GeographicLib  1.46
SphericalHarmonic2.hpp
Go to the documentation of this file.
1 /**
2  * \file SphericalHarmonic2.hpp
3  * \brief Header for GeographicLib::SphericalHarmonic2 class
4  *
5  * Copyright (c) Charles Karney (2011-2012) <charles@karney.com> and licensed
6  * under the MIT/X11 License. For more information, see
7  * http://geographiclib.sourceforge.net/
8  **********************************************************************/
9 
10 #if !defined(GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP)
11 #define GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP 1
12 
13 #include <vector>
17 
18 namespace GeographicLib {
19 
20  /**
21  * \brief Spherical harmonic series with two corrections to the coefficients
22  *
23  * This classes is similar to SphericalHarmonic, except that the coefficients
24  * <i>C</i><sub><i>nm</i></sub> are replaced by
25  * <i>C</i><sub><i>nm</i></sub> + \e tau' <i>C'</i><sub><i>nm</i></sub> + \e
26  * tau'' <i>C''</i><sub><i>nm</i></sub> (and similarly for
27  * <i>S</i><sub><i>nm</i></sub>).
28  *
29  * Example of use:
30  * \include example-SphericalHarmonic2.cpp
31  **********************************************************************/
32 
33  // Don't include the GEOGRPAHIC_EXPORT because this header-only class isn't
34  // used by any other classes in the library.
35  class /*GEOGRAPHICLIB_EXPORT*/ SphericalHarmonic2 {
36  public:
37  /**
38  * Supported normalizations for associate Legendre polynomials.
39  **********************************************************************/
41  /**
42  * Fully normalized associated Legendre polynomials. See
43  * SphericalHarmonic::FULL for documentation.
44  *
45  * @hideinitializer
46  **********************************************************************/
48  /**
49  * Schmidt semi-normalized associated Legendre polynomials. See
50  * SphericalHarmonic::SCHMIDT for documentation.
51  *
52  * @hideinitializer
53  **********************************************************************/
55  };
56 
57  private:
58  typedef Math::real real;
60  real _a;
61  unsigned _norm;
62 
63  public:
64  /**
65  * Constructor with a full set of coefficients specified.
66  *
67  * @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
68  * @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
69  * @param[in] N the maximum degree and order of the sum
70  * @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
71  * @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
72  * @param[in] N1 the maximum degree and order of the first correction
73  * coefficients <i>C'</i><sub><i>nm</i></sub> and
74  * <i>S'</i><sub><i>nm</i></sub>.
75  * @param[in] C2 the coefficients <i>C''</i><sub><i>nm</i></sub>.
76  * @param[in] S2 the coefficients <i>S''</i><sub><i>nm</i></sub>.
77  * @param[in] N2 the maximum degree and order of the second correction
78  * coefficients <i>C'</i><sub><i>nm</i></sub> and
79  * <i>S'</i><sub><i>nm</i></sub>.
80  * @param[in] a the reference radius appearing in the definition of the
81  * sum.
82  * @param[in] norm the normalization for the associated Legendre
83  * polynomials, either SphericalHarmonic2::FULL (the default) or
84  * SphericalHarmonic2::SCHMIDT.
85  * @exception GeographicErr if \e N and \e N1 do not satisfy \e N &ge;
86  * \e N1 &ge; &minus;1, and similarly for \e N2.
87  * @exception GeographicErr if any of the vectors of coefficients is not
88  * large enough.
89  *
90  * See SphericalHarmonic for the way the coefficients should be stored. \e
91  * N1 and \e N2 should satisfy \e N1 &le; \e N and \e N2 &le; \e N.
92  *
93  * The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
94  * C', \e S', \e C'', and \e S''. These arrays should not be altered or
95  * destroyed during the lifetime of a SphericalHarmonic object.
96  **********************************************************************/
97  SphericalHarmonic2(const std::vector<real>& C,
98  const std::vector<real>& S,
99  int N,
100  const std::vector<real>& C1,
101  const std::vector<real>& S1,
102  int N1,
103  const std::vector<real>& C2,
104  const std::vector<real>& S2,
105  int N2,
106  real a, unsigned norm = FULL)
107  : _a(a)
108  , _norm(norm) {
109  if (!(N1 <= N && N2 <= N))
110  throw GeographicErr("N1 and N2 cannot be larger that N");
111  _c[0] = SphericalEngine::coeff(C, S, N);
112  _c[1] = SphericalEngine::coeff(C1, S1, N1);
113  _c[2] = SphericalEngine::coeff(C2, S2, N2);
114  }
115 
116  /**
117  * Constructor with a subset of coefficients specified.
118  *
119  * @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
120  * @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
121  * @param[in] N the degree used to determine the layout of \e C and \e S.
122  * @param[in] nmx the maximum degree used in the sum. The sum over \e n is
123  * from 0 thru \e nmx.
