GeographicLib 1.52
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GeodesicLineExact.hpp
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1/**
2 * \file GeodesicLineExact.hpp
3 * \brief Header for GeographicLib::GeodesicLineExact class
4 *
5 * Copyright (c) Charles Karney (2012-2020) <charles@karney.com> and licensed
6 * under the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
10#if !defined(GEOGRAPHICLIB_GEODESICLINEEXACT_HPP)
11#define GEOGRAPHICLIB_GEODESICLINEEXACT_HPP 1
12
16
17namespace GeographicLib {
18
19 /**
20 * \brief An exact geodesic line
21 *
22 * GeodesicLineExact facilitates the determination of a series of points on a
23 * single geodesic. This is a companion to the GeodesicExact class. For
24 * additional information on this class see the documentation on the
25 * GeodesicLine class.
26 *
27 * Example of use:
28 * \include example-GeodesicLineExact.cpp
29 *
30 * <a href="GeodSolve.1.html">GeodSolve</a> is a command-line utility
31 * providing access to the functionality of GeodesicExact and
32 * GeodesicLineExact (via the -E option).
33 **********************************************************************/
34
36 private:
37 typedef Math::real real;
38 friend class GeodesicExact;
39 static const int nC4_ = GeodesicExact::nC4_;
40
41 real tiny_;
42 real _lat1, _lon1, _azi1;
43 real _a, _f, _b, _c2, _f1, _e2, _salp0, _calp0, _k2,
44 _salp1, _calp1, _ssig1, _csig1, _dn1, _stau1, _ctau1,
45 _somg1, _comg1, _cchi1,
46 _A4, _B41, _E0, _D0, _H0, _E1, _D1, _H1;
47 real _a13, _s13;
48 real _C4a[nC4_]; // all the elements of _C4a are used
50 unsigned _caps;
51
52 void LineInit(const GeodesicExact& g,
53 real lat1, real lon1,
54 real azi1, real salp1, real calp1,
55 unsigned caps);
57 real lat1, real lon1,
58 real azi1, real salp1, real calp1,
59 unsigned caps, bool arcmode, real s13_a13);
60
61 enum captype {
62 CAP_NONE = GeodesicExact::CAP_NONE,
63 CAP_E = GeodesicExact::CAP_E,
64 CAP_D = GeodesicExact::CAP_D,
65 CAP_H = GeodesicExact::CAP_H,
66 CAP_C4 = GeodesicExact::CAP_C4,
67 CAP_ALL = GeodesicExact::CAP_ALL,
68 CAP_MASK = GeodesicExact::CAP_MASK,
69 OUT_ALL = GeodesicExact::OUT_ALL,
70 OUT_MASK = GeodesicExact::OUT_MASK,
71 };
72 public:
73
74 /**
75 * Bit masks for what calculations to do. They signify to the
76 * GeodesicLineExact::GeodesicLineExact constructor and to
77 * GeodesicExact::Line what capabilities should be included in the
78 * GeodesicLineExact object. This is merely a duplication of
79 * GeodesicExact::mask.
80 **********************************************************************/
81 enum mask {
82 /**
83 * No capabilities, no output.
84 * @hideinitializer
85 **********************************************************************/
86 NONE = GeodesicExact::NONE,
87 /**
88 * Calculate latitude \e lat2. (It's not necessary to include this as a
89 * capability to GeodesicLineExact because this is included by default.)
90 * @hideinitializer
91 **********************************************************************/
92 LATITUDE = GeodesicExact::LATITUDE,
93 /**
94 * Calculate longitude \e lon2.
95 * @hideinitializer
96 **********************************************************************/
97 LONGITUDE = GeodesicExact::LONGITUDE,
98 /**
99 * Calculate azimuths \e azi1 and \e azi2. (It's not necessary to
100 * include this as a capability to GeodesicLineExact because this is
101 * included by default.)
102 * @hideinitializer
103 **********************************************************************/
104 AZIMUTH = GeodesicExact::AZIMUTH,
105 /**
106 * Calculate distance \e s12.
