GeographicLib: Intersect.hpp Source File

GeographicLib 2.5.2

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Intersect.hpp
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1/**
2 * \file Intersect.hpp
3 * \brief Header for GeographicLib::Intersect class
4 *
5 * Copyright (c) Charles Karney (2023-2024) <karney@alum.mit.edu> and licensed
6 * under the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
10#if !defined(GEOGRAPHICLIB_INTERSECT_HPP)
11#define GEOGRAPHICLIB_INTERSECT_HPP 1
12
13#include <vector>
14#include <set>
15#include <GeographicLib/Math.hpp>
16#include <GeographicLib/Geodesic.hpp>
17#include <GeographicLib/GeodesicLine.hpp>
18
19namespace GeographicLib {
20
21 /**
22 * \brief %Geodesic intersections
23 *
24 * Find the intersections of two geodesics \e X and \e Y. Four calling
25 * sequences are supported.
26 * - The geodesics are defined by a position (latitude and longitude) and an
27 * azimuth. In this case the \e closest intersection is found.
28 * - The geodesics are defined by two endpoints. The intersection of the two
29 * segments is found. If they don't intersect, then the closest
30 * intersection is returned.
31 * - The geodesics are defined as an intersection point, a single position
32 * and two azimuths. In this case, the next closest intersection is found.
33 * - The geodesics are defined as in the first case and all intersection
34 * within a specified distance are returned.
35 * .
36 * In all cases the position of the intersection is given by the signed
37 * displacements \e x and \e y along the geodesics from the starting point
38 * (the first point in the case of a geodesic segment). The closest
39 * itersection is defined as the one that minimizes the L1 distance,
40 * Intersect::Dist([<i>x</i>, <i>y</i>) = |<i>x</i>| + |<i>y</i>|.
41 *
42 * The routines also optionally return a coincidence indicator \e c. This is
43 * typically 0. However if the geodesics lie on top of one another at the
44 * point of intersection, then \e c is set to +1, if they are parallel, and
45 * &minus;1, if they are antiparallel.
46 *
47 * Example of use:
48 * \include example-Intersect.cpp
49 *
50 * <a href="IntersectTool.1.html">IntersectTool</a> is a command-line utility
51 * providing access to the functionality of this class.
52 *
53 * This solution for intersections is described in
54 * - C. F. F. Karney,<br>
55 * <a href="https://doi.org/10.1061/JSUED2.SUENG-1483">
56 * Geodesic intersections</a>,
57 * J. Surveying Eng. <b>150</b>(3), 04024005:1--9 (2024);
58 * preprint
59 * <a href="https://arxiv.org/abs/2308.00495">arxiv:2308.00495</a>.
60 * .
61 * It is based on the work of
62 * - S. Baseldga and J. C. Martinez-Llario,
63 * <a href="https://doi.org/10.1007/s11200-017-1020-z">
64 * Intersection and point-to-line solutions for geodesics
65 * on the ellipsoid</a>,
66 * Stud. Geophys. Geod. <b>62</b>, 353--363 (2018);
67 * DOI: <a href="https://doi.org/10.1007/s11200-017-1020-z">
68 * 10.1007/s11200-017-1020-z</a>.
69 **********************************************************************/
70
71 class GEOGRAPHICLIB_EXPORT Intersect {
72 private:
73 typedef Math::real real;
74 public:
75 /**
76 * The type used to hold the two displacement along the geodesics. This is
77 * just a std::pair with \e x = \e first and \e y = \e second.
78 **********************************************************************/
79 typedef std::pair<Math::real, Math::real> Point;
80 /**
81 * The minimum capabilities for GeodesicLine objects which are passed to
82 * this class.
