GeographicLib: GeodesicLine.hpp Source File

GeographicLib 2.5

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GeodesicLine.hpp
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1/**
2 * \file GeodesicLine.hpp
3 * \brief Header for GeographicLib::GeodesicLine class
4 *
5 * Copyright (c) Charles Karney (2009-2024) <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_GEODESICLINE_HPP)
11#define GEOGRAPHICLIB_GEODESICLINE_HPP 1
12
13#include <GeographicLib/Constants.hpp>
14#include <GeographicLib/Geodesic.hpp>
15#include <GeographicLib/GeodesicLineExact.hpp>
16
17namespace GeographicLib {
18
19 /**
20 * \brief A geodesic line
21 *
22 * GeodesicLine facilitates the determination of a series of points on a
23 * single geodesic. The starting point (\e lat1, \e lon1) and the azimuth \e
24 * azi1 are specified in the constructor; alternatively, the Geodesic::Line
25 * method can be used to create a GeodesicLine. GeodesicLine.Position
26 * returns the location of point 2 a distance \e s12 along the geodesic. In
27 * addition, GeodesicLine.ArcPosition gives the position of point 2 an arc
28 * length \e a12 along the geodesic.
29 *
30 * You can register the position of a reference point 3 a distance (arc
31 * length), \e s13 (\e a13) along the geodesic with the
32 * GeodesicLine.SetDistance (GeodesicLine.SetArc) functions. Points a
33 * fractional distance along the line can be found by providing, for example,
34 * 0.5 * Distance() as an argument to GeodesicLine.Position. The
35 * Geodesic::InverseLine or Geodesic::DirectLine methods return GeodesicLine
36 * objects with point 3 set to the point 2 of the corresponding geodesic
37 * problem. GeodesicLine objects created with the public constructor or with
38 * Geodesic::Line have \e s13 and \e a13 set to NaNs.
39 *
40 * The default copy constructor and assignment operators work with this
41 * class. Similarly, a vector can be used to hold GeodesicLine objects.
42 *
43 * The calculations are accurate to better than 15 nm (15 nanometers). See
44 * Sec. 9 of
45 * <a href="https://arxiv.org/abs/1102.1215v1">arXiv:1102.1215v1</a> for
46 * details. With \e exact = false (the default) in the constructor for the
47 * Geodesic object, the algorithms used by this class are based on series
48 * expansions using the flattening \e f as a small parameter. These are only
49 * accurate for |<i>f</i>| &lt; 0.02; however reasonably accurate results
50 * will be obtained for |<i>f</i>| &lt; 0.2. For very eccentric ellipsoids,
51 * set \e exact = true in the constructor for the Geodesic object; this will
52 * delegate the calculations to GeodesicLineExact.
53 *
54 * The algorithms are described in
55 * - C. F. F. Karney,
56 * <a href="https://doi.org/10.1007/s00190-012-0578-z">
57 * Algorithms for geodesics</a>,
58 * J. Geodesy <b>87</b>, 43--55 (2013);
59 * DOI: <a href="https://doi.org/10.1007/s00190-012-0578-z">
60 * 10.1007/s00190-012-0578-z</a>;
61 * addenda:
62 * <a href="https://geographiclib.sourceforge.io/geod-addenda.html">
63 * geod-addenda.html</a>.
64 * .
65 * For more information on geodesics see \ref geodesic.
66 *
67 * Example of use:
68 * \include example-GeodesicLine.cpp
69 *
70 * <a href="GeodSolve.1.html">GeodSolve</a> is a command-line utility
71 * providing access to the functionality of Geodesic and GeodesicLine.