107 * @hideinitializer
108 **********************************************************************/
109 DISTANCE = GeodesicExact::DISTANCE,
110 /**
111 * Allow distance \e s12 to be used as input in the direct geodesic
112 * problem.
113 * @hideinitializer
114 **********************************************************************/
115 DISTANCE_IN = GeodesicExact::DISTANCE_IN,
116 /**
117 * Calculate reduced length \e m12.
118 * @hideinitializer
119 **********************************************************************/
120 REDUCEDLENGTH = GeodesicExact::REDUCEDLENGTH,
121 /**
122 * Calculate geodesic scales \e M12 and \e M21.
123 * @hideinitializer
124 **********************************************************************/
125 GEODESICSCALE = GeodesicExact::GEODESICSCALE,
126 /**
127 * Calculate area \e S12.
128 * @hideinitializer
129 **********************************************************************/
130 AREA = GeodesicExact::AREA,
131 /**
132 * Unroll \e lon2 in the direct calculation.
133 * @hideinitializer
134 **********************************************************************/
135 LONG_UNROLL = GeodesicExact::LONG_UNROLL,
136 /**
137 * All capabilities, calculate everything. (LONG_UNROLL is not
138 * included in this mask.)
139 * @hideinitializer
140 **********************************************************************/
141 ALL = GeodesicExact::ALL,
142 };
143
144 /** \name Constructors
145 **********************************************************************/
146 ///@{
147
148 /**
149 * Constructor for a geodesic line staring at latitude \e lat1, longitude
150 * \e lon1, and azimuth \e azi1 (all in degrees).
151 *
152 * @param[in] g A GeodesicExact object used to compute the necessary
153 * information about the GeodesicLineExact.
154 * @param[in] lat1 latitude of point 1 (degrees).
155 * @param[in] lon1 longitude of point 1 (degrees).
156 * @param[in] azi1 azimuth at point 1 (degrees).
157 * @param[in] caps bitor'ed combination of GeodesicLineExact::mask values
158 * specifying the capabilities the GeodesicLineExact object should
159 * possess, i.e., which quantities can be returned in calls to
160 * GeodesicLine::Position.
161 *
162 * \e lat1 should be in the range [&minus;90&deg;, 90&deg;].
163 *
164 * The GeodesicLineExact::mask values are
165 * - \e caps |= GeodesicLineExact::LATITUDE for the latitude \e lat2; this
166 * is added automatically;
167 * - \e caps |= GeodesicLineExact::LONGITUDE for the latitude \e lon2;
168 * - \e caps |= GeodesicLineExact::AZIMUTH for the latitude \e azi2; this
169 * is added automatically;
170 * - \e caps |= GeodesicLineExact::DISTANCE for the distance \e s12;
171 * - \e caps |= GeodesicLineExact::REDUCEDLENGTH for the reduced length \e
172 m12;
173 * - \e caps |= GeodesicLineExact::GEODESICSCALE for the geodesic scales \e
174 * M12 and \e M21;
175 * - \e caps |= GeodesicLineExact::AREA for the area \e S12;
176 * - \e caps |= GeodesicLineExact::DISTANCE_IN permits the length of the
177 * geodesic to be given in terms of \e s12; without this capability the
178 * length can only be specified in terms of arc length;
179 * - \e caps |= GeodesicLineExact::ALL for all of the above.
180 * .
181 * The default value of \e caps is GeodesicLineExact::ALL.
182 *
183 * If the point is at a pole, the azimuth is defined by keeping \e lon1
184 * fixed, writing \e lat1 = &plusmn;(90&deg; &minus; &epsilon;), and taking
185 * the limit &epsilon; &rarr; 0+.
186 **********************************************************************/
187 GeodesicLineExact(const GeodesicExact& g, real lat1, real lon1, real azi1,
188 unsigned caps = ALL);
189
190 /**
191 * A default constructor. If GeodesicLineExact::Position is called on the
192 * resulting object, it returns immediately (without doing any
193 * calculations). The object can be set with a call to
194 * GeodesicExact::Line. Use Init() to test whether object is still in this
195 * uninitialized state.