83 **********************************************************************/
84 static const unsigned LineCaps = Geodesic::LATITUDE | Geodesic::LONGITUDE |
85 Geodesic::AZIMUTH | Geodesic::REDUCEDLENGTH | Geodesic::GEODESICSCALE |
86 Geodesic::DISTANCE_IN;
87 private:
88 static const int numit_ = 100;
89 const Geodesic _geod;
90 real _a, _f, // equatorial radius, flattening
91 _rR, // authalic radius
92 _d, // pi*_rR
93 _eps, // criterion for intersection + coincidence
94 _tol, // convergence for Newton in Solve1
95 _delta, // for equality tests, safety margin for tiling
96 _t1, // min distance between intersections
97 _t2, // furthest dist to closest intersection
98 _t3, // 1/2 furthest min dist to next intersection
99 _t4, // capture radius for spherical sol in Solve0
100 _t5, // longest shortest geodesic
101 _d1, // tile spacing for Closest
102 _d2, // tile spacing for Next
103 _d3; // tile spacing for All
104 // The L1 distance
105 static Math::real d1(Math::real x, Math::real y)
106 { using std::fabs; return fabs(x) + fabs(y); }
107 // An internal version of Point with a little more functionality
108 class XPoint {
109 public:
110 real x, y;
111 int c;
112 XPoint(Math::real x, Math::real y, int c = 0)
113 : x(x), y(y), c(c)
114 {}
115 XPoint()
116 : x(Math::NaN()), y(Math::NaN()), c(0)
117 {}
118 XPoint(const Point& p)
119 : x(p.first), y(p.second), c(0)
120 {}
121 XPoint& operator+=(const XPoint& p) {
122 x += p.x; y += p.y;
123 if (p.c) c = p.c; // pass along a nonzero c from either operand
124 return *this;
125 }
126 XPoint operator+(const XPoint& p) const {
127 XPoint t = *this; t += p; return t;
128 }
129 Math::real Dist() const { return d1(x, y); }
130 Math::real Dist(const XPoint& p) const { return d1(x - p.x, y - p.y); }
131 Point data() const { return Point(x, y); }
132 };
133 // Comparing XPoints for insertions into sets, but ensure that close
134 // XPoints test equal.
135 class GEOGRAPHICLIB_EXPORT SetComp {
136 private:
137 const real _delta;
138 public:
139 SetComp(Math::real delta) : _delta(delta) {}
140 bool eq(const XPoint& p, const XPoint& q) const {
141 return d1(p.x - q.x, p.y - q.y) <= _delta;
142 }
143 bool operator()(const XPoint& p, const XPoint& q) const {
144 return !eq(p, q) && ( p.x != q.x ? p.x < q.x : p.y < q.y );
145 }
146 };
147 SetComp _comp;
148 // For ranking XPoints by closeness
149 class RankPoint {
150 private:
151 const real _x, _y;
152 public:
153 RankPoint(const Point& p0) : _x(p0.first), _y(p0.second) {}
154 RankPoint(const XPoint& p0) : _x(p0.x), _y(p0.y) {}
155 bool operator()(const XPoint& p, const XPoint& q) const {
156 real dp = d1(p.x - _x, p.y - _y),
157 dq = d1(q.x - _x, q.y - _y);
158 return dp != dq ? (dp < dq) :
159 (p.x != q.x ? (p.x < q.x) : (p.y < q.y));
160 }
161 };
162 // The spherical solution
163 XPoint Spherical(const GeodesicLine& lineX, const GeodesicLine& lineY,
164 const XPoint& p) const;
165 // The basic algorithm
166 XPoint Basic(const GeodesicLine& lineX, const GeodesicLine& lineY,
167 const XPoint& p0) const;
168 // The closest intersecton
169 XPoint ClosestInt(const GeodesicLine& lineX, const GeodesicLine& lineY,
170 const XPoint& p0) const;
171 // The next intersecton
172 XPoint NextInt(const GeodesicLine& lineX, const GeodesicLine& lineY) const;
173 // Segment intersecton
174 XPoint SegmentInt(const GeodesicLine& lineX, const GeodesicLine& lineY,
175 int& segmode) const;
176 // All intersectons
177 std::vector<XPoint>
178 AllInt0(const GeodesicLine& lineX, const GeodesicLine& lineY,
179 Math::real maxdist, const XPoint& p0) const;
180 std::vector<Point>
181 AllInternal(const GeodesicLine& lineX, const GeodesicLine& lineY,
182 Math::real maxdist, const Point& p0,
183 std::vector<int>& c, bool cp) const;
184 // Find {semi-,}conjugate point which is close to s3. Optional m12, M12,
185 // M21 use {semi-,}conjugacy relative to point 2
186 Math::real ConjugateDist(const GeodesicLine& line, Math::real s3, bool semi,
