to the Boost Software License, | |
9 | // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at | |
10 | // http://www.boost.org/LICENSE_1_0.txt) | |
11 | ||
12 | #ifndef BOOST_GEOMETRY_STRATEGIES_SPHERICAL_INTERSECTION_HPP | |
13 | #define BOOST_GEOMETRY_STRATEGIES_SPHERICAL_INTERSECTION_HPP | |
14 | ||
15 | #include <algorithm> | |
20effc67 | 16 | #include <type_traits> |
b32b8144 FG |
17 | |
18 | #include <boost/geometry/core/cs.hpp> | |
19 | #include <boost/geometry/core/access.hpp> | |
20 | #include <boost/geometry/core/radian_access.hpp> | |
21 | #include <boost/geometry/core/tags.hpp> | |
22 | ||
23 | #include <boost/geometry/algorithms/detail/assign_values.hpp> | |
24 | #include <boost/geometry/algorithms/detail/assign_indexed_point.hpp> | |
25 | #include <boost/geometry/algorithms/detail/equals/point_point.hpp> | |
26 | #include <boost/geometry/algorithms/detail/recalculate.hpp> | |
27 | ||
28 | #include <boost/geometry/arithmetic/arithmetic.hpp> | |
29 | #include <boost/geometry/arithmetic/cross_product.hpp> | |
30 | #include <boost/geometry/arithmetic/dot_product.hpp> | |
31 | #include <boost/geometry/arithmetic/normalize.hpp> | |
32 | #include <boost/geometry/formulas/spherical.hpp> | |
33 | ||
34 | #include <boost/geometry/geometries/concepts/point_concept.hpp> | |
35 | #include <boost/geometry/geometries/concepts/segment_concept.hpp> | |
20effc67 | 36 | #include <boost/geometry/geometries/segment.hpp> |
b32b8144 FG |
37 | |
38 | #include <boost/geometry/policies/robustness/segment_ratio.hpp> | |
39 | ||
20effc67 TL |
40 | #include <boost/geometry/strategy/spherical/area.hpp> |
41 | #include <boost/geometry/strategy/spherical/envelope.hpp> | |
42 | #include <boost/geometry/strategy/spherical/expand_box.hpp> | |
43 | #include <boost/geometry/strategy/spherical/expand_segment.hpp> | |
44 | ||
b32b8144 FG |
45 | #include <boost/geometry/strategies/covered_by.hpp> |
46 | #include <boost/geometry/strategies/intersection.hpp> | |
47 | #include <boost/geometry/strategies/intersection_result.hpp> | |
48 | #include <boost/geometry/strategies/side.hpp> | |
49 | #include <boost/geometry/strategies/side_info.hpp> | |
92f5a8d4 TL |
50 | #include <boost/geometry/strategies/spherical/disjoint_box_box.hpp> |
51 | #include <boost/geometry/strategies/spherical/disjoint_segment_box.hpp> | |
b32b8144 | 52 | #include <boost/geometry/strategies/spherical/distance_haversine.hpp> |
92f5a8d4 | 53 | #include <boost/geometry/strategies/spherical/point_in_point.hpp> |
b32b8144 FG |
54 | #include <boost/geometry/strategies/spherical/point_in_poly_winding.hpp> |
55 | #include <boost/geometry/strategies/spherical/ssf.hpp> | |
56 | #include <boost/geometry/strategies/within.hpp> | |
57 | ||
58 | #include <boost/geometry/util/math.hpp> | |
59 | #include <boost/geometry/util/select_calculation_type.hpp> | |
60 | ||
61 | ||
62 | namespace boost { namespace geometry | |
63 | { | |
64 | ||
65 | namespace strategy { namespace intersection | |
66 | { | |
67 | ||
68 | // NOTE: | |
69 | // The coordinates of crossing IP may be calculated with small precision in some cases. | |
70 | // For double, near the equator noticed error ~1e-9 so far greater than | |
71 | // machine epsilon which is ~1e-16. This error is ~0.04m. | |
72 | // E.g. consider two cases, one near the origin and the second one rotated by 90 deg around Z or SN axis. | |
73 | // After the conversion from spherical degrees to cartesian 3d the following coordinates | |
74 | // are calculated: | |
75 | // for sph (-1 -1, 1 1) deg cart3d ys are -0.017449748351250485 and 0.017449748351250485 | |
76 | // for sph (89 -1, 91 1) deg cart3d xs are 0.017449748351250571 and -0.017449748351250450 | |
77 | // During the conversion degrees must first be converted to radians and then radians | |
78 | // are passed into trigonometric functions. The error may have several causes: | |
79 | // 1. Radians cannot represent exactly the same angles as degrees. | |
80 | // 2. Different longitudes are passed into sin() for x, corresponding to cos() for y, | |
81 | // and for different angle the error of the result may be different. | |
82 | // 3. These non-corresponding cartesian coordinates are used in calculation, | |
83 | // e.g. multiplied several times in cross and dot products. | |
84 | // If it was a problem this strategy could e.g. "normalize" longitudes before the conversion using the source units | |
85 | // by rotating the globe around Z axis, so moving longitudes always the same way towards the origin, | |
86 | // assuming this could help which is not clear. | |