72 **********************************************************************/
73
74 class GEOGRAPHICLIB_EXPORT GeodesicLine {
75 private:
76 typedef Math::real real;
77 friend class Geodesic;
78 static const int nC1_ = Geodesic::nC1_;
79 static const int nC1p_ = Geodesic::nC1p_;
80 static const int nC2_ = Geodesic::nC2_;
81 static const int nC3_ = Geodesic::nC3_;
82 static const int nC4_ = Geodesic::nC4_;
83
84 real tiny_;
85 real _lat1, _lon1, _azi1;
86 real _a, _f;
87 bool _exact;
88 real _b, _c2, _f1, _salp0, _calp0, _k2,
89 _salp1, _calp1, _ssig1, _csig1, _dn1, _stau1, _ctau1, _somg1, _comg1,
90 _aA1m1, _aA2m1, _aA3c, _bB11, _bB21, _bB31, _aA4, _bB41;
91 real _a13, _s13;
92 // index zero elements of _cC1a, _cC1pa, _cC2a, _cC3a are unused
93 real _cC1a[nC1_ + 1], _cC1pa[nC1p_ + 1], _cC2a[nC2_ + 1], _cC3a[nC3_],
94 _cC4a[nC4_]; // all the elements of _cC4a are used
95 unsigned _caps;
96 GeodesicLineExact _lineexact;
97
98 void LineInit(const Geodesic& g,
99 real lat1, real lon1,
100 real azi1, real salp1, real calp1,
101 unsigned caps);
102 GeodesicLine(const Geodesic& g,
103 real lat1, real lon1,
104 real azi1, real salp1, real calp1,
105 unsigned caps, bool arcmode, real s13_a13);
106
107 static constexpr unsigned CAP_NONE = Geodesic::CAP_NONE;
108 static constexpr unsigned CAP_C1 = Geodesic::CAP_C1;
109 static constexpr unsigned CAP_C1p = Geodesic::CAP_C1p;
110 static constexpr unsigned CAP_C2 = Geodesic::CAP_C2;
111 static constexpr unsigned CAP_C3 = Geodesic::CAP_C3;
112 static constexpr unsigned CAP_C4 = Geodesic::CAP_C4;
113 static constexpr unsigned CAP_ALL = Geodesic::CAP_ALL;
114 static constexpr unsigned CAP_MASK = Geodesic::CAP_MASK;
115 static constexpr unsigned OUT_ALL = Geodesic::OUT_ALL;
116 static constexpr unsigned OUT_MASK = Geodesic::OUT_MASK;
117
118 public:
119
120 /**
121 * Bit masks for what calculations to do. They signify to the
122 * GeodesicLine::GeodesicLine constructor and to Geodesic::Line what
123 * capabilities should be included in the GeodesicLine object. This is
124 * merely a duplication of Geodesic::mask.
125 **********************************************************************/
126 enum mask {
127 /**
128 * No capabilities, no output.
129 * @hideinitializer
130 **********************************************************************/
131 NONE = Geodesic::NONE,
132 /**
133 * Calculate latitude \e lat2. (It's not necessary to include this as a
134 * capability to GeodesicLine because this is included by default.)
135 * @hideinitializer
136 **********************************************************************/
137 LATITUDE = Geodesic::LATITUDE,
138 /**
139 * Calculate longitude \e lon2.
140 * @hideinitializer
141 **********************************************************************/
142 LONGITUDE = Geodesic::LONGITUDE,
143 /**
144 * Calculate azimuths \e azi1 and \e azi2. (It's not necessary to
145 * include this as a capability to GeodesicLine because this is included
146 * by default.)
147 * @hideinitializer
148 **********************************************************************/
149 AZIMUTH = Geodesic::AZIMUTH,
150 /**
151 * Calculate distance \e s12.
152 * @hideinitializer
153 **********************************************************************/
154 DISTANCE = Geodesic::DISTANCE,
155 /**
156 * A combination of the common capabilities: GeodesicLine::LATITUDE,
157 * GeodesicLine::LONGITUDE, GeodesicLine::AZIMUTH, GeodesicLine::DISTANCE.
158 * @hideinitializer
159 **********************************************************************/
160 STANDARD = Geodesic::STANDARD,
161 /**
162 * Allow distance \e s12 to be used as input in the direct geodesic
163 * problem.
164 * @hideinitializer
165 **********************************************************************/
166 DISTANCE_IN = Geodesic::DISTANCE_IN,
167 /**
168 * Calculate reduced length \e m12.
169 * @hideinitializer
170 **********************************************************************/
171 REDUCEDLENGTH = Geodesic::REDUCEDLENGTH,
172 /**
173 * Calculate geodesic scales \e M12 and \e M21.
174 * @hideinitializer
175 **********************************************************************/
176 GEODESICSCALE = Geodesic::GEODESICSCALE,
177 /**
178 * Calculate area \e S12.
179 * @hideinitializer
180 **********************************************************************/
181 AREA = Geodesic::AREA,
182 /**
183 * Unroll \e lon2 in the direct calculation.
184 * @hideinitializer
185 **********************************************************************/
186 LONG_UNROLL = Geodesic::LONG_UNROLL,
187 /**
188 * All capabilities, calculate everything. (GeodesicLine::LONG_UNROLL is
189 * not included in this mask.)
190 * @hideinitializer
191 **********************************************************************/
192 ALL = Geodesic::ALL,
193 };
194
195 /**
196 * Typedef for the base class implementing geodesics.
197 **********************************************************************/
198 typedef Geodesic BaseClass;
199
200 /** \name Constructors
201 **********************************************************************/
202 ///@{
203
204 /**
205 * Constructor for a geodesic line staring at latitude \e lat1, longitude
206 * \e lon1, and azimuth \e azi1 (all in degrees).
207 *
208 * @param[in] g A Geodesic object used to compute the necessary information
209 * about the GeodesicLine.
210 * @param[in] lat1 latitude of point 1 (degrees).
211 * @param[in] lon1 longitude of point 1 (degrees).