187 Math::real m12 = 0, Math::real M12 = 1,
188 Math::real M21 = 1) const;
189 Math::real distpolar(Math::real lat1, Math::real* lat2 = nullptr) const;
190 Math::real polarb(Math::real* lata = nullptr, Math::real* latb = nullptr)
191 const;
192 Math::real conjdist(Math::real azi, Math::real* ds = nullptr,
193 Math::real* sp = nullptr, Math::real* sm = nullptr)
194 const;
195 Math::real distoblique(Math::real* azi = nullptr, Math::real* sp = nullptr,
196 Math::real* sm = nullptr) const;
197 // p is intersection point on coincident lines orientation = c; p0 is
198 // origin point. Change p to center point wrt p0, i.e, abs((p-p0)_x) =
199 // abs((p-p0)_y)
200 static XPoint fixcoincident(const XPoint& p0, const XPoint& p);
201 static XPoint fixcoincident(const XPoint& p0, const XPoint& p, int c);
202 static XPoint fixsegment(Math::real sx, Math::real sy, const XPoint& p);
203 static int segmentmode(Math::real sx, Math::real sy, const XPoint& p) {
204 return (p.x < 0 ? -1 : p.x <= sx ? 0 : 1) * 3
205 + (p.y < 0 ? -1 : p.y <= sy ? 0 : 1);
206 }
207 mutable long long _cnt0, _cnt1, _cnt2, _cnt3, _cnt4;
208 public:
209 /** \name Constructor
210 **********************************************************************/
211 ///@{
212 /**
213 * Constructor for an ellipsoid with
214 *
215 * @param[in] geod a Geodesic object. This sets the parameters \e a and \e
216 * f for the ellipsoid.
217 * @exception GeographicErr if the eccentricity of the elliposdoid is too
218 * large.
219 *
220 * \note This class has been validated for -1/4 &le; \e f &le; 1/5. It may
221 * give satisfactory results slightly outside this range; however
222 * sufficient far outside the range, some internal checks will fail and an
223 * exception thrown.
224 *
225 * \note If |<i>f</i>| > 1/50, then the Geodesic object should be
226 * constructed with \e exact = true.
227 **********************************************************************/
228 Intersect(const Geodesic& geod);
229 ///@}
230
231 /** \name Finding intersections
232 **********************************************************************/
233 ///@{
234 /**
235 * Find the closest intersection point, with each geodesic specified by
236 * position and azimuth.
237 *
238 * @param[in] latX latitude of starting point for geodesic \e X (degrees).
239 * @param[in] lonX longitude of starting point for geodesic \e X (degrees).
240 * @param[in] aziX azimuth at starting point for geodesic \e X (degrees).
241 * @param[in] latY latitude of starting point for geodesic \e Y (degrees).
242 * @param[in] lonY longitude of starting point for geodesic \e Y (degrees).
243 * @param[in] aziY azimuth at starting point for geodesic \e Y (degrees).
244 * @param[in] p0 an optional offset for the starting points (meters),
245 * default = [0,0].
246 * @param[out] c optional pointer to an integer coincidence indicator.
247 * @return \e p the intersection point closest to \e p0.
248 *
249 * The returned intersection minimizes Intersect::Dist(\e p, \e p0).
250 **********************************************************************/
251 Point Closest(Math::real latX, Math::real lonX, Math::real aziX,
252 Math::real latY, Math::real lonY, Math::real aziY,
253 const Point& p0 = Point(0, 0), int* c = nullptr) const;
254 /**
255 * Find the closest intersection point, with each geodesic given as a
256 * GeodesicLine.
257 *
258 * @param[in] lineX geodesic \e X.
259 * @param[in] lineY geodesic \e Y.
260 * @param[in] p0 an optional offset for the starting points (meters),
261 * default = [0,0].
262 * @param[out] c optional pointer to an integer coincidence indicator.
263 * @return \e p the intersection point closest to \e p0.
264 *
265 * The returned intersection minimizes Intersect::Dist(\e p, \e p0).
266 *
267 * \note \e lineX and \e lineY should be created with minimum capabilities
268 * Intersect::LineCaps. The methods for creating a GeodesicLine include
269 * all these capabilities by default.