87 | // For now, intersection points near the endpoints are checked explicitly if needed (if the IP is near the endpoint) | |
88 | // to generate precise result for them. Only the crossing (i) case may suffer from lower precision. | |
89 | ||
90 | template | |
91 | < | |
92 | typename CalcPolicy, | |
93 | typename CalculationType = void | |
94 | > | |
95 | struct ecef_segments | |
96 | { | |
92f5a8d4 TL |
97 | typedef spherical_tag cs_tag; |
98 | ||
b32b8144 FG |
99 | enum intersection_point_flag { ipi_inters = 0, ipi_at_a1, ipi_at_a2, ipi_at_b1, ipi_at_b2 }; |
100 | ||
101 | // segment_intersection_info cannot outlive relate_ecef_segments | |
102 | template <typename CoordinateType, typename SegmentRatio, typename Vector3d> | |
103 | struct segment_intersection_info | |
104 | { | |
b32b8144 FG |
105 | segment_intersection_info(CalcPolicy const& calc) |
106 | : calc_policy(calc) | |
107 | {} | |
108 | ||
b32b8144 | 109 | template <typename Point, typename Segment1, typename Segment2> |
11fdf7f2 | 110 | void calculate(Point& point, Segment1 const& a, Segment2 const& b) const |
b32b8144 FG |
111 | { |
112 | if (ip_flag == ipi_inters) | |
113 | { | |
114 | // TODO: assign the rest of coordinates | |
115 | point = calc_policy.template from_cart3d<Point>(intersection_point); | |
116 | } | |
117 | else if (ip_flag == ipi_at_a1) | |
118 | { | |
119 | detail::assign_point_from_index<0>(a, point); | |
120 | } | |
121 | else if (ip_flag == ipi_at_a2) | |
122 | { | |
123 | detail::assign_point_from_index<1>(a, point); | |
124 | } | |
125 | else if (ip_flag == ipi_at_b1) | |
126 | { | |
127 | detail::assign_point_from_index<0>(b, point); | |
128 | } | |
129 | else // ip_flag == ipi_at_b2 | |
130 | { | |
131 | detail::assign_point_from_index<1>(b, point); | |
132 | } | |
133 | } | |
134 | ||
135 | Vector3d intersection_point; | |
136 | SegmentRatio robust_ra; | |
137 | SegmentRatio robust_rb; | |
138 | intersection_point_flag ip_flag; | |
139 | ||
140 | CalcPolicy const& calc_policy; | |
141 | }; | |
142 | ||
143 | // Relate segments a and b | |
144 | template | |
145 | < | |
92f5a8d4 TL |
146 | typename UniqueSubRange1, |
147 | typename UniqueSubRange2, | |
148 | typename Policy | |
b32b8144 FG |
149 | > |
150 | static inline typename Policy::return_type | |
92f5a8d4 TL |
151 | apply(UniqueSubRange1 const& range_p, UniqueSubRange2 const& range_q, |
152 | Policy const&) | |
b32b8144 FG |
153 | { |
154 | // For now create it using default constructor. In the future it could | |
155 | // be stored in strategy. However then apply() wouldn't be static and | |
156 | // all relops and setops would have to take the strategy or model. | |
157 | // Initialize explicitly to prevent compiler errors in case of PoD type | |
158 | CalcPolicy const calc_policy = CalcPolicy(); | |
159 | ||
92f5a8d4 TL |
160 | typedef typename UniqueSubRange1::point_type point1_type; |
161 | typedef typename UniqueSubRange2::point_type point2_type; | |
162 | ||
163 | BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<point1_type>) ); | |
164 | BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<point2_type>) ); | |
165 | ||
166 | point1_type const& a1 = range_p.at(0); | |
167 | point1_type const& a2 = range_p.at(1); | |
168 | point2_type const& b1 = range_q.at(0); | |
169 | point2_type const& b2 = range_q.at(1); | |
170 | ||
171 | typedef model::referring_segment<point1_type const> segment1_type; | |
172 | typedef model::referring_segment<point2_type const> segment2_type; | |
173 | segment1_type const a(a1, a2); | |
174 | segment2_type const b(b1, b2); | |
b32b8144 FG |
175 | |
176 | // TODO: check only 2 first coordinates here? | |
b32b8144 FG |
177 | bool a_is_point = equals_point_point(a1, a2); |
178 | bool b_is_point = equals_point_point(b1, b2); | |
179 | ||
180 | if(a_is_point && b_is_point) | |
181 | { | |
182 | return equals_point_point(a1, b2) | |
183 | ? Policy::degenerate(a, true) | |
184 | : Policy::disjoint() | |
185 | ; | |
186 | } | |
187 | ||
188 | typedef typename select_calculation_type | |
92f5a8d4 | 189 | <segment1_type, segment2_type, CalculationType>::type calc_t; |
b32b8144 FG |
190 | |
191 | calc_t const c0 = 0; | |
192 | calc_t const c1 = 1; | |
193 | ||
194 | typedef model::point<calc_t, 3, cs::cartesian> vec3d_t; | |
195 | ||
196 | vec3d_t const a1v = calc_policy.template to_cart3d<vec3d_t>(a1); | |
197 | vec3d_t const a2v = calc_policy.template to_cart3d<vec3d_t>(a2); | |
198 | vec3d_t const b1v = calc_policy.template to_cart3d<vec3d_t>(b1); | |
199 | vec3d_t const b2v = calc_policy.template to_cart3d<vec3d_t>(b2); | |
200 | ||
