1 // Boost.Geometry (aka GGL, Generic Geometry Library)
2 
3 // Copyright (c) 2007-2014 Barend Gehrels, Amsterdam, the Netherlands.
4 // Copyright (c) 2013-2014 Adam Wulkiewicz, Lodz, Poland.
5 
6 // This file was modified by Oracle on 2014, 2016, 2017.
7 // Modifications copyright (c) 2014-2017, Oracle and/or its affiliates.
8 
9 // Contributed and/or modified by Menelaos Karavelas, on behalf of Oracle
10 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
11 
12 // Use, modification and distribution is subject to the Boost Software License,
13 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
14 // http://www.boost.org/LICENSE_1_0.txt)
15 
16 #ifndef BOOST_GEOMETRY_STRATEGIES_CARTESIAN_INTERSECTION_HPP
17 #define BOOST_GEOMETRY_STRATEGIES_CARTESIAN_INTERSECTION_HPP
18 
19 #include <algorithm>
20 
21 #include <boost/geometry/core/exception.hpp>
22 
23 #include <boost/geometry/geometries/concepts/point_concept.hpp>
24 #include <boost/geometry/geometries/concepts/segment_concept.hpp>
25 
26 #include <boost/geometry/arithmetic/determinant.hpp>
27 #include <boost/geometry/algorithms/detail/assign_values.hpp>
28 #include <boost/geometry/algorithms/detail/assign_indexed_point.hpp>
29 #include <boost/geometry/algorithms/detail/equals/point_point.hpp>
30 #include <boost/geometry/algorithms/detail/recalculate.hpp>
31 
32 #include <boost/geometry/util/math.hpp>
33 #include <boost/geometry/util/promote_integral.hpp>
34 #include <boost/geometry/util/select_calculation_type.hpp>
35 
36 #include <boost/geometry/strategies/agnostic/point_in_poly_winding.hpp>
37 #include <boost/geometry/strategies/cartesian/area_surveyor.hpp>
38 #include <boost/geometry/strategies/cartesian/distance_pythagoras.hpp>
39 #include <boost/geometry/strategies/cartesian/envelope_segment.hpp>
40 #include <boost/geometry/strategies/cartesian/side_by_triangle.hpp>
41 #include <boost/geometry/strategies/covered_by.hpp>
42 #include <boost/geometry/strategies/intersection.hpp>
43 #include <boost/geometry/strategies/intersection_result.hpp>
44 #include <boost/geometry/strategies/side.hpp>
45 #include <boost/geometry/strategies/side_info.hpp>
46 #include <boost/geometry/strategies/within.hpp>
47 
48 #include <boost/geometry/policies/robustness/robust_point_type.hpp>
49 #include <boost/geometry/policies/robustness/segment_ratio_type.hpp>
50 
51 
52 #if defined(BOOST_GEOMETRY_DEBUG_ROBUSTNESS)
53 #  include <boost/geometry/io/wkt/write.hpp>
54 #endif
55 
56 
57 namespace boost { namespace geometry
58 {
59 
60 
61 namespace strategy { namespace intersection
62 {
63 
64 
65 /*!