270 **********************************************************************/
271 Point Closest(const GeodesicLine& lineX, const GeodesicLine& lineY,
272 const Point& p0 = Point(0, 0), int* c = nullptr) const;
273 /**
274 * Find the intersection of two geodesic segments defined by their
275 * endpoints.
276 *
277 * @param[in] latX1 latitude of first point for segment \e X (degrees).
278 * @param[in] lonX1 longitude of first point for segment \e X (degrees).
279 * @param[in] latX2 latitude of second point for segment \e X (degrees).
280 * @param[in] lonX2 longitude of second point for segment \e X (degrees).
281 * @param[in] latY1 latitude of first point for segment \e Y (degrees).
282 * @param[in] lonY1 longitude of first point for segment \e Y (degrees).
283 * @param[in] latY2 latitude of second point for segment \e Y (degrees).
284 * @param[in] lonY2 longitude of second point for segment \e Y (degrees).
285 * @param[out] segmode an indicator equal to zero if the segments
286 * intersect (see below).
287 * @param[out] c optional pointer to an integer coincidence indicator.
288 * @return \e p the intersection point if the segments intersect, otherwise
289 * the intersection point closest to the midpoints of the two
290 * segments.
291 *
292 * \warning The results are only well defined if there's a \e unique
293 * shortest geodesic between the endpoints of the two segments.
294 *
295 * \e segmode codes up information about the closest intersection in the
296 * case where the segments intersect. Let <i>x</i><sub>12</sub> be the
297 * length of the segment \e X and \e x = <i>p</i>.first, the position of
298 * the intersection on segment \e X. Define
299 * - \e k<sub><i>x</i></sub> = &minus;1, if \e x < 0,
300 * - \e k<sub><i>x</i></sub> = 0,
301 * if 0 &le; \e x &le; <i>x</i><sub>12</sub>,
302 * - \e k<sub><i>x</i></sub> = 1, if <i>x</i><sub>12</sub> < \e x.
303 * .
304 * and similarly for segment \e Y. Then
305 * \e segmode = 3 \e k<sub><i>x</i></sub> + \e k<sub><i>y</i></sub>.
306 **********************************************************************/
307 Point Segment(Math::real latX1, Math::real lonX1,
308 Math::real latX2, Math::real lonX2,
309 Math::real latY1, Math::real lonY1,
310 Math::real latY2, Math::real lonY2,
311 int& segmode, int* c = nullptr) const;
312 /**
313 * Find the intersection of two geodesic segments each defined by a
314 * GeodesicLine.
315 *
316 * @param[in] lineX segment \e X.
317 * @param[in] lineY segment \e Y.
318 * @param[out] segmode an indicator equal to zero if the segments
319 * intersect (see below).
320 * @param[out] c optional pointer to an integer coincidence indicator.
321 * @return \e p the intersection point if the segments intersect, otherwise
322 * the intersection point closest to the midpoints of the two
323 * segments.
324 *
325 * \warning \e lineX and \e lineY must represent shortest geodesics, e.g.,
326 * they can be created by Geodesic::InverseLine. The results are only well
327 * defined if there's a \e unique shortest geodesic between the endpoints
328 * of the two segments.
329 *
330 * \note \e lineX and \e lineY should be created with minimum capabilities
331 * Intersect::LineCaps. The methods for creating a GeodesicLine include
332 * all these capabilities by default.
333 *
334 * See previous definition of Intersect::Segment for more information on \e
335 * segmode.
336 **********************************************************************/
337 Point Segment(const GeodesicLine& lineX, const GeodesicLine& lineY,
338 int& segmode, int* c = nullptr) const;
339 /**
340 * Find the next closest intersection point to a given intersection,
341 * specified by position and two azimuths.
342 *
343 * @param[in] latX latitude of starting points for geodesics \e X and \e Y
344 * (degrees).
345 * @param[in] lonX longitude of starting points for geodesics \e X and \e Y
346 * (degrees).
347 * @param[in] aziX azimuth at starting point for geodesic \e X (degrees).
348 * @param[in] aziY azimuth at starting point for geodesic \e Y (degrees).
349 * @param[out] c optional pointer to an integer coincidence indicator.
350 * @return \e p the next closest intersection point.