201 | bool degen_neq_coords = false; | |
202 | side_info sides; | |
203 | ||
204 | typename CalcPolicy::template plane<vec3d_t> | |
205 | plane2 = calc_policy.get_plane(b1v, b2v); | |
206 | ||
207 | calc_t dist_b1_b2 = 0; | |
208 | if (! b_is_point) | |
209 | { | |
210 | calculate_dist(b1v, b2v, plane2, dist_b1_b2); | |
211 | if (math::equals(dist_b1_b2, c0)) | |
212 | { | |
213 | degen_neq_coords = true; | |
214 | b_is_point = true; | |
215 | dist_b1_b2 = 0; | |
216 | } | |
217 | else | |
218 | { | |
219 | // not normalized normals, the same as in side strategy | |
220 | sides.set<0>(plane2.side_value(a1v), plane2.side_value(a2v)); | |
221 | if (sides.same<0>()) | |
222 | { | |
223 | // Both points are at same side of other segment, we can leave | |
224 | return Policy::disjoint(); | |
225 | } | |
226 | } | |
227 | } | |
228 | ||
229 | typename CalcPolicy::template plane<vec3d_t> | |
230 | plane1 = calc_policy.get_plane(a1v, a2v); | |
231 | ||
232 | calc_t dist_a1_a2 = 0; | |
233 | if (! a_is_point) | |
234 | { | |
235 | calculate_dist(a1v, a2v, plane1, dist_a1_a2); | |
236 | if (math::equals(dist_a1_a2, c0)) | |
237 | { | |
238 | degen_neq_coords = true; | |
239 | a_is_point = true; | |
240 | dist_a1_a2 = 0; | |
241 | } | |
242 | else | |
243 | { | |
244 | // not normalized normals, the same as in side strategy | |
245 | sides.set<1>(plane1.side_value(b1v), plane1.side_value(b2v)); | |
246 | if (sides.same<1>()) | |
247 | { | |
248 | // Both points are at same side of other segment, we can leave | |
249 | return Policy::disjoint(); | |
250 | } | |
251 | } | |
252 | } | |
253 | ||
254 | // NOTE: at this point the segments may still be disjoint | |
255 | ||
256 | calc_t len1 = 0; | |
257 | // point or opposite sides of a sphere/spheroid, assume point | |
258 | if (! a_is_point && ! detail::vec_normalize(plane1.normal, len1)) | |
259 | { | |
260 | a_is_point = true; | |
261 | if (sides.get<0, 0>() == 0 || sides.get<0, 1>() == 0) | |
262 | { | |
263 | sides.set<0>(0, 0); | |
264 | } | |
265 | } | |
266 | ||
267 | calc_t len2 = 0; | |
268 | if (! b_is_point && ! detail::vec_normalize(plane2.normal, len2)) | |
269 | { | |
270 | b_is_point = true; | |
271 | if (sides.get<1, 0>() == 0 || sides.get<1, 1>() == 0) | |
272 | { | |
273 | sides.set<1>(0, 0); | |
274 | } | |
275 | } | |
276 | ||
277 | // check both degenerated once more | |
278 | if (a_is_point && b_is_point) | |
279 | { | |
280 | return equals_point_point(a1, b2) | |
281 | ? Policy::degenerate(a, true) | |
282 | : Policy::disjoint() | |
283 | ; | |
284 | } | |
285 | ||
286 | // NOTE: at this point the segments may still be disjoint | |
287 | // NOTE: at this point one of the segments may be degenerated | |
288 | ||
289 | bool collinear = sides.collinear(); | |
290 | ||
291 | if (! collinear) | |
292 | { | |
293 | // NOTE: for some approximations it's possible that both points may lie | |
294 | // on the same geodesic but still some of the sides may be != 0. | |
295 | // This is e.g. true for long segments represented as elliptic arcs | |
296 | // with origin different than the center of the coordinate system. | |
297 | // So make the sides consistent | |
298 | ||
299 | // WARNING: the side strategy doesn't have the info about the other | |
300 | // segment so it may return results inconsistent with this intersection | |
301 | // strategy, as it checks both segments for consistency | |
302 | ||
303 | if (sides.get<0, 0>() == 0 && sides.get<0, 1>() == 0) | |
304 | { | |
305 | collinear = true; | |
306 | sides.set<1>(0, 0); | |
307 | } | |
308 | else if (sides.get<1, 0>() == 0 && sides.get<1, 1>() == 0) | |
309 | { | |
310 | collinear = true; | |
311 | sides.set<0>(0, 0); | |
312 | } | |
313 | } | |
314 | ||
315 | calc_t dot_n1n2 = dot_product(plane1.normal, plane2.normal); | |
316 | ||
317 | // NOTE: this is technically not needed since theoretically above sides | |
318 | // are calculated, but just in case check the normals. | |
319 | // Have in mind that SSF side strategy doesn't check this. | |
320 | // collinear if normals are equal or opposite: cos(a) in {-1, 1} | |
321 | if (! collinear && math::equals(math::abs(dot_n1n2), c1)) | |
322 | { | |
323 | collinear = true; | |
324 | sides.set<0>(0, 0); | |
325 | sides.set<1>(0, 0); | |
326 | } | |
327 | ||
328 | if (collinear) | |
329 | { | |
330 | if (a_is_point) | |
331 | { | |
332 | return collinear_one_degenerated<Policy, calc_t>(a, true, b1, b2, a1, a2, b1v, b2v, | |
333 | plane2, a1v, a2v, dist_b1_b2, degen_neq_coords); | |
334 | } | |
335 | else if (b_is_point) | |
336 | { | |
