GeographicLib  1.46
GeodesicLine.hpp
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1 /**
2  * \file GeodesicLine.hpp
3  * \brief Header for GeographicLib::GeodesicLine class
4  *
7  * http://geographiclib.sourceforge.net/
8  **********************************************************************/
9
10 #if !defined(GEOGRAPHICLIB_GEODESICLINE_HPP)
11 #define GEOGRAPHICLIB_GEODESICLINE_HPP 1
12
15
16 namespace GeographicLib {
17
18  /**
19  * \brief A geodesic line
20  *
21  * GeodesicLine facilitates the determination of a series of points on a
22  * single geodesic. The starting point (\e lat1, \e lon1) and the azimuth \e
23  * azi1 are specified in the constructor; alternatively, the Geodesic::Line
24  * method can be used to create a GeodesicLine. GeodesicLine.Position
25  * returns the location of point 2 a distance \e s12 along the geodesic. In
26  * addition, GeodesicLine.ArcPosition gives the position of point 2 an arc
27  * length \e a12 along the geodesic.
28  *
29  * You can register the position of a reference point 3 a distance (arc
30  * length), \e s13 (\e a13) along the geodesic with the
31  * GeodesicLine.SetDistance (GeodesicLine.SetArc) functions. Points a
32  * fractional distance along the line can be found by providing, for example,
33  * 0.5 * Distance() as an argument to GeodesicLine.Position. The
34  * Geodesic::InverseLine or Geodesic::DirectLine methods return GeodesicLine
35  * objects with point 3 set to the point 2 of the corresponding geodesic
36  * problem. GeodesicLine objects created with the public constructor or with
37  * Geodesic::Line have \e s13 and \e a13 set to NaNs.
38  *
39  * The default copy constructor and assignment operators work with this
40  * class. Similarly, a vector can be used to hold GeodesicLine objects.
41  *
42  * The calculations are accurate to better than 15 nm (15 nanometers). See
43  * Sec. 9 of
44  * <a href="http://arxiv.org/abs/1102.1215v1">arXiv:1102.1215v1</a> for
45  * details. The algorithms used by this class are based on series expansions
46  * using the flattening \e f as a small parameter. These are only accurate
47  * for |<i>f</i>| &lt; 0.02; however reasonably accurate results will be
48  * obtained for |<i>f</i>| &lt; 0.2. For very eccentric ellipsoids, use
50  *
51  * The algorithms are described in
52  * - C. F. F. Karney,
53  * <a href="https://dx.doi.org/10.1007/s00190-012-0578-z">
54  * Algorithms for geodesics</a>,
55  * J. Geodesy <b>87</b>, 43--55 (2013);
56  * DOI: <a href="https://dx.doi.org/10.1007/s00190-012-0578-z">
57  * 10.1007/s00190-012-0578-z</a>;
60  * .
62  *
63  * Example of use:
64  * \include example-GeodesicLine.cpp
65  *
66  * <a href="GeodSolve.1.html">GeodSolve</a> is a command-line utility
68  **********************************************************************/
69
71  private:
72  typedef Math::real real;
73  friend class Geodesic;
74  static const int nC1_ = Geodesic::nC1_;
75  static const int nC1p_ = Geodesic::nC1p_;
76  static const int nC2_ = Geodesic::nC2_;
77  static const int nC3_ = Geodesic::nC3_;
78  static const int nC4_ = Geodesic::nC4_;
79
80  real tiny_;
81  real _lat1, _lon1, _azi1;
82  real _a, _f, _b, _c2, _f1, _salp0, _calp0, _k2,
83  _salp1, _calp1, _ssig1, _csig1, _dn1, _stau1, _ctau1, _somg1, _comg1,
84  _A1m1, _A2m1, _A3c, _B11, _B21, _B31, _A4, _B41;
85  real _a13, _s13;
86  // index zero elements of _C1a, _C1pa, _C2a, _C3a are unused
87  real _C1a[nC1_ + 1], _C1pa[nC1p_ + 1], _C2a[nC2_ + 1], _C3a[nC3_],
88  _C4a[nC4_]; // all the elements of _C4a are used
89  unsigned _caps;
90
91  void LineInit(const Geodesic& g,
92  real lat1, real lon1,
93  real azi1, real salp1, real calp1,
94  unsigned caps);
95  GeodesicLine(const Geodesic& g,
96  real lat1, real lon1,
97  real azi1, real salp1, real calp1,
98  unsigned caps, bool arcmode, real s13_a13);
99
100  enum captype {
101  CAP_NONE = Geodesic::CAP_NONE,
102  CAP_C1 = Geodesic::CAP_C1,
103  CAP_C1p = Geodesic::CAP_C1p,
104  CAP_C2 = Geodesic::CAP_C2,
105  CAP_C3 = Geodesic::CAP_C3,
106  CAP_C4 = Geodesic::CAP_C4,
107  CAP_ALL = Geodesic::CAP_ALL,
109  OUT_ALL = Geodesic::OUT_ALL,
111  };
112  public:
113
114  /**
115  * Bit masks for what calculations to do. They signify to the
116  * GeodesicLine::GeodesicLine constructor and to Geodesic::Line what
117  * capabilities should be included in the GeodesicLine object. This is
118  * merely a duplication of Geodesic::mask.