212 * @param[in] azi1 azimuth at point 1 (degrees).
213 * @param[in] caps bitor'ed combination of GeodesicLine::mask values
214 * specifying the capabilities the GeodesicLine object should possess,
215 * i.e., which quantities can be returned in calls to
216 * GeodesicLine::Position.
217 *
218 * \e lat1 should be in the range [&minus;90&deg;, 90&deg;].
219 *
220 * The GeodesicLine::mask values are
221 * - \e caps |= GeodesicLine::LATITUDE for the latitude \e lat2; this is
222 * added automatically;
223 * - \e caps |= GeodesicLine::LONGITUDE for the latitude \e lon2;
224 * - \e caps |= GeodesicLine::AZIMUTH for the latitude \e azi2; this is
225 * added automatically;
226 * - \e caps |= GeodesicLine::DISTANCE for the distance \e s12;
227 * - \e caps |= GeodesicLine::REDUCEDLENGTH for the reduced length \e m12;
228 * - \e caps |= GeodesicLine::GEODESICSCALE for the geodesic scales \e M12
229 * and \e M21;
230 * - \e caps |= GeodesicLine::AREA for the area \e S12;
231 * - \e caps |= GeodesicLine::DISTANCE_IN permits the length of the
232 * geodesic to be given in terms of \e s12; without this capability the
233 * length can only be specified in terms of arc length;
234 * - \e caps |= GeodesicLine::ALL for all of the above.
235 * .
236 * The default value of \e caps is GeodesicLine::ALL.
237 *
238 * If the point is at a pole, the azimuth is defined by keeping \e lon1
239 * fixed, writing \e lat1 = &plusmn;(90&deg; &minus; &epsilon;), and taking
240 * the limit &epsilon; &rarr; 0+.
241 **********************************************************************/
242 GeodesicLine(const Geodesic& g, real lat1, real lon1, real azi1,
243 unsigned caps = ALL);
244
245 /**
246 * A default constructor. If GeodesicLine::Position is called on the
247 * resulting object, it returns immediately (without doing any
248 * calculations). The object can be set with a call to Geodesic::Line.
249 * Use Init() to test whether object is still in this uninitialized state.
250 **********************************************************************/
251 GeodesicLine() : _caps(0U) {}
252 ///@}
253
254 /** \name Position in terms of distance
255 **********************************************************************/
256 ///@{
257
258 /**
259 * Compute the position of point 2 which is a distance \e s12 (meters) from
260 * point 1.
261 *
262 * @param[in] s12 distance from point 1 to point 2 (meters); it can be
263 * negative.
264 * @param[out] lat2 latitude of point 2 (degrees).
265 * @param[out] lon2 longitude of point 2 (degrees); requires that the
266 * GeodesicLine object was constructed with \e caps |=
267 * GeodesicLine::LONGITUDE.
268 * @param[out] azi2 (forward) azimuth at point 2 (degrees).
269 * @param[out] m12 reduced length of geodesic (meters); requires that the
270 * GeodesicLine object was constructed with \e caps |=
271 * GeodesicLine::REDUCEDLENGTH.
272 * @param[out] M12 geodesic scale of point 2 relative to point 1
273 * (dimensionless); requires that the GeodesicLine object was constructed
274 * with \e caps |= GeodesicLine::GEODESICSCALE.
275 * @param[out] M21 geodesic scale of point 1 relative to point 2
276 * (dimensionless); requires that the GeodesicLine object was constructed
277 * with \e caps |= GeodesicLine::GEODESICSCALE.
278 * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
279 * that the GeodesicLine object was constructed with \e caps |=
280 * GeodesicLine::AREA.
281 * @return \e a12 arc length from point 1 to point 2 (degrees).
282 *
283 * The values of \e lon2 and \e azi2 returned are in the range
284 * [&minus;180&deg;, 180&deg;].
285 *
286 * The GeodesicLine object \e must have been constructed with \e caps |=
287 * GeodesicLine::DISTANCE_IN; otherwise Math::NaN() is returned and no
288 * parameters are set. Requesting a value which the GeodesicLine object is
289 * not capable of computing is not an error; the corresponding argument
290 * will not be altered.
291 *
292 * The following functions are overloaded versions of
293 * GeodesicLine::Position which omit some of the output parameters. Note,
294 * however, that the arc length is always computed and returned as the
295 * function value.
296 **********************************************************************/
297 Math::real Position(real s12,
298 real& lat2, real& lon2, real& azi2,
299 real& m12, real& M12, real& M21,
300 real& S12) const {
301 real t;
302 return GenPosition(false, s12,
303 LATITUDE | LONGITUDE | AZIMUTH |
304 REDUCEDLENGTH | GEODESICSCALE | AREA,
305 lat2, lon2, azi2, t, m12, M12, M21, S12);
306 }
307
308 /**
309 * See the documentation for GeodesicLine::Position.