351 *
352 * The returned intersection minimizes Intersect::Dist(\e p) (excluding \e
353 * p = [0,0]).
354 *
355 * \note Equidistant closest intersections are surprisingly common. If
356 * this may be a problem, use Intersect::All with a sufficiently large \e
357 * maxdist to capture close intersections.
358 **********************************************************************/
359 Point Next(Math::real latX, Math::real lonX,
360 Math::real aziX, Math::real aziY, int* c = nullptr) const;
361 /**
362 * Find the next closest intersection point to a given intersection,
363 * with each geodesic specified a GeodesicLine.
364 *
365 * @param[in] lineX geodesic \e X.
366 * @param[in] lineY geodesic \e Y.
367 * @param[out] c optional pointer to an integer coincidence indicator.
368 * @return \e p the next closest intersection point.
369 *
370 * \warning \e lineX and \e lineY must both have the same starting point,
371 * i.e., the distance between [<i>lineX</i>.Latitude(),
372 * <i>lineX</i>.Longitude()] and [<i>lineY</i>.Latitude(),
373 * <i>lineY</i>.Longitude()] must be zero.
374 *
375 * \note \e lineX and \e lineY should be created with minimum capabilities
376 * Intersect::LineCaps. The methods for creating a GeodesicLine include
377 * all these capabilities by default.
378 *
379 * \note Equidistant closest intersections are surprisingly common. If
380 * this may be a problem, use Intersect::All with a sufficiently large \e
381 * maxdist to capture close intersections.
382 **********************************************************************/
383 Point Next(const GeodesicLine& lineX, const GeodesicLine& lineY,
384 int* c = nullptr) const;
385 ///@}
386
387 /** \name Finding all intersections
388 **********************************************************************/
389 ///@{
390 /**
391 * Find all intersections within a certain distance, with each geodesic
392 * specified by position and azimuth.
393 *
394 * @param[in] latX latitude of starting point for geodesic \e X (degrees).
395 * @param[in] lonX longitude of starting point for geodesic \e X (degrees).
396 * @param[in] aziX azimuth at starting point for geodesic \e X (degrees).
397 * @param[in] latY latitude of starting point for geodesic \e Y (degrees).
398 * @param[in] lonY longitude of starting point for geodesic \e Y (degrees).
399 * @param[in] aziY azimuth at starting point for geodesic \e Y (degrees).
400 * @param[in] maxdist the maximum distance for the returned intersections
401 * (meters).
402 * @param[out] c vector of coincidences.
403 * @param[in] p0 an optional offset for the starting points (meters),
404 * default = [0,0].
405 * @return \e plist a vector for the intersections closest to \e p0.
406 *
407 * Each intersection point satisfies Intersect::Dist(\e p, \e p0) &le; \e
408 * maxdist. The vector of returned intersections is sorted on the distance
409 * from \e p0.
410 **********************************************************************/
411 std::vector<Point> All(Math::real latX, Math::real lonX, Math::real aziX,
412 Math::real latY, Math::real lonY, Math::real aziY,
413 Math::real maxdist, std::vector<int>& c,
414 const Point& p0 = Point(0, 0))
415 const;
416 /**
417 * Find all intersections within a certain distance, with each geodesic
418 * specified by position and azimuth. Don't return vector of
419 * coincidences.
420 *
421 * @param[in] latX latitude of starting point for geodesic \e X (degrees).
422 * @param[in] lonX longitude of starting point for geodesic \e X (degrees).
423 * @param[in] aziX azimuth at starting point for geodesic \e X (degrees).
424 * @param[in] latY latitude of starting point for geodesic \e Y (degrees).
425 * @param[in] lonY longitude of starting point for geodesic \e Y (degrees).
426 * @param[in] aziY azimuth at starting point for geodesic \e Y (degrees).
427 * @param[in] maxdist the maximum distance for the returned intersections
428 * (meters).
429 * @param[in] p0 an optional offset for the starting points (meters),
430 * default = [0,0].
431 * @return \e plist a vector for the intersections closest to \e p0.
432 *
433 * Each intersection point satisfies Intersect::Dist(\e p, \e p0) &le; \e
434 * maxdist. The vector of returned intersections is sorted on the distance
435 * from \e p0.