196 **********************************************************************/
197 GeodesicLineExact() : _caps(0U) {}
198 ///@}
199
200 /** \name Position in terms of distance
201 **********************************************************************/
202 ///@{
203
204 /**
205 * Compute the position of point 2 which is a distance \e s12 (meters)
206 * from point 1.
207 *
208 * @param[in] s12 distance from point 1 to point 2 (meters); it can be
209 * signed.
210 * @param[out] lat2 latitude of point 2 (degrees).
211 * @param[out] lon2 longitude of point 2 (degrees); requires that the
212 * GeodesicLineExact object was constructed with \e caps |=
213 * GeodesicLineExact::LONGITUDE.
214 * @param[out] azi2 (forward) azimuth at point 2 (degrees).
215 * @param[out] m12 reduced length of geodesic (meters); requires that the
216 * GeodesicLineExact object was constructed with \e caps |=
217 * GeodesicLineExact::REDUCEDLENGTH.
218 * @param[out] M12 geodesic scale of point 2 relative to point 1
219 * (dimensionless); requires that the GeodesicLineExact object was
220 * constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
221 * @param[out] M21 geodesic scale of point 1 relative to point 2
222 * (dimensionless); requires that the GeodesicLineExact object was
223 * constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
224 * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
225 * that the GeodesicLineExact object was constructed with \e caps |=
226 * GeodesicLineExact::AREA.
227 * @return \e a12 arc length from point 1 to point 2 (degrees).
228 *
229 * The values of \e lon2 and \e azi2 returned are in the range
230 * [&minus;180&deg;, 180&deg;].
231 *
232 * The GeodesicLineExact object \e must have been constructed with \e caps
233 * |= GeodesicLineExact::DISTANCE_IN; otherwise Math::NaN() is returned and
234 * no parameters are set. Requesting a value which the GeodesicLineExact
235 * object is not capable of computing is not an error; the corresponding
236 * argument will not be altered.
237 *
238 * The following functions are overloaded versions of
239 * GeodesicLineExact::Position which omit some of the output parameters.
240 * Note, however, that the arc length is always computed and returned as
241 * the function value.
242 **********************************************************************/
244 real& lat2, real& lon2, real& azi2,
245 real& m12, real& M12, real& M21,
246 real& S12) const {
247 real t;
248 return GenPosition(false, s12,
249 LATITUDE | LONGITUDE | AZIMUTH |
250 REDUCEDLENGTH | GEODESICSCALE | AREA,
251 lat2, lon2, azi2, t, m12, M12, M21, S12);
252 }
253
254 /**
255 * See the documentation for GeodesicLineExact::Position.
256 **********************************************************************/
257 Math::real Position(real s12, real& lat2, real& lon2) const {
258 real t;
259 return GenPosition(false, s12,
260 LATITUDE | LONGITUDE,
261 lat2, lon2, t, t, t, t, t, t);
262 }
263
264 /**
265 * See the documentation for GeodesicLineExact::Position.
266 **********************************************************************/
267 Math::real Position(real s12, real& lat2, real& lon2,
268 real& azi2) const {
269 real t;
270 return GenPosition(false, s12,
271 LATITUDE | LONGITUDE | AZIMUTH,
272 lat2, lon2, azi2, t, t, t, t, t);
273 }
274
275 /**
276 * See the documentation for GeodesicLineExact::Position.
277 **********************************************************************/
278 Math::real Position(real s12, real& lat2, real& lon2,
279 real& azi2, real& m12) const {
280 real t;
281 return GenPosition(false, s12,
282 LATITUDE | LONGITUDE |
283 AZIMUTH | REDUCEDLENGTH,
284 lat2, lon2, azi2, t, m12, t, t, t);
285 }
286
287 /**
288 * See the documentation for GeodesicLineExact::Position.
289 **********************************************************************/
290 Math::real Position(real s12, real& lat2, real& lon2,
291 real& azi2, real& M12, real& M21)
292 const {
293 real t;
294 return GenPosition(false, s12,
295 LATITUDE | LONGITUDE |
296 AZIMUTH | GEODESICSCALE,
297 lat2, lon2, azi2, t, t, M12, M21, t);
298 }
299
300 /**
301 * See the documentation for GeodesicLineExact::Position.