337 | // b2 used to be consistent with (degenerated) checks above (is it needed?) | |
338 | return collinear_one_degenerated<Policy, calc_t>(b, false, a1, a2, b1, b2, a1v, a2v, | |
339 | plane1, b1v, b2v, dist_a1_a2, degen_neq_coords); | |
340 | } | |
341 | else | |
342 | { | |
343 | calc_t dist_a1_b1, dist_a1_b2; | |
344 | calc_t dist_b1_a1, dist_b1_a2; | |
92f5a8d4 TL |
345 | calculate_collinear_data(a1, a2, b1, b2, a1v, a2v, plane1, b1v, b2v, dist_a1_a2, dist_a1_b1); |
346 | calculate_collinear_data(a1, a2, b2, b1, a1v, a2v, plane1, b2v, b1v, dist_a1_a2, dist_a1_b2); | |
347 | calculate_collinear_data(b1, b2, a1, a2, b1v, b2v, plane2, a1v, a2v, dist_b1_b2, dist_b1_a1); | |
348 | calculate_collinear_data(b1, b2, a2, a1, b1v, b2v, plane2, a2v, a1v, dist_b1_b2, dist_b1_a2); | |
349 | // NOTE: The following optimization causes problems with consitency | |
350 | // It may either be caused by numerical issues or the way how distance is coded: | |
351 | // as cosine of angle scaled and translated, see: calculate_dist() | |
352 | /*dist_b1_b2 = dist_a1_b2 - dist_a1_b1; | |
353 | dist_b1_a1 = -dist_a1_b1; | |
354 | dist_b1_a2 = dist_a1_a2 - dist_a1_b1; | |
355 | dist_a1_a2 = dist_b1_a2 - dist_b1_a1; | |
356 | dist_a1_b1 = -dist_b1_a1; | |
357 | dist_a1_b2 = dist_b1_b2 - dist_b1_a1;*/ | |
b32b8144 FG |
358 | |
359 | segment_ratio<calc_t> ra_from(dist_b1_a1, dist_b1_b2); | |
360 | segment_ratio<calc_t> ra_to(dist_b1_a2, dist_b1_b2); | |
361 | segment_ratio<calc_t> rb_from(dist_a1_b1, dist_a1_a2); | |
362 | segment_ratio<calc_t> rb_to(dist_a1_b2, dist_a1_a2); | |
363 | ||
364 | // NOTE: this is probably not needed | |
365 | int const a1_wrt_b = position_value(c0, dist_a1_b1, dist_a1_b2); | |
366 | int const a2_wrt_b = position_value(dist_a1_a2, dist_a1_b1, dist_a1_b2); | |
367 | int const b1_wrt_a = position_value(c0, dist_b1_a1, dist_b1_a2); | |
368 | int const b2_wrt_a = position_value(dist_b1_b2, dist_b1_a1, dist_b1_a2); | |
369 | ||
370 | if (a1_wrt_b == 1) | |
371 | { | |
372 | ra_from.assign(0, dist_b1_b2); | |
373 | rb_from.assign(0, dist_a1_a2); | |
374 | } | |
375 | else if (a1_wrt_b == 3) | |
376 | { | |
377 | ra_from.assign(dist_b1_b2, dist_b1_b2); | |
378 | rb_to.assign(0, dist_a1_a2); | |
379 | } | |
380 | ||
381 | if (a2_wrt_b == 1) | |
382 | { | |
383 | ra_to.assign(0, dist_b1_b2); | |
384 | rb_from.assign(dist_a1_a2, dist_a1_a2); | |
385 | } | |
386 | else if (a2_wrt_b == 3) | |
387 | { | |
388 | ra_to.assign(dist_b1_b2, dist_b1_b2); | |
389 | rb_to.assign(dist_a1_a2, dist_a1_a2); | |
390 | } | |
391 | ||
392 | if ((a1_wrt_b < 1 && a2_wrt_b < 1) || (a1_wrt_b > 3 && a2_wrt_b > 3)) | |
393 | { | |
394 | return Policy::disjoint(); | |
395 | } | |
396 | ||
397 | bool const opposite = dot_n1n2 < c0; | |
398 | ||
399 | return Policy::segments_collinear(a, b, opposite, | |
400 | a1_wrt_b, a2_wrt_b, b1_wrt_a, b2_wrt_a, | |
401 | ra_from, ra_to, rb_from, rb_to); | |
402 | } | |
403 | } | |
404 | else // crossing | |
405 | { | |
406 | if (a_is_point || b_is_point) | |
407 | { | |
408 | return Policy::disjoint(); | |
409 | } | |
410 | ||
411 | vec3d_t i1; | |
412 | intersection_point_flag ip_flag; | |
413 | calc_t dist_a1_i1, dist_b1_i1; | |
414 | if (calculate_ip_data(a1, a2, b1, b2, a1v, a2v, b1v, b2v, | |
415 | plane1, plane2, calc_policy, | |
416 | sides, dist_a1_a2, dist_b1_b2, | |
417 | i1, dist_a1_i1, dist_b1_i1, ip_flag)) | |
418 | { | |
419 | // intersects | |
420 | segment_intersection_info | |
421 | < | |
422 | calc_t, | |
423 | segment_ratio<calc_t>, | |
424 | vec3d_t | |
425 | > sinfo(calc_policy); | |
426 | ||
427 | sinfo.robust_ra.assign(dist_a1_i1, dist_a1_a2); | |
428 | sinfo.robust_rb.assign(dist_b1_i1, dist_b1_b2); | |
429 | sinfo.intersection_point = i1; | |
430 | sinfo.ip_flag = ip_flag; | |
431 | ||
432 | return Policy::segments_crosses(sides, sinfo, a, b); | |
433 | } | |
434 | else | |
435 | { | |
436 | return Policy::disjoint(); | |
437 | } | |
438 | } | |
439 | } | |
440 | ||
441 | private: | |
442 | template <typename Policy, typename CalcT, typename Segment, typename Point1, typename Point2, typename Vec3d, typename Plane> | |
443 | static inline typename Policy::return_type | |
444 | collinear_one_degenerated(Segment const& segment, bool degenerated_a, | |
445 | Point1 const& a1, Point1 const& a2, | |
446 | Point2 const& b1, Point2 const& b2, | |
447 | Vec3d const& a1v, Vec3d const& a2v, | |
448 | Plane const& plane, | |
449 | Vec3d const& b1v, Vec3d const& b2v, | |
450 | CalcT const& dist_1_2, | |
451 | bool degen_neq_coords) | |
452 | { | |
453 | CalcT dist_1_o; | |