310 **********************************************************************/
311 Math::real Position(real s12, real& lat2, real& lon2) const {
312 real t;
313 return GenPosition(false, s12,
314 LATITUDE | LONGITUDE,
315 lat2, lon2, t, t, t, t, t, t);
316 }
317
318 /**
319 * See the documentation for GeodesicLine::Position.
320 **********************************************************************/
321 Math::real Position(real s12, real& lat2, real& lon2,
322 real& azi2) const {
323 real t;
324 return GenPosition(false, s12,
325 LATITUDE | LONGITUDE | AZIMUTH,
326 lat2, lon2, azi2, t, t, t, t, t);
327 }
328
329 /**
330 * See the documentation for GeodesicLine::Position.
331 **********************************************************************/
332 Math::real Position(real s12, real& lat2, real& lon2,
333 real& azi2, real& m12) const {
334 real t;
335 return GenPosition(false, s12,
336 LATITUDE | LONGITUDE |
337 AZIMUTH | REDUCEDLENGTH,
338 lat2, lon2, azi2, t, m12, t, t, t);
339 }
340
341 /**
342 * See the documentation for GeodesicLine::Position.
343 **********************************************************************/
344 Math::real Position(real s12, real& lat2, real& lon2,
345 real& azi2, real& M12, real& M21)
346 const {
347 real t;
348 return GenPosition(false, s12,
349 LATITUDE | LONGITUDE |
350 AZIMUTH | GEODESICSCALE,
351 lat2, lon2, azi2, t, t, M12, M21, t);
352 }
353
354 /**
355 * See the documentation for GeodesicLine::Position.
356 **********************************************************************/
357 Math::real Position(real s12,
358 real& lat2, real& lon2, real& azi2,
359 real& m12, real& M12, real& M21)
360 const {
361 real t;
362 return GenPosition(false, s12,
363 LATITUDE | LONGITUDE | AZIMUTH |
364 REDUCEDLENGTH | GEODESICSCALE,
365 lat2, lon2, azi2, t, m12, M12, M21, t);
366 }
367 ///@}
368
369 /** \name Position in terms of arc length
370 **********************************************************************/
371 ///@{
372
373 /**
374 * Compute the position of point 2 which is an arc length \e a12 (degrees)
375 * from point 1.
376 *
377 * @param[in] a12 arc length from point 1 to point 2 (degrees); it can
378 * be negative.
379 * @param[out] lat2 latitude of point 2 (degrees).
380 * @param[out] lon2 longitude of point 2 (degrees); requires that the
381 * GeodesicLine object was constructed with \e caps |=
382 * GeodesicLine::LONGITUDE.
383 * @param[out] azi2 (forward) azimuth at point 2 (degrees).
384 * @param[out] s12 distance from point 1 to point 2 (meters); requires
385 * that the GeodesicLine object was constructed with \e caps |=
386 * GeodesicLine::DISTANCE.
387 * @param[out] m12 reduced length of geodesic (meters); requires that the
388 * GeodesicLine object was constructed with \e caps |=
389 * GeodesicLine::REDUCEDLENGTH.
390 * @param[out] M12 geodesic scale of point 2 relative to point 1
391 * (dimensionless); requires that the GeodesicLine object was constructed
392 * with \e caps |= GeodesicLine::GEODESICSCALE.
393 * @param[out] M21 geodesic scale of point 1 relative to point 2
394 * (dimensionless); requires that the GeodesicLine object was constructed
395 * with \e caps |= GeodesicLine::GEODESICSCALE.
396 * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
397 * that the GeodesicLine object was constructed with \e caps |=
398 * GeodesicLine::AREA.
399 *
400 * The values of \e lon2 and \e azi2 returned are in the range
401 * [&minus;180&deg;, 180&deg;].
402 *
403 * Requesting a value which the GeodesicLine object is not capable of
404 * computing is not an error; the corresponding argument will not be
405 * altered.
406 *
407 * The following functions are overloaded versions of
408 * GeodesicLine::ArcPosition which omit some of the output parameters.
409 **********************************************************************/
410 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
411 real& s12, real& m12, real& M12, real& M21,
412 real& S12) const {
413 GenPosition(true, a12,
414 LATITUDE | LONGITUDE | AZIMUTH | DISTANCE |
415 REDUCEDLENGTH | GEODESICSCALE | AREA,
416 lat2, lon2, azi2, s12, m12, M12, M21, S12);
417 }
418
419 /**
420 * See the documentation for GeodesicLine::ArcPosition.
421 **********************************************************************/
422 void ArcPosition(real a12, real& lat2, real& lon2)
423 const {
424 real t;
425 GenPosition(true, a12,
426 LATITUDE | LONGITUDE,
427 lat2, lon2, t, t, t, t, t, t);
428 }
429
430 /**
431 * See the documentation for GeodesicLine::ArcPosition.
