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GeographicLib::SphericalHarmonic1 Class Reference

Spherical harmonic series with a correction to the coefficients. More...

#include <SphericalHarmonic1.hpp>

Public Types

enum  normalization { FULL, SCHMIDT }
 

Public Member Functions

CircularEngine Circle (real tau, real p, real z, bool gradp) const
 
const SphericalEngine::coeffCoefficients () const
 
const SphericalEngine::coeffCoefficients1 () const
 
Math::real operator() (real tau, real x, real y, real z) const
 
Math::real operator() (real tau, real x, real y, real z, real &gradx, real &grady, real &gradz) const
 
 SphericalHarmonic1 (const std::vector< real > &C, const std::vector< real > &S, int N, const std::vector< real > &C1, const std::vector< real > &S1, int N1, real a, unsigned norm=FULL)
 
 SphericalHarmonic1 (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, real a, unsigned norm=FULL)
 
 SphericalHarmonic1 ()
 

Private Types

typedef Math::real real
 

Private Attributes

real _a
 
SphericalEngine::coeff _c [2]
 
unsigned _norm
 

Detailed Description

Spherical harmonic series with a correction to the coefficients.

This classes is similar to SphericalHarmonic, except that the coefficients Cnm are replaced by Cnm + tau C'nm (and similarly for Snm).

Example of use:

// Example of using the GeographicLib::SphericalHarmonic1 class
#include <iostream>
#include <exception>
#include <vector>
using namespace std;
using namespace GeographicLib;
int main() {
try {
int N = 3, N1 = 2; // The maxium degrees
double ca[] = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; // cosine coefficients
vector<double> C(ca, ca + (N + 1) * (N + 2) / 2);
double sa[] = {6, 5, 4, 3, 2, 1}; // sine coefficients
vector<double> S(sa, sa + N * (N + 1) / 2);
double cb[] = {1, 2, 3, 4, 5, 6};
vector<double> C1(cb, cb + (N1 + 1) * (N1 + 2) / 2);
double sb[] = {3, 2, 1};
vector<double> S1(sb, sb + N1 * (N1 + 1) / 2);
double a = 1;
SphericalHarmonic1 h(C, S, N, C1, S1, N1, a);
double tau = 0.1, x = 2, y = 3, z = 1;
double v, vx, vy, vz;
v = h(tau, x, y, z, vx, vy, vz);
cout << v << " " << vx << " " << vy << " " << vz << "\n";
}
catch (const exception& e) {
cerr << "Caught exception: " << e.what() << "\n";
return 1;
}
}

Definition at line 32 of file SphericalHarmonic1.hpp.

Member Typedef Documentation

Definition at line 55 of file SphericalHarmonic1.hpp.

Member Enumeration Documentation

Supported normalizations for associate Legendre polynomials.

Enumerator
FULL 

Fully normalized associated Legendre polynomials. See SphericalHarmonic::FULL for documentation.

SCHMIDT 

Schmidt semi-normalized associated Legendre polynomials. See SphericalHarmonic::SCHMIDT for documentation.

Definition at line 37 of file SphericalHarmonic1.hpp.

Constructor & Destructor Documentation

GeographicLib::SphericalHarmonic1::SphericalHarmonic1 ( const std::vector< real > &  C,
const std::vector< real > &  S,
int  N,
const std::vector< real > &  C1,
const std::vector< real > &  S1,
int  N1,
real  a,
unsigned  norm = FULL 
)
inline

Constructor with a full set of coefficients specified.

Parameters
[in]Cthe coefficients Cnm.
[in]Sthe coefficients Snm.
[in]Nthe maximum degree and order of the sum
[in]C1the coefficients C'nm.
[in]S1the coefficients S'nm.
[in]N1the maximum degree and order of the correction coefficients C'nm and S'nm.
[in]athe reference radius appearing in the definition of the sum.
[in]normthe normalization for the associated Legendre polynomials, either SphericalHarmonic1::FULL (the default) or SphericalHarmonic1::SCHMIDT.
Exceptions
GeographicErrif N and N1 do not satisfy NN1 ≥ −1.
GeographicErrif any of the vectors of coefficients is not large enough.

See SphericalHarmonic for the way the coefficients should be stored.

The class stores pointers to the first elements of C, S, C', and S'. These arrays should not be altered or destroyed during the lifetime of a SphericalHarmonic object.

Definition at line 88 of file SphericalHarmonic1.hpp.

GeographicLib::SphericalHarmonic1::SphericalHarmonic1 ( 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,
real  a,
unsigned  norm = FULL 
)
inline

Constructor with a subset of coefficients specified.