119  **********************************************************************/
121  /**
122  * No capabilities, no output.
123  * @hideinitializer
124  **********************************************************************/
126  /**
127  * Calculate latitude \e lat2. (It's not necessary to include this as a
128  * capability to GeodesicLine because this is included by default.)
129  * @hideinitializer
130  **********************************************************************/
131  LATITUDE = Geodesic::LATITUDE,
132  /**
133  * Calculate longitude \e lon2.
134  * @hideinitializer
135  **********************************************************************/
136  LONGITUDE = Geodesic::LONGITUDE,
137  /**
138  * Calculate azimuths \e azi1 and \e azi2. (It's not necessary to
139  * include this as a capability to GeodesicLine because this is included
140  * by default.)
141  * @hideinitializer
142  **********************************************************************/
143  AZIMUTH = Geodesic::AZIMUTH,
144  /**
145  * Calculate distance \e s12.
146  * @hideinitializer
147  **********************************************************************/
148  DISTANCE = Geodesic::DISTANCE,
149  /**
150  * Allow distance \e s12 to be used as input in the direct geodesic
151  * problem.
152  * @hideinitializer
153  **********************************************************************/
154  DISTANCE_IN = Geodesic::DISTANCE_IN,
155  /**
156  * Calculate reduced length \e m12.
157  * @hideinitializer
158  **********************************************************************/
159  REDUCEDLENGTH = Geodesic::REDUCEDLENGTH,
160  /**
161  * Calculate geodesic scales \e M12 and \e M21.
162  * @hideinitializer
163  **********************************************************************/
164  GEODESICSCALE = Geodesic::GEODESICSCALE,
165  /**
166  * Calculate area \e S12.
167  * @hideinitializer
168  **********************************************************************/
170  /**
171  * Unroll \e lon2 in the direct calculation.
172  * @hideinitializer
173  **********************************************************************/
174  LONG_UNROLL = Geodesic::LONG_UNROLL,
175  /**
176  * All capabilities, calculate everything. (LONG_UNROLL is not
177  * included in this mask.)
178  * @hideinitializer
179  **********************************************************************/
181  };
182
183  /** \name Constructors
184  **********************************************************************/
185  ///@{
186
187  /**
188  * Constructor for a geodesic line staring at latitude \e lat1, longitude
189  * \e lon1, and azimuth \e azi1 (all in degrees).
190  *
191  * @param[in] g A Geodesic object used to compute the necessary information
193  * @param[in] lat1 latitude of point 1 (degrees).
194  * @param[in] lon1 longitude of point 1 (degrees).
195  * @param[in] azi1 azimuth at point 1 (degrees).
196  * @param[in] caps bitor'ed combination of GeodesicLine::mask values
197  * specifying the capabilities the GeodesicLine object should possess,
198  * i.e., which quantities can be returned in calls to
199  * GeodesicLine::Position.
200  *
201  * \e lat1 should be in the range [&minus;90&deg;, 90&deg;].