454 | return ! calculate_collinear_data(a1, a2, b1, b2, a1v, a2v, plane, b1v, b2v, dist_1_2, dist_1_o, degen_neq_coords) | |
455 | ? Policy::disjoint() | |
456 | : Policy::one_degenerate(segment, segment_ratio<CalcT>(dist_1_o, dist_1_2), degenerated_a); | |
457 | } | |
458 | ||
459 | template <typename Point1, typename Point2, typename Vec3d, typename Plane, typename CalcT> | |
460 | static inline bool calculate_collinear_data(Point1 const& a1, Point1 const& a2, // in | |
92f5a8d4 | 461 | Point2 const& b1, Point2 const& /*b2*/, // in |
b32b8144 FG |
462 | Vec3d const& a1v, // in |
463 | Vec3d const& a2v, // in | |
464 | Plane const& plane1, // in | |
465 | Vec3d const& b1v, // in | |
466 | Vec3d const& b2v, // in | |
467 | CalcT const& dist_a1_a2, // in | |
92f5a8d4 | 468 | CalcT& dist_a1_b1, // out |
b32b8144 FG |
469 | bool degen_neq_coords = false) // in |
470 | { | |
92f5a8d4 TL |
471 | // calculate dist_a1_b1 |
472 | calculate_dist(a1v, a2v, plane1, b1v, dist_a1_b1); | |
b32b8144 | 473 | |
92f5a8d4 TL |
474 | // if b1 is equal to a1 |
475 | if (is_endpoint_equal(dist_a1_b1, a1, b1)) | |
b32b8144 | 476 | { |
92f5a8d4 | 477 | dist_a1_b1 = 0; |
b32b8144 FG |
478 | return true; |
479 | } | |
92f5a8d4 TL |
480 | // or b1 is equal to a2 |
481 | else if (is_endpoint_equal(dist_a1_a2 - dist_a1_b1, a2, b1)) | |
b32b8144 | 482 | { |
92f5a8d4 | 483 | dist_a1_b1 = dist_a1_a2; |
b32b8144 FG |
484 | return true; |
485 | } | |
486 | ||
92f5a8d4 | 487 | // check the other endpoint of degenerated segment near a pole |
b32b8144 FG |
488 | if (degen_neq_coords) |
489 | { | |
490 | static CalcT const c0 = 0; | |
491 | ||
92f5a8d4 TL |
492 | CalcT dist_a1_b2 = 0; |
493 | calculate_dist(a1v, a2v, plane1, b2v, dist_a1_b2); | |
b32b8144 | 494 | |
92f5a8d4 | 495 | if (math::equals(dist_a1_b2, c0)) |
b32b8144 | 496 | { |
92f5a8d4 | 497 | dist_a1_b1 = 0; |
b32b8144 FG |
498 | return true; |
499 | } | |
92f5a8d4 | 500 | else if (math::equals(dist_a1_a2 - dist_a1_b2, c0)) |
b32b8144 | 501 | { |
92f5a8d4 | 502 | dist_a1_b1 = dist_a1_a2; |
b32b8144 FG |
503 | return true; |
504 | } | |
505 | } | |
506 | ||
507 | // or i1 is on b | |
92f5a8d4 | 508 | return segment_ratio<CalcT>(dist_a1_b1, dist_a1_a2).on_segment(); |
b32b8144 FG |
509 | } |
510 | ||
511 | template <typename Point1, typename Point2, typename Vec3d, typename Plane, typename CalcT> | |
512 | static inline bool calculate_ip_data(Point1 const& a1, Point1 const& a2, // in | |
513 | Point2 const& b1, Point2 const& b2, // in | |
514 | Vec3d const& a1v, Vec3d const& a2v, // in | |
515 | Vec3d const& b1v, Vec3d const& b2v, // in | |
516 | Plane const& plane1, // in | |
517 | Plane const& plane2, // in | |
518 | CalcPolicy const& calc_policy, // in | |
519 | side_info const& sides, // in | |
520 | CalcT const& dist_a1_a2, // in | |
521 | CalcT const& dist_b1_b2, // in | |
522 | Vec3d & ip, // out | |
523 | CalcT& dist_a1_ip, // out | |
524 | CalcT& dist_b1_ip, // out | |
525 | intersection_point_flag& ip_flag) // out | |
526 | { | |
527 | Vec3d ip1, ip2; | |
528 | calc_policy.intersection_points(plane1, plane2, ip1, ip2); | |
529 | ||
530 | calculate_dist(a1v, a2v, plane1, ip1, dist_a1_ip); | |
531 | ip = ip1; | |
532 | ||
533 | // choose the opposite side of the globe if the distance is shorter | |
534 | { | |
535 | CalcT const d = abs_distance(dist_a1_a2, dist_a1_ip); | |
536 | if (d > CalcT(0)) | |
537 | { | |
538 | // TODO: this should be ok not only for sphere | |
539 | // but requires more investigation | |
540 | CalcT const dist_a1_i2 = dist_of_i2(dist_a1_ip); | |
541 | CalcT const d2 = abs_distance(dist_a1_a2, dist_a1_i2); | |
542 | if (d2 < d) | |
543 | { | |
544 | dist_a1_ip = dist_a1_i2; | |
545 | ip = ip2; | |
546 | } | |
547 | } | |
548 | } | |
549 | ||
550 | bool is_on_a = false, is_near_a1 = false, is_near_a2 = false; | |
551 | if (! is_potentially_crossing(dist_a1_a2, dist_a1_ip, is_on_a, is_near_a1, is_near_a2)) | |
552 | { | |
553 | return false; | |
554 | } | |
555 | ||
556 | calculate_dist(b1v, b2v, plane2, ip, dist_b1_ip); | |
557 | ||
558 | bool is_on_b = false, is_near_b1 = false, is_near_b2 = false; | |
559 | if (! is_potentially_crossing(dist_b1_b2, dist_b1_ip, is_on_b, is_near_b1, is_near_b2)) | |
560 | { | |
561 | return false; | |
562 | } | |
563 | ||
564 | // reassign the IP if some endpoints overlap | |
b32b8144 FG |
565 | if (is_near_a1) |
566 | { | |
567 | if (is_near_b1 && equals_point_point(a1, b1)) | |
568 | { | |
569 | dist_a1_ip = 0; | |
570 | dist_b1_ip = 0; | |
571 | //i1 = a1v; | |
572 | ip_flag = ipi_at_a1; | |
573 | return true; | |
574 | } | |
575 | ||
576 | if (is_near_b2 && equals_point_point(a1, b2)) | |