66     \see http://mathworld.wolfram.com/Line-LineIntersection.html
67  */
68 template
69 <
70     typename CalculationType = void
71 >
72 struct cartesian_segments
73 {
74     typedef side::side_by_triangle<CalculationType> side_strategy_type;
75 
get_side_strategyboost::geometry::strategy::intersection::cartesian_segments76     static inline side_strategy_type get_side_strategy()
77     {
78         return side_strategy_type();
79     }
80 
81     template <typename Geometry1, typename Geometry2>
82     struct point_in_geometry_strategy
83     {
84         typedef strategy::within::winding
85             <
86                 typename point_type<Geometry1>::type,
87                 typename point_type<Geometry2>::type,
88                 side_strategy_type,
89                 CalculationType
90             > type;
91     };
92 
93     template <typename Geometry1, typename Geometry2>
94     static inline typename point_in_geometry_strategy<Geometry1, Geometry2>::type
get_point_in_geometry_strategyboost::geometry::strategy::intersection::cartesian_segments95         get_point_in_geometry_strategy()
96     {
97         typedef typename point_in_geometry_strategy
98             <
99                 Geometry1, Geometry2
100             >::type strategy_type;
101         return strategy_type();
102     }
103 
104     template <typename Geometry>
105     struct area_strategy
106     {
107         typedef area::surveyor
108             <
109                 typename point_type<Geometry>::type,
110                 CalculationType
111             > type;
112     };
113 
114     template <typename Geometry>
get_area_strategyboost::geometry::strategy::intersection::cartesian_segments115     static inline typename area_strategy<Geometry>::type get_area_strategy()
116     {
117         typedef typename area_strategy<Geometry>::type strategy_type;
118         return strategy_type();
119     }
120 
121     template <typename Geometry>
122     struct distance_strategy
123     {
124         typedef distance::pythagoras
125             <
126                 CalculationType
127             > type;
128     };
129 
130     template <typename Geometry>
get_distance_strategyboost::geometry::strategy::intersection::cartesian_segments131     static inline typename distance_strategy<Geometry>::type get_distance_strategy()
132     {
133         typedef typename distance_strategy<Geometry>::type strategy_type;
134         return strategy_type();
135     }
136 
137     typedef envelope::cartesian_segment<CalculationType>
138         envelope_strategy_type;
139 
get_envelope_strategyboost::geometry::strategy::intersection::cartesian_segments140     static inline envelope_strategy_type get_envelope_strategy()
141     {
142         return envelope_strategy_type();
143     }
144 
145     template <typename CoordinateType, typename SegmentRatio>
146     struct segment_intersection_info
147     {
148         typedef typename select_most_precise
149             <
150                 CoordinateType, double
151             >::type promoted_type;
152 
comparable_length_aboost::geometry::strategy::intersection::cartesian_segments::segment_intersection_info153         promoted_type comparable_length_a() const
154         {
155             return dx_a * dx_a + dy_a * dy_a;
156         }
157 
comparable_length_bboost::geometry::strategy::intersection::cartesian_segments::segment_intersection_info158         promoted_type comparable_length_b() const
159         {
160             return dx_b * dx_b + dy_b * dy_b;
161         }
162 
163         template <typename Point, typename Segment1, typename Segment2>
assign_aboost::geometry::strategy::intersection::cartesian_segments::segment_intersection_info164         void assign_a(Point& point, Segment1 const& a, Segment2 const& ) const
165         {
166             assign(point, a, dx_a, dy_a, robust_ra);
167         }
168         template <typename Point, typename Segment1, typename Segment2>
assign_bboost::geometry::strategy::intersection::cartesian_segments::segment_intersection_info169         void assign_b(Point& point, Segment1 const& , Segment2 const& b) const
170         {
171             assign(point, b, dx_b, dy_b, robust_rb);
172         }
173 
174         template <typename Point, typename Segment>
assignboost::geometry::strategy::intersection::cartesian_segments::segment_intersection_info175         void assign(Point& point, Segment const& segment, CoordinateType const& dx, CoordinateType const& dy, SegmentRatio const& ratio) const
176         {
177             // Calculate the intersection point based on segment_ratio
178             // Up to now, division was postponed. Here we divide using numerator/
179             // denominator. In case of integer this results in an integer
180             // division.