202  *
203  * The GeodesicLine::mask values are
204  * - \e caps |= GeodesicLine::LATITUDE for the latitude \e lat2; this is
206  * - \e caps |= GeodesicLine::LONGITUDE for the latitude \e lon2;
207  * - \e caps |= GeodesicLine::AZIMUTH for the latitude \e azi2; this is
209  * - \e caps |= GeodesicLine::DISTANCE for the distance \e s12;
210  * - \e caps |= GeodesicLine::REDUCEDLENGTH for the reduced length \e m12;
211  * - \e caps |= GeodesicLine::GEODESICSCALE for the geodesic scales \e M12
212  * and \e M21;
213  * - \e caps |= GeodesicLine::AREA for the area \e S12;
214  * - \e caps |= GeodesicLine::DISTANCE_IN permits the length of the
215  * geodesic to be given in terms of \e s12; without this capability the
216  * length can only be specified in terms of arc length;
217  * - \e caps |= GeodesicLine::ALL for all of the above.
218  * .
219  * The default value of \e caps is GeodesicLine::ALL.
220  *
221  * If the point is at a pole, the azimuth is defined by keeping \e lon1
222  * fixed, writing \e lat1 = &plusmn;(90&deg; &minus; &epsilon;), and taking
223  * the limit &epsilon; &rarr; 0+.
224  **********************************************************************/
225  GeodesicLine(const Geodesic& g, real lat1, real lon1, real azi1,
226  unsigned caps = ALL);
227
228  /**
229  * A default constructor. If GeodesicLine::Position is called on the
230  * resulting object, it returns immediately (without doing any
231  * calculations). The object can be set with a call to Geodesic::Line.
232  * Use Init() to test whether object is still in this uninitialized state.
233  **********************************************************************/
234  GeodesicLine() : _caps(0U) {}
235  ///@}
236
237  /** \name Position in terms of distance
238  **********************************************************************/
239  ///@{
240
241  /**
242  * Compute the position of point 2 which is a distance \e s12 (meters) from
243  * point 1.
244  *
245  * @param[in] s12 distance from point 1 to point 2 (meters); it can be
246  * negative.
247  * @param[out] lat2 latitude of point 2 (degrees).
248  * @param[out] lon2 longitude of point 2 (degrees); requires that the
249  * GeodesicLine object was constructed with \e caps |=
250  * GeodesicLine::LONGITUDE.
251  * @param[out] azi2 (forward) azimuth at point 2 (degrees).
252  * @param[out] m12 reduced length of geodesic (meters); requires that the
253  * GeodesicLine object was constructed with \e caps |=
254  * GeodesicLine::REDUCEDLENGTH.
255  * @param[out] M12 geodesic scale of point 2 relative to point 1
256  * (dimensionless); requires that the GeodesicLine object was constructed
257  * with \e caps |= GeodesicLine::GEODESICSCALE.
258  * @param[out] M21 geodesic scale of point 1 relative to point 2
259  * (dimensionless); requires that the GeodesicLine object was constructed
260  * with \e caps |= GeodesicLine::GEODESICSCALE.
261  * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
262  * that the GeodesicLine object was constructed with \e caps |=
263  * GeodesicLine::AREA.
264  * @return \e a12 arc length from point 1 to point 2 (degrees).
265  *
266  * The values of \e lon2 and \e azi2 returned are in the range
267  * [&minus;180&deg;, 180&deg;).
268  *
269  * The GeodesicLine object \e must have been constructed with \e caps |=
270  * GeodesicLine::DISTANCE_IN; otherwise Math::NaN() is returned and no
271  * parameters are set. Requesting a value which the GeodesicLine object is
272  * not capable of computing is not an error; the corresponding argument
273  * will not be altered.
274  *
275  * The following functions are overloaded versions of
276  * GeodesicLine::Position which omit some of the output parameters. Note,
277  * however, that the arc length is always computed and returned as the
278  * function value.
279  **********************************************************************/
281  real& lat2, real& lon2, real& azi2,
282  real& m12, real& M12, real& M21,
283  real& S12) const {
284  real t;
285  return GenPosition(false, s12,
286  LATITUDE | LONGITUDE | AZIMUTH |
287  REDUCEDLENGTH | GEODESICSCALE | AREA,
288  lat2, lon2, azi2, t, m12, M12, M21, S12);
289  }
290
291  /**
292  * See the documentation for GeodesicLine::Position.