577 | { | |
578 | dist_a1_ip = 0; | |
579 | dist_b1_ip = dist_b1_b2; | |
580 | //i1 = a1v; | |
581 | ip_flag = ipi_at_a1; | |
582 | return true; | |
583 | } | |
584 | } | |
585 | ||
586 | if (is_near_a2) | |
587 | { | |
588 | if (is_near_b1 && equals_point_point(a2, b1)) | |
589 | { | |
590 | dist_a1_ip = dist_a1_a2; | |
591 | dist_b1_ip = 0; | |
592 | //i1 = a2v; | |
593 | ip_flag = ipi_at_a2; | |
594 | return true; | |
595 | } | |
596 | ||
597 | if (is_near_b2 && equals_point_point(a2, b2)) | |
598 | { | |
599 | dist_a1_ip = dist_a1_a2; | |
600 | dist_b1_ip = dist_b1_b2; | |
601 | //i1 = a2v; | |
602 | ip_flag = ipi_at_a2; | |
603 | return true; | |
604 | } | |
605 | } | |
606 | ||
607 | // at this point we know that the endpoints doesn't overlap | |
608 | // reassign IP and distance if the IP is on a segment and one of | |
609 | // the endpoints of the other segment lies on the former segment | |
610 | if (is_on_a) | |
611 | { | |
612 | if (is_near_b1 && sides.template get<1, 0>() == 0) // b1 wrt a | |
613 | { | |
92f5a8d4 | 614 | calculate_dist(a1v, a2v, plane1, b1v, dist_a1_ip); // for consistency |
b32b8144 FG |
615 | dist_b1_ip = 0; |
616 | //i1 = b1v; | |
617 | ip_flag = ipi_at_b1; | |
618 | return true; | |
619 | } | |
620 | ||
621 | if (is_near_b2 && sides.template get<1, 1>() == 0) // b2 wrt a | |
622 | { | |
92f5a8d4 | 623 | calculate_dist(a1v, a2v, plane1, b2v, dist_a1_ip); // for consistency |
b32b8144 FG |
624 | dist_b1_ip = dist_b1_b2; |
625 | //i1 = b2v; | |
626 | ip_flag = ipi_at_b2; | |
627 | return true; | |
628 | } | |
629 | } | |
630 | ||
631 | if (is_on_b) | |
632 | { | |
633 | if (is_near_a1 && sides.template get<0, 0>() == 0) // a1 wrt b | |
634 | { | |
635 | dist_a1_ip = 0; | |
92f5a8d4 | 636 | calculate_dist(b1v, b2v, plane2, a1v, dist_b1_ip); // for consistency |
b32b8144 FG |
637 | //i1 = a1v; |
638 | ip_flag = ipi_at_a1; | |
639 | return true; | |
640 | } | |
641 | ||
642 | if (is_near_a2 && sides.template get<0, 1>() == 0) // a2 wrt b | |
643 | { | |
644 | dist_a1_ip = dist_a1_a2; | |
92f5a8d4 | 645 | calculate_dist(b1v, b2v, plane2, a2v, dist_b1_ip); // for consistency |
b32b8144 FG |
646 | //i1 = a2v; |
647 | ip_flag = ipi_at_a2; | |
648 | return true; | |
649 | } | |
650 | } | |
651 | ||
652 | ip_flag = ipi_inters; | |
653 | ||
654 | return is_on_a && is_on_b; | |
655 | } | |
656 | ||
657 | template <typename Vec3d, typename Plane, typename CalcT> | |
658 | static inline void calculate_dist(Vec3d const& a1v, // in | |
659 | Vec3d const& a2v, // in | |
660 | Plane const& plane1, // in | |
661 | CalcT& dist_a1_a2) // out | |
662 | { | |
663 | static CalcT const c1 = 1; | |
664 | CalcT const cos_a1_a2 = plane1.cos_angle_between(a1v, a2v); | |
665 | dist_a1_a2 = -cos_a1_a2 + c1; // [1, -1] -> [0, 2] representing [0, pi] | |
666 | } | |
667 | ||
668 | template <typename Vec3d, typename Plane, typename CalcT> | |
669 | static inline void calculate_dist(Vec3d const& a1v, // in | |
670 | Vec3d const& /*a2v*/, // in | |
671 | Plane const& plane1, // in | |
672 | Vec3d const& i1, // in | |
673 | CalcT& dist_a1_i1) // out | |
674 | { | |
675 | static CalcT const c1 = 1; | |
676 | static CalcT const c2 = 2; | |
677 | static CalcT const c4 = 4; | |
678 | ||
679 | bool is_forward = true; | |
680 | CalcT cos_a1_i1 = plane1.cos_angle_between(a1v, i1, is_forward); | |
681 | dist_a1_i1 = -cos_a1_i1 + c1; // [0, 2] representing [0, pi] | |
682 | if (! is_forward) // left or right of a1 on a | |
683 | { | |
684 | dist_a1_i1 = -dist_a1_i1; // [0, 2] -> [0, -2] representing [0, -pi] | |
685 | } | |
686 | if (dist_a1_i1 <= -c2) // <= -pi | |
687 | { | |
688 | dist_a1_i1 += c4; // += 2pi | |
689 | } | |
690 | } | |
691 | /* | |
692 | template <typename Vec3d, typename Plane, typename CalcT> | |
693 | static inline void calculate_dists(Vec3d const& a1v, // in | |
694 | Vec3d const& a2v, // in | |
695 | Plane const& plane1, // in | |
696 | Vec3d const& i1, // in | |
697 | CalcT& dist_a1_a2, // out | |
698 | CalcT& dist_a1_i1) // out | |
699 | { | |
700 | calculate_dist(a1v, a2v, plane1, dist_a1_a2); | |
701 | calculate_dist(a1v, a2v, plane1, i1, dist_a1_i1); | |
702 | } | |
703 | */ | |
704 | // the dist of the ip on the other side of the sphere | |
705 | template <typename CalcT> | |
706 | static inline CalcT dist_of_i2(CalcT const& dist_a1_i1) | |
707 | { | |
708 | CalcT const c2 = 2; | |
709 | CalcT const c4 = 4; | |
710 | ||
711 | CalcT dist_a1_i2 = dist_a1_i1 - c2; // dist_a1_i2 = dist_a1_i1 - pi; | |
712 | if (dist_a1_i2 <= -c2) // <= -pi | |
713 | { | |
714 | dist_a1_i2 += c4; // += 2pi; | |