302 **********************************************************************/
304 real& lat2, real& lon2, real& azi2,
305 real& m12, real& M12, real& M21)
306 const {
307 real t;
308 return GenPosition(false, s12,
309 LATITUDE | LONGITUDE | AZIMUTH |
310 REDUCEDLENGTH | GEODESICSCALE,
311 lat2, lon2, azi2, t, m12, M12, M21, t);
312 }
313 ///@}
314
315 /** \name Position in terms of arc length
316 **********************************************************************/
317 ///@{
318
319 /**
320 * Compute the position of point 2 which is an arc length \e a12 (degrees)
321 * from point 1.
322 *
323 * @param[in] a12 arc length from point 1 to point 2 (degrees); it can
324 * be signed.
325 * @param[out] lat2 latitude of point 2 (degrees).
326 * @param[out] lon2 longitude of point 2 (degrees); requires that the
327 * GeodesicLineExact object was constructed with \e caps |=
328 * GeodesicLineExact::LONGITUDE.
329 * @param[out] azi2 (forward) azimuth at point 2 (degrees).
330 * @param[out] s12 distance from point 1 to point 2 (meters); requires
331 * that the GeodesicLineExact object was constructed with \e caps |=
332 * GeodesicLineExact::DISTANCE.
333 * @param[out] m12 reduced length of geodesic (meters); requires that the
334 * GeodesicLineExact object was constructed with \e caps |=
335 * GeodesicLineExact::REDUCEDLENGTH.
336 * @param[out] M12 geodesic scale of point 2 relative to point 1
337 * (dimensionless); requires that the GeodesicLineExact object was
338 * constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
339 * @param[out] M21 geodesic scale of point 1 relative to point 2
340 * (dimensionless); requires that the GeodesicLineExact object was
341 * constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
342 * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
343 * that the GeodesicLineExact object was constructed with \e caps |=
344 * GeodesicLineExact::AREA.
345 *
346 * The values of \e lon2 and \e azi2 returned are in the range
347 * [&minus;180&deg;, 180&deg;].
348 *
349 * Requesting a value which the GeodesicLineExact object is not capable of
350 * computing is not an error; the corresponding argument will not be
351 * altered.
352 *
353 * The following functions are overloaded versions of
354 * GeodesicLineExact::ArcPosition which omit some of the output parameters.
355 **********************************************************************/
356 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
357 real& s12, real& m12, real& M12, real& M21,
358 real& S12) const {
359 GenPosition(true, a12,
360 LATITUDE | LONGITUDE | AZIMUTH | DISTANCE |
361 REDUCEDLENGTH | GEODESICSCALE | AREA,
362 lat2, lon2, azi2, s12, m12, M12, M21, S12);
363 }
364
365 /**
366 * See the documentation for GeodesicLineExact::ArcPosition.
367 **********************************************************************/
368 void ArcPosition(real a12, real& lat2, real& lon2)
369 const {
370 real t;
371 GenPosition(true, a12,
372 LATITUDE | LONGITUDE,
373 lat2, lon2, t, t, t, t, t, t);
374 }
375
376 /**
377 * See the documentation for GeodesicLineExact::ArcPosition.
378 **********************************************************************/
379 void ArcPosition(real a12,
380 real& lat2, real& lon2, real& azi2)
381 const {
382 real t;
383 GenPosition(true, a12,
384 LATITUDE | LONGITUDE | AZIMUTH,
385 lat2, lon2, azi2, t, t, t, t, t);
386 }
387
388 /**
389 * See the documentation for GeodesicLineExact::ArcPosition.
390 **********************************************************************/
391 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
392 real& s12) const {
393 real t;
394 GenPosition(true, a12,
395 LATITUDE | LONGITUDE | AZIMUTH | DISTANCE,
396 lat2, lon2, azi2, s12, t, t, t, t);
397 }
398
399 /**
400 * See the documentation for GeodesicLineExact::ArcPosition.