293  **********************************************************************/
294  Math::real Position(real s12, real& lat2, real& lon2) const {
295  real t;
296  return GenPosition(false, s12,
297  LATITUDE | LONGITUDE,
298  lat2, lon2, t, t, t, t, t, t);
299  }
300
301  /**
302  * See the documentation for GeodesicLine::Position.
303  **********************************************************************/
304  Math::real Position(real s12, real& lat2, real& lon2,
305  real& azi2) const {
306  real t;
307  return GenPosition(false, s12,
308  LATITUDE | LONGITUDE | AZIMUTH,
309  lat2, lon2, azi2, t, t, t, t, t);
310  }
311
312  /**
313  * See the documentation for GeodesicLine::Position.
314  **********************************************************************/
315  Math::real Position(real s12, real& lat2, real& lon2,
316  real& azi2, real& m12) const {
317  real t;
318  return GenPosition(false, s12,
319  LATITUDE | LONGITUDE |
320  AZIMUTH | REDUCEDLENGTH,
321  lat2, lon2, azi2, t, m12, t, t, t);
322  }
323
324  /**
325  * See the documentation for GeodesicLine::Position.
326  **********************************************************************/
327  Math::real Position(real s12, real& lat2, real& lon2,
328  real& azi2, real& M12, real& M21)
329  const {
330  real t;
331  return GenPosition(false, s12,
332  LATITUDE | LONGITUDE |
333  AZIMUTH | GEODESICSCALE,
334  lat2, lon2, azi2, t, t, M12, M21, t);
335  }
336
337  /**
338  * See the documentation for GeodesicLine::Position.
339  **********************************************************************/
341  real& lat2, real& lon2, real& azi2,
342  real& m12, real& M12, real& M21)
343  const {
344  real t;
345  return GenPosition(false, s12,
346  LATITUDE | LONGITUDE | AZIMUTH |
347  REDUCEDLENGTH | GEODESICSCALE,
348  lat2, lon2, azi2, t, m12, M12, M21, t);
349  }
350  ///@}
351
352  /** \name Position in terms of arc length
353  **********************************************************************/
354  ///@{
355
356  /**
357  * Compute the position of point 2 which is an arc length \e a12 (degrees)
358  * from point 1.
359  *
360  * @param[in] a12 arc length from point 1 to point 2 (degrees); it can
361  * be negative.
362  * @param[out] lat2 latitude of point 2 (degrees).
363  * @param[out] lon2 longitude of point 2 (degrees); requires that the
364  * GeodesicLine object was constructed with \e caps |=
365  * GeodesicLine::LONGITUDE.
366  * @param[out] azi2 (forward) azimuth at point 2 (degrees).
367  * @param[out] s12 distance from point 1 to point 2 (meters); requires
368  * that the GeodesicLine object was constructed with \e caps |=
369  * GeodesicLine::DISTANCE.
370  * @param[out] m12 reduced length of geodesic (meters); requires that the
371  * GeodesicLine object was constructed with \e caps |=
372  * GeodesicLine::REDUCEDLENGTH.
373  * @param[out] M12 geodesic scale of point 2 relative to point 1
374  * (dimensionless); requires that the GeodesicLine object was constructed
375  * with \e caps |= GeodesicLine::GEODESICSCALE.
376  * @param[out] M21 geodesic scale of point 1 relative to point 2
377  * (dimensionless); requires that the GeodesicLine object was constructed
378  * with \e caps |= GeodesicLine::GEODESICSCALE.
379  * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
380  * that the GeodesicLine object was constructed with \e caps |=
381  * GeodesicLine::AREA.
382  *
383  * The values of \e lon2 and \e azi2 returned are in the range
384  * [&minus;180&deg;, 180&deg;).
385  *
386  * Requesting a value which the GeodesicLine object is not capable of
387  * computing is not an error; the corresponding argument will not be
388  * altered.
389  *
390  * The following functions are overloaded versions of
391  * GeodesicLine::ArcPosition which omit some of the output parameters.
392  **********************************************************************/
393  void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
394  real& s12, real& m12, real& M12, real& M21,
395  real& S12) const {
396  GenPosition(true, a12,
397  LATITUDE | LONGITUDE | AZIMUTH | DISTANCE |
398  REDUCEDLENGTH | GEODESICSCALE | AREA,
399  lat2, lon2, azi2, s12, m12, M12, M21, S12);
400  }
401
402  /**
403  * See the documentation for GeodesicLine::ArcPosition.