715 | } | |
716 | return dist_a1_i2; | |
717 | } | |
718 | ||
719 | template <typename CalcT> | |
720 | static inline CalcT abs_distance(CalcT const& dist_a1_a2, CalcT const& dist_a1_i1) | |
721 | { | |
722 | if (dist_a1_i1 < CalcT(0)) | |
723 | return -dist_a1_i1; | |
724 | else if (dist_a1_i1 > dist_a1_a2) | |
725 | return dist_a1_i1 - dist_a1_a2; | |
726 | else | |
727 | return CalcT(0); | |
728 | } | |
729 | ||
730 | template <typename CalcT> | |
731 | static inline bool is_potentially_crossing(CalcT const& dist_a1_a2, CalcT const& dist_a1_i1, // in | |
732 | bool& is_on_a, bool& is_near_a1, bool& is_near_a2) // out | |
733 | { | |
734 | is_on_a = segment_ratio<CalcT>(dist_a1_i1, dist_a1_a2).on_segment(); | |
735 | is_near_a1 = is_near(dist_a1_i1); | |
736 | is_near_a2 = is_near(dist_a1_a2 - dist_a1_i1); | |
737 | return is_on_a || is_near_a1 || is_near_a2; | |
738 | } | |
739 | ||
740 | template <typename CalcT, typename P1, typename P2> | |
741 | static inline bool is_endpoint_equal(CalcT const& dist, | |
92f5a8d4 | 742 | P1 const& ai, P2 const& b1) |
b32b8144 FG |
743 | { |
744 | static CalcT const c0 = 0; | |
92f5a8d4 | 745 | return is_near(dist) && (math::equals(dist, c0) || equals_point_point(ai, b1)); |
b32b8144 FG |
746 | } |
747 | ||
748 | template <typename CalcT> | |
749 | static inline bool is_near(CalcT const& dist) | |
750 | { | |
20effc67 | 751 | CalcT const small_number = CalcT(std::is_same<CalcT, float>::value ? 0.0001 : 0.00000001); |
b32b8144 FG |
752 | return math::abs(dist) <= small_number; |
753 | } | |
754 | ||
755 | template <typename ProjCoord1, typename ProjCoord2> | |
756 | static inline int position_value(ProjCoord1 const& ca1, | |
757 | ProjCoord2 const& cb1, | |
758 | ProjCoord2 const& cb2) | |
759 | { | |
760 | // S1x 0 1 2 3 4 | |
761 | // S2 |----------> | |
762 | return math::equals(ca1, cb1) ? 1 | |
763 | : math::equals(ca1, cb2) ? 3 | |
764 | : cb1 < cb2 ? | |
765 | ( ca1 < cb1 ? 0 | |
766 | : ca1 > cb2 ? 4 | |
767 | : 2 ) | |
768 | : ( ca1 > cb1 ? 0 | |
769 | : ca1 < cb2 ? 4 | |
770 | : 2 ); | |
771 | } | |
92f5a8d4 TL |
772 | |
773 | template <typename Point1, typename Point2> | |
774 | static inline bool equals_point_point(Point1 const& point1, Point2 const& point2) | |
775 | { | |
1e59de90 | 776 | return strategy::within::spherical_point_point::apply(point1, point2); |
92f5a8d4 | 777 | } |
b32b8144 FG |
778 | }; |
779 | ||
780 | struct spherical_segments_calc_policy | |
781 | { | |
782 | template <typename Point, typename Point3d> | |
783 | static Point from_cart3d(Point3d const& point_3d) | |
784 | { | |
785 | return formula::cart3d_to_sph<Point>(point_3d); | |
786 | } | |
787 | ||
788 | template <typename Point3d, typename Point> | |
789 | static Point3d to_cart3d(Point const& point) | |
790 | { | |
791 | return formula::sph_to_cart3d<Point3d>(point); | |
792 | } | |
793 | ||
794 | template <typename Point3d> | |
795 | struct plane | |
796 | { | |
797 | typedef typename coordinate_type<Point3d>::type coord_t; | |
798 | ||
799 | // not normalized | |
800 | plane(Point3d const& p1, Point3d const& p2) | |
801 | : normal(cross_product(p1, p2)) | |
802 | {} | |
803 | ||
804 | int side_value(Point3d const& pt) const | |
805 | { | |
806 | return formula::sph_side_value(normal, pt); | |
807 | } | |
808 | ||
809 | static coord_t cos_angle_between(Point3d const& p1, Point3d const& p2) | |
810 | { | |
811 | return dot_product(p1, p2); | |
812 | } | |
813 | ||
814 | coord_t cos_angle_between(Point3d const& p1, Point3d const& p2, bool & is_forward) const | |
815 | { | |
816 | coord_t const c0 = 0; | |
817 | is_forward = dot_product(normal, cross_product(p1, p2)) >= c0; | |
818 | return dot_product(p1, p2); | |
819 | } | |
820 | ||
821 | Point3d normal; | |
822 | }; | |
823 | ||
824 | template <typename Point3d> | |
825 | static plane<Point3d> get_plane(Point3d const& p1, Point3d const& p2) | |
826 | { | |
827 | return plane<Point3d>(p1, p2); | |
828 | } | |
829 | ||
830 | template <typename Point3d> | |
831 | static bool intersection_points(plane<Point3d> const& plane1, | |
832 | plane<Point3d> const& plane2, | |
833 | Point3d & ip1, Point3d & ip2) | |
834 | { | |
835 | typedef typename coordinate_type<Point3d>::type coord_t; | |
836 | ||
837 | ip1 = cross_product(plane1.normal, plane2.normal); | |
838 | // NOTE: the length should be greater than 0 at this point | |
839 | // if the normals were not normalized and their dot product | |
840 | // not checked before this function is called the length | |
841 | // should be checked here (math::equals(len, c0)) | |