181             BOOST_GEOMETRY_ASSERT(ratio.denominator() != 0);
182 
183             typedef typename promote_integral<CoordinateType>::type promoted_type;
184 
185             promoted_type const numerator
186                 = boost::numeric_cast<promoted_type>(ratio.numerator());
187             promoted_type const denominator
188                 = boost::numeric_cast<promoted_type>(ratio.denominator());
189             promoted_type const dx_promoted = boost::numeric_cast<promoted_type>(dx);
190             promoted_type const dy_promoted = boost::numeric_cast<promoted_type>(dy);
191 
192             set<0>(point, get<0, 0>(segment) + boost::numeric_cast
193                 <
194                     CoordinateType
195                 >(numerator * dx_promoted / denominator));
196             set<1>(point, get<0, 1>(segment) + boost::numeric_cast
197                 <
198                     CoordinateType
199                 >(numerator * dy_promoted / denominator));
200         }
201 
202         CoordinateType dx_a, dy_a;
203         CoordinateType dx_b, dy_b;
204         SegmentRatio robust_ra;
205         SegmentRatio robust_rb;
206     };
207 
208     template <typename D, typename W, typename ResultType>
cramers_ruleboost::geometry::strategy::intersection::cartesian_segments209     static inline void cramers_rule(D const& dx_a, D const& dy_a,
210         D const& dx_b, D const& dy_b, W const& wx, W const& wy,
211         // out:
212         ResultType& d, ResultType& da)
213     {
214         // Cramers rule
215         d = geometry::detail::determinant<ResultType>(dx_a, dy_a, dx_b, dy_b);
216         da = geometry::detail::determinant<ResultType>(dx_b, dy_b, wx, wy);
217         // Ratio is da/d , collinear if d == 0, intersecting if 0 <= r <= 1
218         // IntersectionPoint = (x1 + r * dx_a, y1 + r * dy_a)
219     }
220 
221 
222     // Relate segments a and b
223     template
224     <
225         typename Segment1,
226         typename Segment2,
227         typename Policy,
228         typename RobustPolicy
229     >
230     static inline typename Policy::return_type
applyboost::geometry::strategy::intersection::cartesian_segments231         apply(Segment1 const& a, Segment2 const& b,
232               Policy const& policy, RobustPolicy const& robust_policy)
233     {
234         // type them all as in Segment1 - TODO reconsider this, most precise?
235         typedef typename geometry::point_type<Segment1>::type point_type;
236 
237         typedef typename geometry::robust_point_type
238             <
239                 point_type, RobustPolicy
240             >::type robust_point_type;
241 
242         point_type a0, a1, b0, b1;
243         robust_point_type a0_rob, a1_rob, b0_rob, b1_rob;
244 
245         detail::assign_point_from_index<0>(a, a0);
246         detail::assign_point_from_index<1>(a, a1);
247         detail::assign_point_from_index<0>(b, b0);
248         detail::assign_point_from_index<1>(b, b1);
249 
250         geometry::recalculate(a0_rob, a0, robust_policy);
251         geometry::recalculate(a1_rob, a1, robust_policy);
252         geometry::recalculate(b0_rob, b0, robust_policy);
253         geometry::recalculate(b1_rob, b1, robust_policy);
254 
255         return apply(a, b, policy, robust_policy, a0_rob, a1_rob, b0_rob, b1_rob);
256     }
257 
258     // The main entry-routine, calculating intersections of segments a / b
259     // NOTE: Robust* types may be the same as Segments' point types
260     template
261     <
262         typename Segment1,
263         typename Segment2,
264         typename Policy,
265         typename RobustPolicy,
266         typename RobustPoint1,
267         typename RobustPoint2
268     >
269     static inline typename Policy::return_type
applyboost::geometry::strategy::intersection::cartesian_segments270         apply(Segment1 const& a, Segment2 const& b,
271               Policy const&, RobustPolicy const& /*robust_policy*/,
272               RobustPoint1 const& robust_a1, RobustPoint1 const& robust_a2,
273               RobustPoint2 const& robust_b1, RobustPoint2 const& robust_b2)
274     {
275         BOOST_CONCEPT_ASSERT( (concepts::ConstSegment<Segment1>) );
276         BOOST_CONCEPT_ASSERT( (concepts::ConstSegment<Segment2>) );
277 
278         using geometry::detail::equals::equals_point_point;
279         bool const a_is_point = equals_point_point(robust_a1, robust_a2);
280         bool const b_is_point = equals_point_point(robust_b1, robust_b2);
281 
282         if(a_is_point && b_is_point)
283         {
284             return equals_point_point(robust_a1, robust_b2)
285                 ? Policy::degenerate(a, true)
286                 : Policy::disjoint()
287                 ;
288         }
289 
290         side_info sides;
291         sides.set<0>(side_strategy_type::apply(robust_b1, robust_b2, robust_a1),
292                      side_strategy_type::apply(robust_b1, robust_b2, robust_a2));
293 
294         if (sides.same<0>())
295         {
296             // Both points are at same side of other segment, we can leave
297             return Policy::disjoint();
298         }
299 
300         sides.set<1>(side_strategy_type::apply(robust_a1, robust_a2, robust_b1),
301                      side_strategy_type::apply(robust_a1, robust_a2, robust_b2));
302 
303         if (sides.same<1>())
304         {
305             // Both points are at same side of other segment, we can leave
306             return Policy::disjoint();
307         }
308 
309         bool collinear = sides.collinear();
310 
311         typedef typename select_most_precise
312             <
313                 typename geometry::coordinate_type<RobustPoint1>::type,
314                 typename geometry::coordinate_type<RobustPoint2>::type
315             >::type robust_coordinate_type;
316 
317         typedef typename segment_ratio_type
318             <
319                 typename geometry::point_type<Segment1>::type, // TODO: most precise point?