404  **********************************************************************/
405  void ArcPosition(real a12, real& lat2, real& lon2)
406  const {
407  real t;
408  GenPosition(true, a12,
409  LATITUDE | LONGITUDE,
410  lat2, lon2, t, t, t, t, t, t);
411  }
412
413  /**
414  * See the documentation for GeodesicLine::ArcPosition.
415  **********************************************************************/
416  void ArcPosition(real a12,
417  real& lat2, real& lon2, real& azi2)
418  const {
419  real t;
420  GenPosition(true, a12,
421  LATITUDE | LONGITUDE | AZIMUTH,
422  lat2, lon2, azi2, t, t, t, t, t);
423  }
424
425  /**
426  * See the documentation for GeodesicLine::ArcPosition.
427  **********************************************************************/
428  void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
429  real& s12) const {
430  real t;
431  GenPosition(true, a12,
432  LATITUDE | LONGITUDE | AZIMUTH | DISTANCE,
433  lat2, lon2, azi2, s12, t, t, t, t);
434  }
435
436  /**
437  * See the documentation for GeodesicLine::ArcPosition.
438  **********************************************************************/
439  void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
440  real& s12, real& m12) const {
441  real t;
442  GenPosition(true, a12,
443  LATITUDE | LONGITUDE | AZIMUTH |
444  DISTANCE | REDUCEDLENGTH,
445  lat2, lon2, azi2, s12, m12, t, t, t);
446  }
447
448  /**
449  * See the documentation for GeodesicLine::ArcPosition.
450  **********************************************************************/
451  void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
452  real& s12, real& M12, real& M21)
453  const {
454  real t;
455  GenPosition(true, a12,
456  LATITUDE | LONGITUDE | AZIMUTH |
457  DISTANCE | GEODESICSCALE,
458  lat2, lon2, azi2, s12, t, M12, M21, t);
459  }
460
461  /**
462  * See the documentation for GeodesicLine::ArcPosition.
463  **********************************************************************/
464  void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
465  real& s12, real& m12, real& M12, real& M21)
466  const {
467  real t;
468  GenPosition(true, a12,
469  LATITUDE | LONGITUDE | AZIMUTH |
470  DISTANCE | REDUCEDLENGTH | GEODESICSCALE,
471  lat2, lon2, azi2, s12, m12, M12, M21, t);
472  }
473  ///@}
474
475  /** \name The general position function.
476  **********************************************************************/
477  ///@{
478
479  /**
480  * The general position function. GeodesicLine::Position and
481  * GeodesicLine::ArcPosition are defined in terms of this function.
482  *
483  * @param[in] arcmode boolean flag determining the meaning of the second
484  * parameter; if \e arcmode is false, then the GeodesicLine object must
485  * have been constructed with \e caps |= GeodesicLine::DISTANCE_IN.
486  * @param[in] s12_a12 if \e arcmode is false, this is the distance between
487  * point 1 and point 2 (meters); otherwise it is the arc length between
488  * point 1 and point 2 (degrees); it can be negative.
490  * specifying which of the following parameters should be set.
491  * @param[out] lat2 latitude of point 2 (degrees).
492  * @param[out] lon2 longitude of point 2 (degrees); requires that the
493  * GeodesicLine object was constructed with \e caps |=
494  * GeodesicLine::LONGITUDE.
495  * @param[out] azi2 (forward) azimuth at point 2 (degrees).
496  * @param[out] s12 distance from point 1 to point 2 (meters); requires
497  * that the GeodesicLine object was constructed with \e caps |=
498  * GeodesicLine::DISTANCE.
499  * @param[out] m12 reduced length of geodesic (meters); requires that the
500  * GeodesicLine object was constructed with \e caps |=
501  * GeodesicLine::REDUCEDLENGTH.
502  * @param[out] M12 geodesic scale of point 2 relative to point 1
503  * (dimensionless); requires that the GeodesicLine object was constructed
504  * with \e caps |= GeodesicLine::GEODESICSCALE.