842 | coord_t const len = math::sqrt(dot_product(ip1, ip1)); | |
1e59de90 TL |
843 | geometry::detail::for_each_dimension<Point3d>([&](auto index) |
844 | { | |
845 | coord_t const coord = get<index>(ip1) / len; // normalize | |
846 | set<index>(ip1, coord); | |
847 | set<index>(ip2, -coord); | |
848 | }); | |
b32b8144 FG |
849 | |
850 | return true; | |
92f5a8d4 | 851 | } |
b32b8144 FG |
852 | }; |
853 | ||
854 | ||
855 | template | |
856 | < | |
857 | typename CalculationType = void | |
858 | > | |
859 | struct spherical_segments | |
860 | : ecef_segments | |
861 | < | |
862 | spherical_segments_calc_policy, | |
863 | CalculationType | |
864 | > | |
865 | {}; | |
866 | ||
867 | ||
868 | #ifndef DOXYGEN_NO_STRATEGY_SPECIALIZATIONS | |
869 | namespace services | |
870 | { | |
871 | ||
872 | /*template <typename CalculationType> | |
873 | struct default_strategy<spherical_polar_tag, CalculationType> | |
874 | { | |
875 | typedef spherical_segments<CalculationType> type; | |
876 | };*/ | |
877 | ||
878 | template <typename CalculationType> | |
879 | struct default_strategy<spherical_equatorial_tag, CalculationType> | |
880 | { | |
881 | typedef spherical_segments<CalculationType> type; | |
882 | }; | |
883 | ||
884 | template <typename CalculationType> | |
885 | struct default_strategy<geographic_tag, CalculationType> | |
886 | { | |
887 | // NOTE: Spherical strategy returns the same result as the geographic one | |
888 | // representing segments as great elliptic arcs. If the elliptic arcs are | |
889 | // not great elliptic arcs (the origin not in the center of the coordinate | |
890 | // system) then there may be problems with consistency of the side and | |
891 | // intersection strategies. | |
892 | typedef spherical_segments<CalculationType> type; | |
893 | }; | |
894 | ||
895 | } // namespace services | |
896 | #endif // DOXYGEN_NO_STRATEGY_SPECIALIZATIONS | |
897 | ||
898 | ||
899 | }} // namespace strategy::intersection | |
900 | ||
901 | ||
902 | namespace strategy | |
903 | { | |
904 | ||
905 | namespace within { namespace services | |
906 | { | |
907 | ||
908 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
909 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, linear_tag, spherical_tag, spherical_tag> | |
910 | { | |
911 | typedef strategy::intersection::spherical_segments<> type; | |
912 | }; | |
913 | ||
914 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
915 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, polygonal_tag, spherical_tag, spherical_tag> | |
916 | { | |
917 | typedef strategy::intersection::spherical_segments<> type; | |
918 | }; | |
919 | ||
920 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
921 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, linear_tag, spherical_tag, spherical_tag> | |
922 | { | |
923 | typedef strategy::intersection::spherical_segments<> type; | |
924 | }; | |
925 | ||
926 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
927 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, polygonal_tag, spherical_tag, spherical_tag> | |
928 | { | |
929 | typedef strategy::intersection::spherical_segments<> type; | |
930 | }; | |
931 | ||
932 | }} // within::services | |
933 | ||
934 | namespace covered_by { namespace services | |
935 | { | |
936 | ||
937 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
938 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, linear_tag, spherical_tag, spherical_tag> | |
939 | { | |
940 | typedef strategy::intersection::spherical_segments<> type; | |
941 | }; | |
942 | ||
943 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
944 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, polygonal_tag, spherical_tag, spherical_tag> | |
945 | { | |
946 | typedef strategy::intersection::spherical_segments<> type; | |
947 | }; | |
948 | ||
949 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
950 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, linear_tag, spherical_tag, spherical_tag> | |
951 | { | |
952 | typedef strategy::intersection::spherical_segments<> type; | |
953 | }; | |
954 | ||
955 | template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2> | |
956 | struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, polygonal_tag, spherical_tag, spherical_tag> | |
957 | { | |
958 | typedef strategy::intersection::spherical_segments<> type; | |
959 | }; | |
960 | ||
961 | }} // within::services | |
962 | ||
963 | } // strategy | |
964 | ||
965 | ||
966 | }} // namespace boost::geometry | |
967 | ||
968 | ||
969 | #endif // BOOST_GEOMETRY_STRATEGIES_SPHERICAL_INTERSECTION_HPP |