401 **********************************************************************/
402 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
403 real& s12, real& m12) const {
404 real t;
405 GenPosition(true, a12,
406 LATITUDE | LONGITUDE | AZIMUTH |
407 DISTANCE | REDUCEDLENGTH,
408 lat2, lon2, azi2, s12, m12, t, t, t);
409 }
410
411 /**
412 * See the documentation for GeodesicLineExact::ArcPosition.
413 **********************************************************************/
414 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
415 real& s12, real& M12, real& M21)
416 const {
417 real t;
418 GenPosition(true, a12,
419 LATITUDE | LONGITUDE | AZIMUTH |
420 DISTANCE | GEODESICSCALE,
421 lat2, lon2, azi2, s12, t, M12, M21, t);
422 }
423
424 /**
425 * See the documentation for GeodesicLineExact::ArcPosition.
426 **********************************************************************/
427 void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
428 real& s12, real& m12, real& M12, real& M21)
429 const {
430 real t;
431 GenPosition(true, a12,
432 LATITUDE | LONGITUDE | AZIMUTH |
433 DISTANCE | REDUCEDLENGTH | GEODESICSCALE,
434 lat2, lon2, azi2, s12, m12, M12, M21, t);
435 }
436 ///@}
437
438 /** \name The general position function.
439 **********************************************************************/
440 ///@{
441
442 /**
443 * The general position function. GeodesicLineExact::Position and
444 * GeodesicLineExact::ArcPosition are defined in terms of this function.
445 *
446 * @param[in] arcmode boolean flag determining the meaning of the second
447 * parameter; if \e arcmode is false, then the GeodesicLineExact object
448 * must have been constructed with \e caps |=
449 * GeodesicLineExact::DISTANCE_IN.
450 * @param[in] s12_a12 if \e arcmode is false, this is the distance between
451 * point 1 and point 2 (meters); otherwise it is the arc length between
452 * point 1 and point 2 (degrees); it can be signed.
453 * @param[in] outmask a bitor'ed combination of GeodesicLineExact::mask
454 * values specifying which of the following parameters should be set.
455 * @param[out] lat2 latitude of point 2 (degrees).
456 * @param[out] lon2 longitude of point 2 (degrees); requires that the
457 * GeodesicLineExact object was constructed with \e caps |=
458 * GeodesicLineExact::LONGITUDE.
459 * @param[out] azi2 (forward) azimuth at point 2 (degrees).
460 * @param[out] s12 distance from point 1 to point 2 (meters); requires
461 * that the GeodesicLineExact object was constructed with \e caps |=
462 * GeodesicLineExact::DISTANCE.
463 * @param[out] m12 reduced length of geodesic (meters); requires that the
464 * GeodesicLineExact object was constructed with \e caps |=
465 * GeodesicLineExact::REDUCEDLENGTH.
466 * @param[out] M12 geodesic scale of point 2 relative to point 1
467 * (dimensionless); requires that the GeodesicLineExact object was
468 * constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
469 * @param[out] M21 geodesic scale of point 1 relative to point 2
470 * (dimensionless); requires that the GeodesicLineExact object was
471 * constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
472 * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
473 * that the GeodesicLineExact object was constructed with \e caps |=
474 * GeodesicLineExact::AREA.
475 * @return \e a12 arc length from point 1 to point 2 (degrees).
476 *
477 * The GeodesicLineExact::mask values possible for \e outmask are
478 * - \e outmask |= GeodesicLineExact::LATITUDE for the latitude \e lat2;
479 * - \e outmask |= GeodesicLineExact::LONGITUDE for the latitude \e lon2;
480 * - \e outmask |= GeodesicLineExact::AZIMUTH for the latitude \e azi2;
481 * - \e outmask |= GeodesicLineExact::DISTANCE for the distance \e s12;
482 * - \e outmask |= GeodesicLineExact::REDUCEDLENGTH for the reduced length
483 * \e m12;
484 * - \e outmask |= GeodesicLineExact::GEODESICSCALE for the geodesic scales
485 * \e M12 and \e M21;
486 * - \e outmask |= GeodesicLineExact::AREA for the area \e S12;
487 * - \e outmask |= GeodesicLineExact::ALL for all of the above;
488 * - \e outmask |= GeodesicLineExact::LONG_UNROLL to unroll \e lon2 instead
489 * of wrapping it into the range [&minus;180&deg;, 180&deg;].