436 **********************************************************************/
437 std::vector<Point> All(Math::real latX, Math::real lonX, Math::real aziX,
438 Math::real latY, Math::real lonY, Math::real aziY,
439 Math::real maxdist, const Point& p0 = Point(0, 0))
440 const;
441 /**
442 * Find all intersections within a certain distance, with each geodesic
443 * specified by a GeodesicLine.
444 *
445 * @param[in] lineX geodesic \e X.
446 * @param[in] lineY geodesic \e Y.
447 * @param[in] maxdist the maximum distance for the returned intersections
448 * (meters).
449 * @param[out] c vector of coincidences.
450 * @param[in] p0 an optional offset for the starting points (meters),
451 * default = [0,0].
452 * @return \e plist a vector for the intersections closest to \e p0.
453 *
454 * Each intersection point satisfies Intersect::Dist(\e p, \e p0) &le; \e
455 * maxdist. The vector of returned intersections is sorted on the distance
456 * from \e p0.
457 *
458 * \note \e lineX and \e lineY should be created with minimum capabilities
459 * Intersect::LineCaps. The methods for creating a GeodesicLine include
460 * all these capabilities by default.
461 **********************************************************************/
462 std::vector<Point> All(const GeodesicLine& lineX, const GeodesicLine& lineY,
463 Math::real maxdist, std::vector<int>& c,
464 const Point& p0 = Point(0, 0))
465 const;
466 /**
467 * Find all intersections within a certain distance, with each geodesic
468 * specified by a GeodesicLine. Don't return vector or coincidences.
469 *
470 * @param[in] lineX geodesic \e X.
471 * @param[in] lineY geodesic \e Y.
472 * @param[in] maxdist the maximum distance for the returned intersections
473 * (meters).
474 * @param[in] p0 an optional offset for the starting points (meters),
475 * default = [0,0].
476 * @return \e plist a vector for the intersections closest to \e p0.
477 *
478 * Each intersection point satisfies Intersect::Dist(\e p, \e p0) &le; \e
479 * maxdist. The vector of returned intersections is sorted on the distance
480 * from \e p0.
481 *
482 * \note \e lineX and \e lineY should be created with minimum capabilities
483 * Intersect::LineCaps. The methods for creating a GeodesicLine include
484 * all these capabilities by default.
485 **********************************************************************/
486 std::vector<Point> All(const GeodesicLine& lineX, const GeodesicLine& lineY,
487 Math::real maxdist, const Point& p0 = Point(0, 0))
488 const;
489 ///@}
490
491 /** \name Diagnostic counters
492 **********************************************************************/
493 ///@{
494 /**
495 * @return the cumulative number of invocations of **h**.
496 *
497 * This is a count of the number of times the spherical triangle needs to
498 * be solved. Each involves a call to Geodesic::Inverse and this is a good
499 * metric for the overall cost. This counter is set to zero by the
500 * constructor.
501 *
502 * \warning The counter is a mutable variable and so is not thread safe.
503 **********************************************************************/
504 long long NumInverse() const { return _cnt0; }
505 /**
506 * @return the cumulative number of invocations of **b**.
507 *
508 * This is a count of the number of invocations of the basic algorithm,
509 * which is used by all the intersection methods. This counter is set to
510 * zero by the constructor.
511 *
512 * \warning The counter is a mutable variable and so is not thread safe.
513 **********************************************************************/
514 long long NumBasic() const { return _cnt1; }
515 /**
516 * @return the number of times intersection point was changed in
517 * Intersect::Closest and Intersect::Next.
518 *
519 * If this counter is incremented by just 1 in Intersect::Closest, then the
520 * initial result of the basic algorithm was eventually accepted. This
521 * counter is set to zero by the constructor.
522 *
523 * \note This counter is also incremented by Intersect::Segment, which
524 * calls Intersect::Closest.
525 *
526 * \warning The counter is a mutable variable and so is not thread safe.
527 **********************************************************************/
528 long long NumChange() const { return _cnt2; }
529 /**
530 * @return the number of times a corner point is checked in
531 * Intersect::Segment.
532 *
533 * This counter is set to zero by the constructor.
534 *
535 * \warning The counter is a mutable variable and so is not thread safe.