432 **********************************************************************/
433 void ArcPosition(real a12,
434 real& lat2, real& lon2, real& azi2)
435 const {
436 real t;
437 GenPosition(true, a12,
438 LATITUDE | LONGITUDE | AZIMUTH,
439 lat2, lon2, azi2, t, t, t, t, t);
440 }
441
442 /**
443 * See the documentation for GeodesicLine::ArcPosition.
444 **********************************************************************/
445 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
446 real& s12) const {
447 real t;
448 GenPosition(true, a12,
449 LATITUDE | LONGITUDE | AZIMUTH | DISTANCE,
450 lat2, lon2, azi2, s12, t, t, t, t);
451 }
452
453 /**
454 * See the documentation for GeodesicLine::ArcPosition.
455 **********************************************************************/
456 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
457 real& s12, real& m12) const {
458 real t;
459 GenPosition(true, a12,
460 LATITUDE | LONGITUDE | AZIMUTH |
461 DISTANCE | REDUCEDLENGTH,
462 lat2, lon2, azi2, s12, m12, t, t, t);
463 }
464
465 /**
466 * See the documentation for GeodesicLine::ArcPosition.
467 **********************************************************************/
468 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
469 real& s12, real& M12, real& M21)
470 const {
471 real t;
472 GenPosition(true, a12,
473 LATITUDE | LONGITUDE | AZIMUTH |
474 DISTANCE | GEODESICSCALE,
475 lat2, lon2, azi2, s12, t, M12, M21, t);
476 }
477
478 /**
479 * See the documentation for GeodesicLine::ArcPosition.
480 **********************************************************************/
481 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
482 real& s12, real& m12, real& M12, real& M21)
483 const {
484 real t;
485 GenPosition(true, a12,
486 LATITUDE | LONGITUDE | AZIMUTH |
487 DISTANCE | REDUCEDLENGTH | GEODESICSCALE,
488 lat2, lon2, azi2, s12, m12, M12, M21, t);
489 }
490 ///@}
491
492 /** \name The general position function.
493 **********************************************************************/
494 ///@{
495
496 /**
497 * The general position function. GeodesicLine::Position and
498 * GeodesicLine::ArcPosition are defined in terms of this function.
499 *
500 * @param[in] arcmode boolean flag determining the meaning of the second
501 * parameter; if \e arcmode is false, then the GeodesicLine object must
502 * have been constructed with \e caps |= GeodesicLine::DISTANCE_IN.
503 * @param[in] s12_a12 if \e arcmode is false, this is the distance between
504 * point 1 and point 2 (meters); otherwise it is the arc length between
505 * point 1 and point 2 (degrees); it can be negative.
506 * @param[in] outmask a bitor'ed combination of GeodesicLine::mask values
507 * specifying which of the following parameters should be set.
508 * @param[out] lat2 latitude of point 2 (degrees).
509 * @param[out] lon2 longitude of point 2 (degrees); requires that the
510 * GeodesicLine object was constructed with \e caps |=
511 * GeodesicLine::LONGITUDE.
512 * @param[out] azi2 (forward) azimuth at point 2 (degrees).
513 * @param[out] s12 distance from point 1 to point 2 (meters); requires
514 * that the GeodesicLine object was constructed with \e caps |=
515 * GeodesicLine::DISTANCE.
516 * @param[out] m12 reduced length of geodesic (meters); requires that the
517 * GeodesicLine object was constructed with \e caps |=
518 * GeodesicLine::REDUCEDLENGTH.
519 * @param[out] M12 geodesic scale of point 2 relative to point 1
520 * (dimensionless); requires that the GeodesicLine object was constructed
521 * with \e caps |= GeodesicLine::GEODESICSCALE.
522 * @param[out] M21 geodesic scale of point 1 relative to point 2
523 * (dimensionless); requires that the GeodesicLine object was constructed
524 * with \e caps |= GeodesicLine::GEODESICSCALE.
525 * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
526 * that the GeodesicLine object was constructed with \e caps |=
527 * GeodesicLine::AREA.
528 * @return \e a12 arc length from point 1 to point 2 (degrees).
529 *
530 * The GeodesicLine::mask values possible for \e outmask are
531 * - \e outmask |= GeodesicLine::LATITUDE for the latitude \e lat2;
532 * - \e outmask |= GeodesicLine::LONGITUDE for the latitude \e lon2;
533 * - \e outmask |= GeodesicLine::AZIMUTH for the latitude \e azi2;
534 * - \e outmask |= GeodesicLine::DISTANCE for the distance \e s12;
535 * - \e outmask |= GeodesicLine::REDUCEDLENGTH for the reduced length \e
536 * m12;
537 * - \e outmask |= GeodesicLine::GEODESICSCALE for the geodesic scales \e
538 * M12 and \e M21;
539 * - \e outmask |= GeodesicLine::AREA for the area \e S12;
540 * - \e outmask |= GeodesicLine::ALL for all of the above;
541 * - \e outmask |= GeodesicLine::LONG_UNROLL to unroll \e lon2 instead of
542 * reducing it into the range [&minus;180&deg;, 180&deg;].