320                 RobustPolicy
321             >::type ratio_type;
322 
323         segment_intersection_info
324             <
325                 typename select_calculation_type<Segment1, Segment2, CalculationType>::type,
326                 ratio_type
327             > sinfo;
328 
329         sinfo.dx_a = get<1, 0>(a) - get<0, 0>(a); // distance in x-dir
330         sinfo.dx_b = get<1, 0>(b) - get<0, 0>(b);
331         sinfo.dy_a = get<1, 1>(a) - get<0, 1>(a); // distance in y-dir
332         sinfo.dy_b = get<1, 1>(b) - get<0, 1>(b);
333 
334         robust_coordinate_type const robust_dx_a = get<0>(robust_a2) - get<0>(robust_a1);
335         robust_coordinate_type const robust_dx_b = get<0>(robust_b2) - get<0>(robust_b1);
336         robust_coordinate_type const robust_dy_a = get<1>(robust_a2) - get<1>(robust_a1);
337         robust_coordinate_type const robust_dy_b = get<1>(robust_b2) - get<1>(robust_b1);
338 
339         // r: ratio 0-1 where intersection divides A/B
340         // (only calculated for non-collinear segments)
341         if (! collinear)
342         {
343             robust_coordinate_type robust_da0, robust_da;
344             robust_coordinate_type robust_db0, robust_db;
345 
346             cramers_rule(robust_dx_a, robust_dy_a, robust_dx_b, robust_dy_b,
347                 get<0>(robust_a1) - get<0>(robust_b1),
348                 get<1>(robust_a1) - get<1>(robust_b1),
349                 robust_da0, robust_da);
350 
351             cramers_rule(robust_dx_b, robust_dy_b, robust_dx_a, robust_dy_a,
352                 get<0>(robust_b1) - get<0>(robust_a1),
353                 get<1>(robust_b1) - get<1>(robust_a1),
354                 robust_db0, robust_db);
355 
356             math::detail::equals_factor_policy<robust_coordinate_type>
357                 policy(robust_dx_a, robust_dy_a, robust_dx_b, robust_dy_b);
358             robust_coordinate_type const zero = 0;
359             if (math::detail::equals_by_policy(robust_da0, zero, policy)
360              || math::detail::equals_by_policy(robust_db0, zero, policy))
361             {
362                 // If this is the case, no rescaling is done for FP precision.
363                 // We set it to collinear, but it indicates a robustness issue.