505  * @param[out] M21 geodesic scale of point 1 relative to point 2
506  * (dimensionless); requires that the GeodesicLine object was constructed
507  * with \e caps |= GeodesicLine::GEODESICSCALE.
508  * @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
509  * that the GeodesicLine object was constructed with \e caps |=
510  * GeodesicLine::AREA.
511  * @return \e a12 arc length from point 1 to point 2 (degrees).
512  *
514  * - \e outmask |= GeodesicLine::LATITUDE for the latitude \e lat2;
515  * - \e outmask |= GeodesicLine::LONGITUDE for the latitude \e lon2;
516  * - \e outmask |= GeodesicLine::AZIMUTH for the latitude \e azi2;
517  * - \e outmask |= GeodesicLine::DISTANCE for the distance \e s12;
518  * - \e outmask |= GeodesicLine::REDUCEDLENGTH for the reduced length \e
519  * m12;
520  * - \e outmask |= GeodesicLine::GEODESICSCALE for the geodesic scales \e
521  * M12 and \e M21;
522  * - \e outmask |= GeodesicLine::AREA for the area \e S12;
523  * - \e outmask |= GeodesicLine::ALL for all of the above;
524  * - \e outmask |= GeodesicLine::LONG_UNROLL to unroll \e lon2 instead of
525  * reducing it into the range [&minus;180&deg;, 180&deg;).
526  * .
527  * Requesting a value which the GeodesicLine object is not capable of
528  * computing is not an error; the corresponding argument will not be
529  * altered. Note, however, that the arc length is always computed and
530  * returned as the function value.
531  *
532  * With the GeodesicLine::LONG_UNROLL bit set, the quantity \e lon2 &minus;
533  * \e lon1 indicates how many times and in what sense the geodesic
534  * encircles the ellipsoid.
535  **********************************************************************/
536  Math::real GenPosition(bool arcmode, real s12_a12, unsigned outmask,
537  real& lat2, real& lon2, real& azi2,
538  real& s12, real& m12, real& M12, real& M21,
539  real& S12) const;
540  ///@}
541
542  /** \name Setting point 3
543  **********************************************************************/
544  ///@{
545
546  /**
547  * Specify position of point 3 in terms of distance.
548  *
549  * @param[in] s13 the distance from point 1 to point 3 (meters); it
550  * can be negative.
551  *
552  * This is only useful if the GeodesicLine object has been constructed
553  * with \e caps |= GeodesicLine::DISTANCE_IN.
554  **********************************************************************/
555  void SetDistance(real s13);
556
557  /**
558  * Specify position of point 3 in terms of arc length.
559  *
560  * @param[in] a13 the arc length from point 1 to point 3 (degrees); it
561  * can be negative.
562  *
563  * The distance \e s13 is only set if the GeodesicLine object has been
564  * constructed with \e caps |= GeodesicLine::DISTANCE.
565  **********************************************************************/
566  void SetArc(real a13);
567
568  /**
569  * Specify position of point 3 in terms of either distance or arc length.
570  *
571  * @param[in] arcmode boolean flag determining the meaning of the second
572  * parameter; if \e arcmode is false, then the GeodesicLine object must
573  * have been constructed with \e caps |= GeodesicLine::DISTANCE_IN.
574  * @param[in] s13_a13 if \e arcmode is false, this is the distance from
575  * point 1 to point 3 (meters); otherwise it is the arc length from
576  * point 1 to point 3 (degrees); it can be negative.
577  **********************************************************************/
578  void GenSetDistance(bool arcmode, real s13_a13);
579  ///@}
580
581  /** \name Inspector functions
582  **********************************************************************/
583  ///@{
584
585  /**
586  * @return true if the object has been initialized.
587  **********************************************************************/
588  bool Init() const { return _caps != 0U; }
589
590  /**
591  * @return \e lat1 the latitude of point 1 (degrees).
592  **********************************************************************/
594  { return Init() ? _lat1 : Math::NaN(); }
595
596  /**
597  * @return \e lon1 the longitude of point 1 (degrees).
598  **********************************************************************/
600  { return Init() ? _lon1 : Math::NaN(); }
601
602  /**
603  * @return \e azi1 the azimuth (degrees) of the geodesic line at point 1.