543 * .
544 * Requesting a value which the GeodesicLine object is not capable of
545 * computing is not an error; the corresponding argument will not be
546 * altered. Note, however, that the arc length is always computed and
547 * returned as the function value.
548 *
549 * With the GeodesicLine::LONG_UNROLL bit set, the quantity \e lon2 &minus;
550 * \e lon1 indicates how many times and in what sense the geodesic
551 * encircles the ellipsoid.
552 **********************************************************************/
553 Math::real GenPosition(bool arcmode, real s12_a12, unsigned outmask,
554 real& lat2, real& lon2, real& azi2,
555 real& s12, real& m12, real& M12, real& M21,
556 real& S12) const;
557 ///@}
558
559 /** \name Setting point 3
560 **********************************************************************/
561 ///@{
562
563 /**
564 * Specify position of point 3 in terms of distance.
565 *
566 * @param[in] s13 the distance from point 1 to point 3 (meters); it
567 * can be negative.
568 *
569 * This is only useful if the GeodesicLine object has been constructed
570 * with \e caps |= GeodesicLine::DISTANCE_IN.
571 **********************************************************************/
572 void SetDistance(real s13);
573
574 /**
575 * Specify position of point 3 in terms of arc length.
576 *
577 * @param[in] a13 the arc length from point 1 to point 3 (degrees); it
578 * can be negative.
579 *
580 * The distance \e s13 is only set if the GeodesicLine object has been
581 * constructed with \e caps |= GeodesicLine::DISTANCE.
582 **********************************************************************/
583 void SetArc(real a13);
584
585 /**
586 * Specify position of point 3 in terms of either distance or arc length.
587 *
588 * @param[in] arcmode boolean flag determining the meaning of the second
589 * parameter; if \e arcmode is false, then the GeodesicLine object must
590 * have been constructed with \e caps |= GeodesicLine::DISTANCE_IN.
591 * @param[in] s13_a13 if \e arcmode is false, this is the distance from
592 * point 1 to point 3 (meters); otherwise it is the arc length from
593 * point 1 to point 3 (degrees); it can be negative.
594 **********************************************************************/
595 void GenSetDistance(bool arcmode, real s13_a13);
596 ///@}
597
598 /** \name Inspector functions
599 **********************************************************************/
600 ///@{
601
602 /**
603 * @return true if the object has been initialized.
604 **********************************************************************/
605 bool Init() const { return _caps != 0U; }
606
607 /**
608 * @return \e lat1 the latitude of point 1 (degrees).
609 **********************************************************************/
610 Math::real Latitude() const
611 { return Init() ? _lat1 : Math::NaN(); }
612
613 /**
614 * @return \e lon1 the longitude of point 1 (degrees).
615 **********************************************************************/
616 Math::real Longitude() const
617 { return Init() ? _lon1 : Math::NaN(); }
618
619 /**
620 * @return \e azi1 the azimuth (degrees) of the geodesic line at point 1.
621 **********************************************************************/
622 Math::real Azimuth() const
623 { return Init() ? _azi1 : Math::NaN(); }
624
625 /**
626 * The sine and cosine of \e azi1.
627 *
628 * @param[out] sazi1 the sine of \e azi1.
629 * @param[out] cazi1 the cosine of \e azi1.
630 **********************************************************************/
631 void Azimuth(real& sazi1, real& cazi1) const
632 { if (Init()) { sazi1 = _salp1; cazi1 = _calp1; } }
633
634 /**
635 * @return \e azi0 the azimuth (degrees) of the geodesic line as it crosses
636 * the equator in a northward direction.
637 *
638 * The result lies in [&minus;90&deg;, 90&deg;].
639 **********************************************************************/
640 Math::real EquatorialAzimuth() const
641 { return Init() ? Math::atan2d(_salp0, _calp0) : Math::NaN(); }
642
643 /**
644 * The sine and cosine of \e azi0.
645 *
646 * @param[out] sazi0 the sine of \e azi0.
647 * @param[out] cazi0 the cosine of \e azi0.
648 **********************************************************************/
649 void EquatorialAzimuth(real& sazi0, real& cazi0) const
650 { if (Init()) { sazi0 = _salp0; cazi0 = _calp0; } }
651
652 /**
653 * @return \e a1 the arc length (degrees) between the northward equatorial
654 * crossing and point 1.
655 *
656 * The result lies in [&minus;180&deg;, 180&deg;].