364                 sides.set<0>(0,0);
365                 sides.set<1>(0,0);
366                 collinear = true;
367             }
368             else
369             {
370                 sinfo.robust_ra.assign(robust_da, robust_da0);
371                 sinfo.robust_rb.assign(robust_db, robust_db0);
372             }
373         }
374 
375         if (collinear)
376         {
377             std::pair<bool, bool> const collinear_use_first
378                     = is_x_more_significant(geometry::math::abs(robust_dx_a),
379                                             geometry::math::abs(robust_dy_a),
380                                             geometry::math::abs(robust_dx_b),
381                                             geometry::math::abs(robust_dy_b),
382                                             a_is_point, b_is_point);
383 
384             if (collinear_use_first.second)
385             {
386                 // Degenerate cases: segments of single point, lying on other segment, are not disjoint
387                 // This situation is collinear too
388 
389                 if (collinear_use_first.first)
390                 {
391                     return relate_collinear<0, Policy, ratio_type>(a, b,
392                             robust_a1, robust_a2, robust_b1, robust_b2,
393                             a_is_point, b_is_point);
394                 }
395                 else
396                 {
397                     // Y direction contains larger segments (maybe dx is zero)
398                     return relate_collinear<1, Policy, ratio_type>(a, b,
399                             robust_a1, robust_a2, robust_b1, robust_b2,
400                             a_is_point, b_is_point);
401                 }
402             }
403         }
404 
405         return Policy::segments_crosses(sides, sinfo, a, b);
406     }
407 
408 private:
409     // first is true if x is more significant
410     // second is true if the more significant difference is not 0
411     template <typename RobustCoordinateType>
412     static inline std::pair<bool, bool>
is_x_more_significantboost::geometry::strategy::intersection::cartesian_segments413         is_x_more_significant(RobustCoordinateType const& abs_robust_dx_a,
414                               RobustCoordinateType const& abs_robust_dy_a,
415                               RobustCoordinateType const& abs_robust_dx_b,
416                               RobustCoordinateType const& abs_robust_dy_b,
417                               bool const a_is_point,
418                               bool const b_is_point)
419     {
420         //BOOST_GEOMETRY_ASSERT_MSG(!(a_is_point && b_is_point), "both segments shouldn't be degenerated");
421 
422         // for degenerated segments the second is always true because this function
423         // shouldn't be called if both segments were degenerated
424 
425         if (a_is_point)
426         {
427             return std::make_pair(abs_robust_dx_b >= abs_robust_dy_b, true);
428         }
429         else if (b_is_point)
430         {
431             return std::make_pair(abs_robust_dx_a >= abs_robust_dy_a, true);
432         }
433         else
434         {
435             RobustCoordinateType const min_dx = (std::min)(abs_robust_dx_a, abs_robust_dx_b);
436             RobustCoordinateType const min_dy = (std::min)(abs_robust_dy_a, abs_robust_dy_b);
437             return min_dx == min_dy ?
438                     std::make_pair(true, min_dx > RobustCoordinateType(0)) :
439                     std::make_pair(min_dx > min_dy, true);
440         }
441     }
442 
443     template
444     <
445         std::size_t Dimension,
446         typename Policy,
447         typename RatioType,
448         typename Segment1,
449         typename Segment2,
450         typename RobustPoint1,
451         typename RobustPoint2
452     >
453     static inline typename Policy::return_type
relate_collinearboost::geometry::strategy::intersection::cartesian_segments454         relate_collinear(Segment1 const& a,
455                          Segment2 const& b,
456                          RobustPoint1 const& robust_a1, RobustPoint1 const& robust_a2,
457                          RobustPoint2 const& robust_b1, RobustPoint2 const& robust_b2,
458                          bool a_is_point, bool b_is_point)
459     {
460         if (a_is_point)
461         {
462             return relate_one_degenerate<Policy, RatioType>(a,
463                 get<Dimension>(robust_a1),
464                 get<Dimension>(robust_b1), get<Dimension>(robust_b2),
465                 true);
466         }
467         if (b_is_point)
468         {
469             return relate_one_degenerate<Policy, RatioType>(b,
470                 get<Dimension>(robust_b1),