490 * .
491 * Requesting a value which the GeodesicLineExact object is not capable of
492 * computing is not an error; the corresponding argument will not be
493 * altered. Note, however, that the arc length is always computed and
494 * returned as the function value.
495 *
496 * With the GeodesicLineExact::LONG_UNROLL bit set, the quantity \e lon2
497 * &minus; \e lon1 indicates how many times and in what sense the geodesic
498 * encircles the ellipsoid.
499 **********************************************************************/
500 Math::real GenPosition(bool arcmode, real s12_a12, unsigned outmask,
501 real& lat2, real& lon2, real& azi2,
502 real& s12, real& m12, real& M12, real& M21,
503 real& S12) const;
504 ///@}
505
506 /** \name Setting point 3
507 **********************************************************************/
508 ///@{
509
510 /**
511 * Specify position of point 3 in terms of distance.
512 *
513 * @param[in] s13 the distance from point 1 to point 3 (meters); it
514 * can be negative.
515 *
516 * This is only useful if the GeodesicLineExact object has been constructed
517 * with \e caps |= GeodesicLineExact::DISTANCE_IN.
518 **********************************************************************/
519 void SetDistance(real s13);
520
521 /**
522 * Specify position of point 3 in terms of arc length.
523 *
524 * @param[in] a13 the arc length from point 1 to point 3 (degrees); it
525 * can be negative.
526 *
527 * The distance \e s13 is only set if the GeodesicLineExact object has been
528 * constructed with \e caps |= GeodesicLineExact::DISTANCE.
529 **********************************************************************/
530 void SetArc(real a13);
531
532 /**
533 * Specify position of point 3 in terms of either distance or arc length.
534 *
535 * @param[in] arcmode boolean flag determining the meaning of the second
536 * parameter; if \e arcmode is false, then the GeodesicLineExact object
537 * must have been constructed with \e caps |=
538 * GeodesicLineExact::DISTANCE_IN.
539 * @param[in] s13_a13 if \e arcmode is false, this is the distance from
540 * point 1 to point 3 (meters); otherwise it is the arc length from
541 * point 1 to point 3 (degrees); it can be negative.
542 **********************************************************************/
543 void GenSetDistance(bool arcmode, real s13_a13);
544
545 /** \name Inspector functions
546 **********************************************************************/
547 ///@{
548
549 /**
550 * @return true if the object has been initialized.
551 **********************************************************************/
552 bool Init() const { return _caps != 0U; }
553
554 /**
555 * @return \e lat1 the latitude of point 1 (degrees).
556 **********************************************************************/
558 { return Init() ? _lat1 : Math::NaN(); }
559
560 /**
561 * @return \e lon1 the longitude of point 1 (degrees).
562 **********************************************************************/
564 { return Init() ? _lon1 : Math::NaN(); }
565
566 /**
567 * @return \e azi1 the azimuth (degrees) of the geodesic line at point 1.
568 **********************************************************************/
570 { return Init() ? _azi1 : Math::NaN(); }
571
572 /**
573 * The sine and cosine of \e azi1.
574 *
575 * @param[out] sazi1 the sine of \e azi1.
576 * @param[out] cazi1 the cosine of \e azi1.
577 **********************************************************************/
578 void Azimuth(real& sazi1, real& cazi1) const
579 { if (Init()) { sazi1 = _salp1; cazi1 = _calp1; } }
580
581 /**
582 * @return \e azi0 the azimuth (degrees) of the geodesic line as it crosses
583 * the equator in a northward direction.
584 *
585 * The result lies in [&minus;90&deg;, 90&deg;].
586 **********************************************************************/
588 { return Init() ? Math::atan2d(_salp0, _calp0) : Math::NaN(); }
589
590 /**
591 * The sine and cosine of \e azi0.