604  **********************************************************************/
606  { return Init() ? _azi1 : Math::NaN(); }
607
608  /**
609  * The sine and cosine of \e azi1.
610  *
611  * @param[out] sazi1 the sine of \e azi1.
612  * @param[out] cazi1 the cosine of \e azi1.
613  **********************************************************************/
614  void Azimuth(real& sazi1, real& cazi1) const
615  { if (Init()) { sazi1 = _salp1; cazi1 = _calp1; } }
616
617  /**
618  * @return \e azi0 the azimuth (degrees) of the geodesic line as it crosses
619  * the equator in a northward direction.
620  *
621  * The result lies in [&minus;90&deg;, 90&deg;].
622  **********************************************************************/
624  { return Init() ? Math::atan2d(_salp0, _calp0) : Math::NaN(); }
625
626  /**
627  * The sine and cosine of \e azi0.
628  *
629  * @param[out] sazi0 the sine of \e azi0.
630  * @param[out] cazi0 the cosine of \e azi0.
631  **********************************************************************/
632  void EquatorialAzimuth(real& sazi0, real& cazi0) const
633  { if (Init()) { sazi0 = _salp0; cazi0 = _calp0; } }
634
635  /**
636  * @return \e a1 the arc length (degrees) between the northward equatorial
637  * crossing and point 1.
638  *
639  * The result lies in (&minus;180&deg;, 180&deg;].
640  **********************************************************************/
642  return Init() ? Math::atan2d(_ssig1, _csig1) : Math::NaN();
643  }
644
645  /**
646  * @return \e a the equatorial radius of the ellipsoid (meters). This is
647  * the value inherited from the Geodesic object used in the constructor.
648  **********************************************************************/
650  { return Init() ? _a : Math::NaN(); }
651
652  /**
653  * @return \e f the flattening of the ellipsoid. This is the value
654  * inherited from the Geodesic object used in the constructor.
655  **********************************************************************/
657  { return Init() ? _f : Math::NaN(); }
658
659  /**
660  * @return \e caps the computational capabilities that this object was
661  * constructed with. LATITUDE and AZIMUTH are always included.
662  **********************************************************************/
663  unsigned Capabilities() const { return _caps; }
664
665  /**
666  * Test what capabilities are available.
667  *
668  * @param[in] testcaps a set of bitor'ed GeodesicLine::mask values.
669  * @return true if the GeodesicLine object has all these capabilities.
670  **********************************************************************/
671  bool Capabilities(unsigned testcaps) const {
672  testcaps &= OUT_ALL;
673  return (_caps & testcaps) == testcaps;
674  }
675
676  /**
677  * The distance or arc length to point 3.
678  *
679  * @param[in] arcmode boolean flag determining the meaning of returned
680  * value.
681  * @return \e s13 if \e arcmode is false; \e a13 if \e arcmode is true.
682  **********************************************************************/
683  Math::real GenDistance(bool arcmode) const
684  { return Init() ? (arcmode ? _a13 : _s13) : Math::NaN(); }
685
686  /**
687  * @return \e s13, the distance to point 3 (meters).
688  **********************************************************************/
689  Math::real Distance() const { return GenDistance(false); }
690
691  /**
692  * @return \e a13, the arc length to point 3 (degrees).
693  **********************************************************************/
694  Math::real Arc() const { return GenDistance(true); }
695  ///@}
696
697  };
698
699 } // namespace GeographicLib
700
701 #endif // GEOGRAPHICLIB_GEODESICLINE_HPP
Math::real Position(real s12, real &lat2, real &lon2, real &azi2) const
static T NaN()
Definition: Math.hpp:805
#define GEOGRAPHICLIB_EXPORT
Definition: Constants.hpp:90
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
Math::real Arc() 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) const
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12) const
Math::real Distance() const
Math::real Flattening() 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) const
void ArcPosition(real a12, real &lat2, real &lon2) const
static T atan2d(T y, T x)
Definition: Math.hpp:671
Math::real Longitude() const
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
Math::real EquatorialArc() const
Math::real Latitude() const
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const
void Azimuth(real &sazi1, real &cazi1) const
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12) const
unsigned Capabilities() const
Math::real Azimuth() const
bool Capabilities(unsigned testcaps) const
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const