471                 get<Dimension>(robust_a1), get<Dimension>(robust_a2),
472                 false);
473         }
474         return relate_collinear<Policy, RatioType>(a, b,
475                                 get<Dimension>(robust_a1),
476                                 get<Dimension>(robust_a2),
477                                 get<Dimension>(robust_b1),
478                                 get<Dimension>(robust_b2));
479     }
480 
481     /// Relate segments known collinear
482     template
483     <
484         typename Policy,
485         typename RatioType,
486         typename Segment1,
487         typename Segment2,
488         typename RobustType1,
489         typename RobustType2
490     >
491     static inline typename Policy::return_type
relate_collinearboost::geometry::strategy::intersection::cartesian_segments492         relate_collinear(Segment1 const& a, Segment2 const& b,
493                          RobustType1 oa_1, RobustType1 oa_2,
494                          RobustType2 ob_1, RobustType2 ob_2)
495     {
496         // Calculate the ratios where a starts in b, b starts in a
497         //         a1--------->a2         (2..7)
498         //                b1----->b2      (5..8)
499         // length_a: 7-2=5
500         // length_b: 8-5=3
501         // b1 is located w.r.t. a at ratio: (5-2)/5=3/5 (on a)
502         // b2 is located w.r.t. a at ratio: (8-2)/5=6/5 (right of a)
503         // a1 is located w.r.t. b at ratio: (2-5)/3=-3/3 (left of b)
504         // a2 is located w.r.t. b at ratio: (7-5)/3=2/3 (on b)
505         // A arrives (a2 on b), B departs (b1 on a)
506 
507         // If both are reversed:
508         //         a2<---------a1         (7..2)
509         //                b2<-----b1      (8..5)
510         // length_a: 2-7=-5
511         // length_b: 5-8=-3
512         // b1 is located w.r.t. a at ratio: (8-7)/-5=-1/5 (before a starts)
513         // b2 is located w.r.t. a at ratio: (5-7)/-5=2/5 (on a)
514         // a1 is located w.r.t. b at ratio: (7-8)/-3=1/3 (on b)
515         // a2 is located w.r.t. b at ratio: (2-8)/-3=6/3 (after b ends)
516 
517         // If both one is reversed:
518         //         a1--------->a2         (2..7)
519         //                b2<-----b1      (8..5)
520         // length_a: 7-2=+5
521         // length_b: 5-8=-3
522         // b1 is located w.r.t. a at ratio: (8-2)/5=6/5 (after a ends)
523         // b2 is located w.r.t. a at ratio: (5-2)/5=3/5 (on a)
524         // a1 is located w.r.t. b at ratio: (2-8)/-3=6/3 (after b ends)
525         // a2 is located w.r.t. b at ratio: (7-8)/-3=1/3 (on b)
526         RobustType1 const length_a = oa_2 - oa_1; // no abs, see above
527         RobustType2 const length_b = ob_2 - ob_1;
528 
529         RatioType ra_from(oa_1 - ob_1, length_b);
530         RatioType ra_to(oa_2 - ob_1, length_b);
531         RatioType rb_from(ob_1 - oa_1, length_a);
532         RatioType rb_to(ob_2 - oa_1, length_a);
533 
534         // use absolute measure to detect endpoints intersection
535         // NOTE: it'd be possible to calculate bx_wrt_a using ax_wrt_b values
536         int const a1_wrt_b = position_value(oa_1, ob_1, ob_2);
537         int const a2_wrt_b = position_value(oa_2, ob_1, ob_2);
538         int const b1_wrt_a = position_value(ob_1, oa_1, oa_2);
539         int const b2_wrt_a = position_value(ob_2, oa_1, oa_2);
540 
541         // fix the ratios if necessary
542         // CONSIDER: fixing ratios also in other cases, if they're inconsistent
543         // e.g. if ratio == 1 or 0 (so IP at the endpoint)
544         // but position value indicates that the IP is in the middle of the segment
545         // because one of the segments is very long
546         // In such case the ratios could be moved into the middle direction
547         // by some small value (e.g. EPS+1ULP)
548         if (a1_wrt_b == 1)
549         {
550             ra_from.assign(0, 1);
551             rb_from.assign(0, 1);
552         }
553         else if (a1_wrt_b == 3)
554         {
555             ra_from.assign(1, 1);
556             rb_to.assign(0, 1);
557         }
558 
559         if (a2_wrt_b == 1)
560         {
561             ra_to.assign(0, 1);
562             rb_from.assign(1, 1);
563         }
564         else if (a2_wrt_b == 3)
565         {
566             ra_to.assign(1, 1);
567             rb_to.assign(1, 1);
568         }
569 
570         if ((a1_wrt_b < 1 && a2_wrt_b < 1) || (a1_wrt_b > 3 && a2_wrt_b > 3))
571         //if ((ra_from.left() && ra_to.left()) || (ra_from.right() && ra_to.right()))
572         {
573             return Policy::disjoint();
574         }
575 
576         bool const opposite = math::sign(length_a) != math::sign(length_b);
577 
578         return Policy::segments_collinear(a, b, opposite,