592 *
593 * @param[out] sazi0 the sine of \e azi0.
594 * @param[out] cazi0 the cosine of \e azi0.
595 **********************************************************************/
596 void EquatorialAzimuth(real& sazi0, real& cazi0) const
597 { if (Init()) { sazi0 = _salp0; cazi0 = _calp0; } }
598
599 /**
600 * @return \e a1 the arc length (degrees) between the northward equatorial
601 * crossing and point 1.
602 *
603 * The result lies in (&minus;180&deg;, 180&deg;].
604 **********************************************************************/
606 using std::atan2;
607 return Init() ? atan2(_ssig1, _csig1) / Math::degree() : Math::NaN();
608 }
609
610 /**
611 * @return \e a the equatorial radius of the ellipsoid (meters). This is
612 * the value inherited from the GeodesicExact object used in the
613 * constructor.
614 **********************************************************************/
616 { return Init() ? _a : Math::NaN(); }
617
618 /**
619 * @return \e f the flattening of the ellipsoid. This is the value
620 * inherited from the GeodesicExact object used in the constructor.
621 **********************************************************************/
623 { return Init() ? _f : Math::NaN(); }
624
625 /**
626 * @return \e caps the computational capabilities that this object was
627 * constructed with. LATITUDE and AZIMUTH are always included.
628 **********************************************************************/
629 unsigned Capabilities() const { return _caps; }
630
631 /**
632 * Test what capabilities are available.
633 *
634 * @param[in] testcaps a set of bitor'ed GeodesicLineExact::mask values.
635 * @return true if the GeodesicLineExact object has all these capabilities.
636 **********************************************************************/
637 bool Capabilities(unsigned testcaps) const {
638 testcaps &= OUT_ALL;
639 return (_caps & testcaps) == testcaps;
640 }
641
642 /**
643 * The distance or arc length to point 3.
644 *
645 * @param[in] arcmode boolean flag determining the meaning of returned
646 * value.
647 * @return \e s13 if \e arcmode is false; \e a13 if \e arcmode is true.
648 **********************************************************************/
649 Math::real GenDistance(bool arcmode) const
650 { return Init() ? (arcmode ? _a13 : _s13) : Math::NaN(); }
651
652 /**
653 * @return \e s13, the distance to point 3 (meters).
654 **********************************************************************/
655 Math::real Distance() const { return GenDistance(false); }
656
657 /**
658 * @return \e a13, the arc length to point 3 (degrees).
659 **********************************************************************/
660 Math::real Arc() const { return GenDistance(true); }
661
662 /**
663 * \deprecated An old name for EquatorialRadius().
664 **********************************************************************/
665 GEOGRAPHICLIB_DEPRECATED("Use EquatorialRadius()")
666 Math::real MajorRadius() const { return EquatorialRadius(); }
667 ///@}
668
669 };
670
671} // namespace GeographicLib
672
673#endif // GEOGRAPHICLIB_GEODESICLINEEXACT_HPP
Header for GeographicLib::Constants class.
#define GEOGRAPHICLIB_EXPORT
Definition: Constants.hpp:66
#define GEOGRAPHICLIB_DEPRECATED(msg)
Definition: Constants.hpp:81
Header for GeographicLib::EllipticFunction class.
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
Header for GeographicLib::GeodesicExact class.
Elliptic integrals and functions.
Exact geodesic calculations.
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2) const
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12) const
void EquatorialAzimuth(real &sazi0, real &cazi0) const
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const
void ArcPosition(real a12, real &lat2, real &lon2) const
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const
Math::real GenDistance(bool arcmode) const
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const
Math::real Position(real s12, real &lat2, real &lon2) const
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const
bool Capabilities(unsigned testcaps) const
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21) const
void Azimuth(real &sazi1, real &cazi1) const
Math::real Position(real s12, real &lat2, real &lon2, real &azi2) const
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12) const
Mathematical functions needed by GeographicLib.
Definition: Math.hpp:76
Namespace for GeographicLib.
Definition: Accumulator.cpp:12