124  * @param[in] mmx the maximum order used in the sum. The sum over \e m is
125  * from 0 thru min(\e n, \e mmx).
126  * @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
127  * @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
128  * @param[in] N1 the degree used to determine the layout of \e C' and \e
129  * S'.
130  * @param[in] nmx1 the maximum degree used for \e C' and \e S'.
131  * @param[in] mmx1 the maximum order used for \e C' and \e S'.
132  * @param[in] C2 the coefficients <i>C''</i><sub><i>nm</i></sub>.
133  * @param[in] S2 the coefficients <i>S''</i><sub><i>nm</i></sub>.
134  * @param[in] N2 the degree used to determine the layout of \e C'' and \e
135  * S''.
136  * @param[in] nmx2 the maximum degree used for \e C'' and \e S''.
137  * @param[in] mmx2 the maximum order used for \e C'' and \e S''.
138  * @param[in] a the reference radius appearing in the definition of the
139  * sum.
140  * @param[in] norm the normalization for the associated Legendre
141  * polynomials, either SphericalHarmonic2::FULL (the default) or
142  * SphericalHarmonic2::SCHMIDT.
143  * @exception GeographicErr if the parameters do not satisfy \e N &ge; \e
144  * nmx &ge; \e mmx &ge; &minus;1; \e N1 &ge; \e nmx1 &ge; \e mmx1 &ge;
145  * &minus;1; \e N &ge; \e N1; \e nmx &ge; \e nmx1; \e mmx &ge; \e mmx1;
146  * and similarly for \e N2, \e nmx2, and \e mmx2.
147  * @exception GeographicErr if any of the vectors of coefficients is not
148  * large enough.
149  *
150  * The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
151  * C', \e S', \e C'', and \e S''. These arrays should not be altered or
152  * destroyed during the lifetime of a SphericalHarmonic object.
153  **********************************************************************/
154  SphericalHarmonic2(const std::vector<real>& C,
155  const std::vector<real>& S,
156  int N, int nmx, int mmx,
157  const std::vector<real>& C1,
158  const std::vector<real>& S1,
159  int N1, int nmx1, int mmx1,
160  const std::vector<real>& C2,
161  const std::vector<real>& S2,
162  int N2, int nmx2, int mmx2,
163  real a, unsigned norm = FULL)
164  : _a(a)
165  , _norm(norm) {
166  if (!(nmx1 <= nmx && nmx2 <= nmx))
167  throw GeographicErr("nmx1 and nmx2 cannot be larger that nmx");
168  if (!(mmx1 <= mmx && mmx2 <= mmx))
169  throw GeographicErr("mmx1 and mmx2 cannot be larger that mmx");
170  _c[0] = SphericalEngine::coeff(C, S, N, nmx, mmx);
171  _c[1] = SphericalEngine::coeff(C1, S1, N1, nmx1, mmx1);
172  _c[2] = SphericalEngine::coeff(C2, S2, N2, nmx2, mmx2);
173  }
174 
175  /**
176  * A default constructor so that the object can be created when the
177  * constructor for another object is initialized. This default object can
178  * then be reset with the default copy assignment operator.
179  **********************************************************************/
181 
182  /**
183  * Compute a spherical harmonic sum with two correction terms.
184  *
185  * @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
186  * @param[in] tau2 multiplier for correction coefficients \e C'' and \e S''.
187  * @param[in] x cartesian coordinate.
188  * @param[in] y cartesian coordinate.
189  * @param[in] z cartesian coordinate.
190  * @return \e V the spherical harmonic sum.
191  *
192  * This routine requires constant memory and thus never throws an
193  * exception.
194  **********************************************************************/
195  Math::real operator()(real tau1, real tau2, real x, real y, real z)
196  const {
197  real f[] = {1, tau1, tau2};
198  real v = 0;
199  real dummy;
200  switch (_norm) {
201  case FULL:
202  v = SphericalEngine::Value<false, SphericalEngine::FULL, 3>
203  (_c, f, x, y, z, _a, dummy, dummy, dummy);
204  break;
205  case SCHMIDT:
206  v = SphericalEngine::Value<false, SphericalEngine::SCHMIDT, 3>
207  (_c, f, x, y, z, _a, dummy, dummy, dummy);
208  break;
209  }
210  return v;
211  }
212 
213  /**
214  * Compute a spherical harmonic sum with two correction terms and its
215  * gradient.
216  *
217  * @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
218  * @param[in] tau2 multiplier for correction coefficients \e C'' and \e S''.
219  * @param[in] x cartesian coordinate.
220  * @param[in] y cartesian coordinate.
221  * @param[in] z cartesian coordinate.
222  * @param[out] gradx \e x component of the gradient
223  * @param[out] grady \e y component of the gradient
224  * @param[out] gradz \e z component of the gradient
225  * @return \e V the spherical harmonic sum.
226  *
227  * This is the same as the previous function, except that the components of
228  * the gradients of the sum in the \e x, \e y, and \e z directions are
229  * computed. This routine requires constant memory and thus never throws
230  * an exception.