536 **********************************************************************/
537 long long NumCorner() const { return _cnt3; }
538 /**
539 * @return the number of times a corner point is returned by
540 * Intersect::Segment.
541 *
542 * This counter is set to zero by the constructor.
543 *
544 * \note A conjecture is that a corner point never results in an
545 * intersection that overrides the intersection closest to the midpoints of
546 * the segments; i.e., NumCorner() always returns 0.
547 *
548 * \warning The counter is a mutable variable and so is not thread safe.
549 **********************************************************************/
550 long long NumOverride() const { return _cnt4; }
551 ///@}
552
553 /** \name Insepctor function
554 **********************************************************************/
555 ///@{
556 /**
557 * @return \e geod the Geodesic object used in the constructor.
558 *
559 * This can be used to query Geodesic::EquatorialRadius(),
560 * Geodesic::Flattening(), Geodesic::Exact(), and
561 * Geodesic::EllipsoidArea().
562 **********************************************************************/
563 const Geodesic& GeodesicObject() const { return _geod; }
564 ///@}
565
566 /**
567 * The L1 distance.
568 *
569 * @param[in] p the position along geodesics \e X and \e Y.
570 * @param[in] p0 [optional] the reference position, default = [0, 0].
571
572 * @return the L1 distance of \e p from \e p0, i.e.,
573 * |<i>p</i><sub><i>x</i></sub> &minus; <i>p0</i><sub><i>x</i></sub>| +
574 * |<i>p</i><sub><i>y</i></sub> &minus; <i>p0</i><sub><i>y</i></sub>|.
575 **********************************************************************/
576 static Math::real Dist(const Point& p, const Point& p0 = Point(0, 0)) {
577 using std::fabs;
578 return fabs(p.first - p0.first) + fabs(p.second - p0.second);
579 }
580 };
581
582} // namespace GeographicLib
583
584#endif // GEOGRAPHICLIB_INTERSECT_HPP
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition Constants.hpp:67
real
GeographicLib::Math::real real
Definition GeodSolve.cpp:28
GeodesicLine.hpp
Header for GeographicLib::GeodesicLine class.
Geodesic.hpp
Header for GeographicLib::Geodesic class.
Math.hpp
Header for GeographicLib::Math class.
GeographicLib::Geodesic
Geodesic calculations
Definition Geodesic.hpp:175
GeographicLib::Geodesic::REDUCEDLENGTH
@ REDUCEDLENGTH
Definition Geodesic.hpp:311
GeographicLib::Geodesic::LATITUDE
@ LATITUDE
Definition Geodesic.hpp:277
GeographicLib::Geodesic::LONGITUDE
@ LONGITUDE
Definition Geodesic.hpp:282
GeographicLib::Geodesic::AZIMUTH
@ AZIMUTH
Definition Geodesic.hpp:289
GeographicLib::Geodesic::DISTANCE_IN
@ DISTANCE_IN
Definition Geodesic.hpp:306
GeographicLib::Geodesic::GEODESICSCALE
@ GEODESICSCALE
Definition Geodesic.hpp:316
GeographicLib::Intersect::GeodesicObject
const Geodesic & GeodesicObject() const
Definition Intersect.hpp:563
GeographicLib::Intersect::NumChange
long long NumChange() const
Definition Intersect.hpp:528
GeographicLib::Intersect::NumBasic
long long NumBasic() const
Definition Intersect.hpp:514
GeographicLib::Intersect::NumInverse
long long NumInverse() const
Definition Intersect.hpp:504
GeographicLib::Intersect::LineCaps
static const unsigned LineCaps
Definition Intersect.hpp:84
GeographicLib::Intersect::Dist
static Math::real Dist(const Point &p, const Point &p0=Point(0, 0))
Definition Intersect.hpp:576
GeographicLib::Intersect::Point
std::pair< Math::real, Math::real > Point
Definition Intersect.hpp:79
GeographicLib::Intersect::NumOverride
long long NumOverride() const
Definition Intersect.hpp:550
GeographicLib::Intersect::Intersect
Intersect(const Geodesic &geod)
Definition Intersect.cpp:20
GeographicLib::Intersect::NumCorner
long long NumCorner() const
Definition Intersect.hpp:537
GeographicLib::Math::real
double real
Definition Math.hpp:115
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12