579                                           a1_wrt_b, a2_wrt_b, b1_wrt_a, b2_wrt_a,
580                                           ra_from, ra_to, rb_from, rb_to);
581     }
582 
583     /// Relate segments where one is degenerate
584     template
585     <
586         typename Policy,
587         typename RatioType,
588         typename DegenerateSegment,
589         typename RobustType1,
590         typename RobustType2
591     >
592     static inline typename Policy::return_type
relate_one_degenerateboost::geometry::strategy::intersection::cartesian_segments593         relate_one_degenerate(DegenerateSegment const& degenerate_segment,
594                               RobustType1 d, RobustType2 s1, RobustType2 s2,
595                               bool a_degenerate)
596     {
597         // Calculate the ratios where ds starts in s
598         //         a1--------->a2         (2..6)
599         //              b1/b2      (4..4)
600         // Ratio: (4-2)/(6-2)
601         RatioType const ratio(d - s1, s2 - s1);
602 
603         if (!ratio.on_segment())
604         {
605             return Policy::disjoint();
606         }
607 
608         return Policy::one_degenerate(degenerate_segment, ratio, a_degenerate);
609     }
610 
611     template <typename ProjCoord1, typename ProjCoord2>
position_valueboost::geometry::strategy::intersection::cartesian_segments612     static inline int position_value(ProjCoord1 const& ca1,
613                                      ProjCoord2 const& cb1,
614                                      ProjCoord2 const& cb2)
615     {
616         // S1x  0   1    2     3   4
617         // S2       |---------->
618         return math::equals(ca1, cb1) ? 1
619              : math::equals(ca1, cb2) ? 3
620              : cb1 < cb2 ?
621                 ( ca1 < cb1 ? 0
622                 : ca1 > cb2 ? 4
623                 : 2 )
624               : ( ca1 > cb1 ? 0
625                 : ca1 < cb2 ? 4
626                 : 2 );
627     }
628 };
629 
630 
631 #ifndef DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
632 namespace services
633 {
634 
635 template <typename CalculationType>
636 struct default_strategy<cartesian_tag, CalculationType>
637 {
638     typedef cartesian_segments<CalculationType> type;
639 };
640 
641 } // namespace services
642 #endif // DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
643 
644 
645 }} // namespace strategy::intersection
646 
647 namespace strategy
648 {
649 
650 namespace within { namespace services
651 {
652 
653 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
654 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, linear_tag, cartesian_tag, cartesian_tag>
655 {
656     typedef strategy::intersection::cartesian_segments<> type;
657 };
658 
659 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
660 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, polygonal_tag, cartesian_tag, cartesian_tag>
661 {
662     typedef strategy::intersection::cartesian_segments<> type;
663 };
664 
665 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
666 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, linear_tag, cartesian_tag, cartesian_tag>
667 {
668     typedef strategy::intersection::cartesian_segments<> type;
669 };
670 
671 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
672 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, polygonal_tag, cartesian_tag, cartesian_tag>
673 {
674     typedef strategy::intersection::cartesian_segments<> type;
675 };
676 
677 }} // within::services
678 
679 namespace covered_by { namespace services
680 {
681 
682 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
683 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, linear_tag, cartesian_tag, cartesian_tag>
684 {
685     typedef strategy::intersection::cartesian_segments<> type;
686 };
687 
688 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
689 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, linear_tag, polygonal_tag, cartesian_tag, cartesian_tag>
690 {
691     typedef strategy::intersection::cartesian_segments<> type;
692 };
693 
694 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
695 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, linear_tag, cartesian_tag, cartesian_tag>
696 {
697     typedef strategy::intersection::cartesian_segments<> type;
698 };
699 
700 template <typename Geometry1, typename Geometry2, typename AnyTag1, typename AnyTag2>
701 struct default_strategy<Geometry1, Geometry2, AnyTag1, AnyTag2, polygonal_tag, polygonal_tag, cartesian_tag, cartesian_tag>
702 {
703     typedef strategy::intersection::cartesian_segments<> type;
704 };
705 
706 }} // within::services
707 
708 } // strategy
709 
710 }} // namespace boost::geometry
711 
712 
713 #endif // BOOST_GEOMETRY_STRATEGIES_CARTESIAN_INTERSECTION_HPP
714