231  **********************************************************************/
232  Math::real operator()(real tau1, real tau2, real x, real y, real z,
233  real& gradx, real& grady, real& gradz) const {
234  real f[] = {1, tau1, tau2};
235  real v = 0;
236  switch (_norm) {
237  case FULL:
238  v = SphericalEngine::Value<true, SphericalEngine::FULL, 3>
239  (_c, f, x, y, z, _a, gradx, grady, gradz);
240  break;
241  case SCHMIDT:
242  v = SphericalEngine::Value<true, SphericalEngine::SCHMIDT, 3>
243  (_c, f, x, y, z, _a, gradx, grady, gradz);
244  break;
245  }
246  return v;
247  }
248 
249  /**
250  * Create a CircularEngine to allow the efficient evaluation of several
251  * points on a circle of latitude at fixed values of \e tau1 and \e tau2.
252  *
253  * @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
254  * @param[in] tau2 multiplier for correction coefficients \e C'' and \e S''.
255  * @param[in] p the radius of the circle.
256  * @param[in] z the height of the circle above the equatorial plane.
257  * @param[in] gradp if true the returned object will be able to compute the
258  * gradient of the sum.
259  * @exception std::bad_alloc if the memory for the CircularEngine can't be
260  * allocated.
261  * @return the CircularEngine object.
262  *
263  * SphericalHarmonic2::operator()() exchanges the order of the sums in the
264  * definition, i.e., &sum;<sub><i>n</i> = 0..<i>N</i></sub>
265  * &sum;<sub><i>m</i> = 0..<i>n</i></sub> becomes &sum;<sub><i>m</i> =
266  * 0..<i>N</i></sub> &sum;<sub><i>n</i> = <i>m</i>..<i>N</i></sub>..
267  * SphericalHarmonic2::Circle performs the inner sum over degree \e n
268  * (which entails about <i>N</i><sup>2</sup> operations). Calling
269  * CircularEngine::operator()() on the returned object performs the outer
270  * sum over the order \e m (about \e N operations).
271  *
272  * See SphericalHarmonic::Circle for an example of its use.
273  **********************************************************************/
274  CircularEngine Circle(real tau1, real tau2, real p, real z, bool gradp)
275  const {
276  real f[] = {1, tau1, tau2};
277  switch (_norm) {
278  case FULL:
279  return gradp ?
280  SphericalEngine::Circle<true, SphericalEngine::FULL, 3>
281  (_c, f, p, z, _a) :
282  SphericalEngine::Circle<false, SphericalEngine::FULL, 3>
283  (_c, f, p, z, _a);
284  break;
285  case SCHMIDT:
286  default: // To avoid compiler warnings
287  return gradp ?
288  SphericalEngine::Circle<true, SphericalEngine::SCHMIDT, 3>
289  (_c, f, p, z, _a) :
290  SphericalEngine::Circle<false, SphericalEngine::SCHMIDT, 3>
291  (_c, f, p, z, _a);
292  break;
293  }
294  }
295 
296  /**
297  * @return the zeroth SphericalEngine::coeff object.
298  **********************************************************************/
300  { return _c[0]; }
301  /**
302  * @return the first SphericalEngine::coeff object.
303  **********************************************************************/
305  { return _c[1]; }
306  /**
307  * @return the second SphericalEngine::coeff object.
308  **********************************************************************/
310  { return _c[2]; }
311  };
312 
313 } // namespace GeographicLib
314 
315 #endif // GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
Package up coefficients for SphericalEngine.
const SphericalEngine::coeff & Coefficients1() const
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
const SphericalEngine::coeff & Coefficients2() const
Spherical harmonic series with two corrections to the coefficients.
CircularEngine Circle(real tau1, real tau2, real p, real z, bool gradp) const
SphericalHarmonic2(const std::vector< real > &C, const std::vector< real > &S, int N, int nmx, int mmx, const std::vector< real > &C1, const std::vector< real > &S1, int N1, int nmx1, int mmx1, const std::vector< real > &C2, const std::vector< real > &S2, int N2, int nmx2, int mmx2, real a, unsigned norm=FULL)
Header for GeographicLib::CircularEngine class.
Spherical harmonic sums for a circle.
Exception handling for GeographicLib.
Definition: Constants.hpp:373
Header for GeographicLib::Constants class.
SphericalHarmonic2(const std::vector< real > &C, const std::vector< real > &S, int N, const std::vector< real > &C1, const std::vector< real > &S1, int N1, const std::vector< real > &C2, const std::vector< real > &S2, int N2, real a, unsigned norm=FULL)
Header for GeographicLib::SphericalEngine class.
Math::real operator()(real tau1, real tau2, real x, real y, real z, real &gradx, real &grady, real &gradz) const
const SphericalEngine::coeff & Coefficients() const
Math::real operator()(real tau1, real tau2, real x, real y, real z) const