657 **********************************************************************/
658 Math::real EquatorialArc() const {
659 return Init() ? Math::atan2d(_ssig1, _csig1) : Math::NaN();
660 }
661
662 /**
663 * @return \e a the equatorial radius of the ellipsoid (meters). This is
664 * the value inherited from the Geodesic object used in the constructor.
665 **********************************************************************/
666 Math::real EquatorialRadius() const
667 { return Init() ? _a : Math::NaN(); }
668
669 /**
670 * @return \e f the flattening of the ellipsoid. This is the value
671 * inherited from the Geodesic object used in the constructor.
672 **********************************************************************/
673 Math::real Flattening() const
674 { return Init() ? _f : Math::NaN(); }
675
676 /**
677 * @return \e exact whether the exact formulation is used. This is the
678 * value returned by the Geodesic object used in the constructor.
679 **********************************************************************/
680 bool Exact() const { return _exact; }
681
682 /**
683 * @return \e caps the computational capabilities that this object was
684 * constructed with. LATITUDE and AZIMUTH are always included.
685 **********************************************************************/
686 unsigned Capabilities() const { return _caps; }
687
688 /**
689 * Test what capabilities are available.
690 *
691 * @param[in] testcaps a set of bitor'ed GeodesicLine::mask values.
692 * @return true if the GeodesicLine object has all these capabilities.
693 **********************************************************************/
694 bool Capabilities(unsigned testcaps) const {
695 testcaps &= OUT_ALL;
696 return (_caps & testcaps) == testcaps;
697 }
698
699 /**
700 * The distance or arc length to point 3.
701 *
702 * @param[in] arcmode boolean flag determining the meaning of returned
703 * value.
704 * @return \e s13 if \e arcmode is false; \e a13 if \e arcmode is true.
705 **********************************************************************/
706 Math::real GenDistance(bool arcmode) const
707 { return Init() ? (arcmode ? _a13 : _s13) : Math::NaN(); }
708
709 /**
710 * @return \e s13, the distance to point 3 (meters).
711 **********************************************************************/
712 Math::real Distance() const { return GenDistance(false); }
713
714 /**
715 * @return \e a13, the arc length to point 3 (degrees).
716 **********************************************************************/
717 Math::real Arc() const { return GenDistance(true); }
718 ///@}
719
720 };
721
722} // namespace GeographicLib
723
724#endif // GEOGRAPHICLIB_GEODESICLINE_HPP
Constants.hpp
Header for GeographicLib::Constants class.
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition Constants.hpp:67
real
GeographicLib::Math::real real
Definition GeodSolve.cpp:28
GeodesicLineExact.hpp
Header for GeographicLib::GeodesicLineExact class.
Geodesic.hpp
Header for GeographicLib::Geodesic class.
GeographicLib::GeodesicLineExact
An exact geodesic line.
Definition GeodesicLineExact.hpp:42
GeographicLib::GeodesicLine::Geodesic
friend class Geodesic
Definition GeodesicLine.hpp:77
GeographicLib::GeodesicLine::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const
Definition GeodesicLine.hpp:468
GeographicLib::GeodesicLine::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12) const
Definition GeodesicLine.hpp:445
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12) const
Definition GeodesicLine.hpp:332
GeographicLib::GeodesicLine::Init
bool Init() const
Definition GeodesicLine.hpp:605
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const
Definition GeodesicLine.hpp:344
GeographicLib::GeodesicLine::Capabilities
unsigned Capabilities() const
Definition GeodesicLine.hpp:686
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2) const
Definition GeodesicLine.hpp:311
GeographicLib::GeodesicLine::Latitude
Math::real Latitude() const
Definition GeodesicLine.hpp:610
GeographicLib::GeodesicLine::Distance
Math::real Distance() const
Definition GeodesicLine.hpp:712
GeographicLib::GeodesicLine::EquatorialAzimuth
Math::real EquatorialAzimuth() const
Definition GeodesicLine.hpp:640
GeographicLib::GeodesicLine::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21) const
Definition GeodesicLine.hpp:481
GeographicLib::GeodesicLine::Azimuth
Math::real Azimuth() const
Definition GeodesicLine.hpp:622
GeographicLib::GeodesicLine::Azimuth
void Azimuth(real &sazi1, real &cazi1) const
Definition GeodesicLine.hpp:631
GeographicLib::GeodesicLine::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
Definition GeodesicLine.hpp:410
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition GeodesicLine.hpp:297
GeographicLib::GeodesicLine::GenDistance
Math::real GenDistance(bool arcmode) const
Definition GeodesicLine.hpp:706
GeographicLib::GeodesicLine::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2) const
Definition GeodesicLine.hpp:422
GeographicLib::GeodesicLine::Arc
Math::real Arc() const
Definition GeodesicLine.hpp:717
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const
Definition GeodesicLine.hpp:357
GeographicLib::GeodesicLine::GenPosition
Math::real GenPosition(bool arcmode, real s12_a12, unsigned outmask, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
Definition GeodesicLine.cpp:142
GeographicLib::GeodesicLine::EquatorialRadius
Math::real EquatorialRadius() const
Definition GeodesicLine.hpp:666
GeographicLib::GeodesicLine::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const
Definition GeodesicLine.hpp:456
GeographicLib::GeodesicLine::EquatorialAzimuth
void EquatorialAzimuth(real &sazi0, real &cazi0) const
Definition GeodesicLine.hpp:649
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2) const
Definition GeodesicLine.hpp:321
GeographicLib::GeodesicLine::Exact
bool Exact() const
Definition GeodesicLine.hpp:680
GeographicLib::GeodesicLine::Capabilities
bool Capabilities(unsigned testcaps) const
Definition GeodesicLine.hpp:694
GeographicLib::GeodesicLine::mask
mask
Definition GeodesicLine.hpp:126
GeographicLib::GeodesicLine::NONE
@ NONE
Definition GeodesicLine.hpp:131
GeographicLib::GeodesicLine::LATITUDE
@ LATITUDE
Definition GeodesicLine.hpp:137
GeographicLib::GeodesicLine::AZIMUTH
@ AZIMUTH
Definition GeodesicLine.hpp:149
GeographicLib::GeodesicLine::DISTANCE
@ DISTANCE
Definition GeodesicLine.hpp:154
GeographicLib::GeodesicLine::AREA
@ AREA
Definition GeodesicLine.hpp:181
GeographicLib::GeodesicLine::GEODESICSCALE
@ GEODESICSCALE
Definition GeodesicLine.hpp:176
GeographicLib::GeodesicLine::DISTANCE_IN
@ DISTANCE_IN
Definition GeodesicLine.hpp:166
GeographicLib::GeodesicLine::REDUCEDLENGTH
@ REDUCEDLENGTH
Definition GeodesicLine.hpp:171
GeographicLib::GeodesicLine::ALL
@ ALL
Definition GeodesicLine.hpp:192
GeographicLib::GeodesicLine::STANDARD
@ STANDARD
Definition GeodesicLine.hpp:160
GeographicLib::GeodesicLine::LONGITUDE
@ LONGITUDE
Definition GeodesicLine.hpp:142
GeographicLib::GeodesicLine::LONG_UNROLL
@ LONG_UNROLL
Definition GeodesicLine.hpp:186
GeographicLib::GeodesicLine::GeodesicLine
GeodesicLine()
Definition GeodesicLine.hpp:251
GeographicLib::GeodesicLine::Longitude
Math::real Longitude() const
Definition GeodesicLine.hpp:616
GeographicLib::GeodesicLine::EquatorialArc
Math::real EquatorialArc() const
Definition GeodesicLine.hpp:658
GeographicLib::GeodesicLine::Flattening
Math::real Flattening() const
Definition GeodesicLine.hpp:673
GeographicLib::GeodesicLine::BaseClass
Geodesic BaseClass
Definition GeodesicLine.hpp:198
GeographicLib::GeodesicLine::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2) const
Definition GeodesicLine.hpp:433
GeographicLib::Geodesic::DISTANCE
@ DISTANCE
Definition Geodesic.hpp:294
GeographicLib::Geodesic::ALL
@ ALL
Definition Geodesic.hpp:332
GeographicLib::Geodesic::LONG_UNROLL
@ LONG_UNROLL
Definition Geodesic.hpp:326
GeographicLib::Geodesic::REDUCEDLENGTH
@ REDUCEDLENGTH
Definition Geodesic.hpp:311
GeographicLib::Geodesic::LATITUDE
@ LATITUDE
Definition Geodesic.hpp:277
GeographicLib::Geodesic::STANDARD
@ STANDARD
Definition Geodesic.hpp:300
GeographicLib::Geodesic::AREA
@ AREA
Definition Geodesic.hpp:321
GeographicLib::Geodesic::LONGITUDE
@ LONGITUDE
Definition Geodesic.hpp:282
GeographicLib::Geodesic::AZIMUTH
@ AZIMUTH
Definition Geodesic.hpp:289
GeographicLib::Geodesic::NONE
@ NONE
Definition Geodesic.hpp:271
GeographicLib::Geodesic::DISTANCE_IN
@ DISTANCE_IN
Definition Geodesic.hpp:306
GeographicLib::Geodesic::GEODESICSCALE
@ GEODESICSCALE
Definition Geodesic.hpp:316
GeographicLib::Math::atan2d
static T atan2d(T y, T x)
Definition Math.cpp:199
GeographicLib::Math::NaN
static T NaN()
Definition Math.cpp:277
GeographicLib::Math::real
double real
Definition Math.hpp:110
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12