Parameters
[in]Cthe coefficients Cnm.
[in]Sthe coefficients Snm.
[in]Nthe degree used to determine the layout of C and S.
[in]nmxthe maximum degree used in the sum. The sum over n is from 0 thru nmx.
[in]mmxthe maximum order used in the sum. The sum over m is from 0 thru min(n, mmx).
[in]C1the coefficients C'nm.
[in]S1the coefficients S'nm.
[in]N1the degree used to determine the layout of C' and S'.
[in]nmx1the maximum degree used for C' and S'.
[in]mmx1the maximum order used for C' and S'.
[in]athe reference radius appearing in the definition of the sum.
[in]normthe normalization for the associated Legendre polynomials, either SphericalHarmonic1::FULL (the default) or SphericalHarmonic1::SCHMIDT.
Exceptions
GeographicErrif the parameters do not satisfy Nnmxmmx ≥ −1; N1nmx1mmx1 ≥ −1; NN1; nmxnmx1; mmxmmx1.
GeographicErrif any of the vectors of coefficients is not large enough.

The class stores pointers to the first elements of C, S, C', and S'. These arrays should not be altered or destroyed during the lifetime of a SphericalHarmonic object.

Definition at line 134 of file SphericalHarmonic1.hpp.

GeographicLib::SphericalHarmonic1::SphericalHarmonic1 ( )
inline

A default constructor so that the object can be created when the constructor for another object is initialized. This default object can then be reset with the default copy assignment operator.

Definition at line 156 of file SphericalHarmonic1.hpp.

Member Function Documentation

CircularEngine GeographicLib::SphericalHarmonic1::Circle ( real  tau,
real  p,
real  z,
bool  gradp 
) const
inline

Create a CircularEngine to allow the efficient evaluation of several points on a circle of latitude at a fixed value of tau.

Parameters
[in]tauthe multiplier for the correction coefficients.
[in]pthe radius of the circle.
[in]zthe height of the circle above the equatorial plane.
[in]gradpif true the returned object will be able to compute the gradient of the sum.
Exceptions
std::bad_allocif the memory for the CircularEngine can't be allocated.
Returns
the CircularEngine object.

SphericalHarmonic1::operator()() exchanges the order of the sums in the definition, i.e., ∑n = 0..Nm = 0..n becomes ∑m = 0..Nn = m..N. SphericalHarmonic1::Circle performs the inner sum over degree n (which entails about N2 operations). Calling CircularEngine::operator()() on the returned object performs the outer sum over the order m (about N operations).

See SphericalHarmonic::Circle for an example of its use.

Definition at line 246 of file SphericalHarmonic1.hpp.

const SphericalEngine::coeff& GeographicLib::SphericalHarmonic1::Coefficients ( ) const
inline
Returns
the zeroth SphericalEngine::coeff object.

Definition at line 270 of file SphericalHarmonic1.hpp.

const SphericalEngine::coeff& GeographicLib::SphericalHarmonic1::Coefficients1 ( ) const
inline
Returns
the first SphericalEngine::coeff object.

Definition at line 275 of file SphericalHarmonic1.hpp.

Math::real GeographicLib::SphericalHarmonic1::operator() ( real  tau,
real  x,
real  y,
real  z 
) const
inline

Compute a spherical harmonic sum with a correction term.

Parameters
[in]taumultiplier for correction coefficients C' and S'.
[in]xcartesian coordinate.
[in]ycartesian coordinate.
[in]zcartesian coordinate.
Returns
V the spherical harmonic sum.

This routine requires constant memory and thus never throws an exception.

Definition at line 170 of file SphericalHarmonic1.hpp.

Math::real GeographicLib::SphericalHarmonic1::operator() ( real  tau,
real  x,
real  y,
real  z,
real gradx,
real grady,
real gradz 
) const
inline

Compute a spherical harmonic sum with a correction term and its gradient.

Parameters
[in]taumultiplier for correction coefficients C' and S'.
[in]xcartesian coordinate.
[in]ycartesian coordinate.
[in]zcartesian coordinate.
[out]gradxx component of the gradient
[out]gradyy component of the gradient
[out]gradzz component of the gradient
Returns
V the spherical harmonic sum.

This is the same as the previous function, except that the components of the gradients of the sum in the x, y, and z directions are computed. This routine requires constant memory and thus never throws an exception.

Definition at line 205 of file SphericalHarmonic1.hpp.

Member Data Documentation

real GeographicLib::SphericalHarmonic1::_a
private

Definition at line 57 of file SphericalHarmonic1.hpp.

SphericalEngine::coeff GeographicLib::SphericalHarmonic1::_c[2]
private

Definition at line 56 of file SphericalHarmonic1.hpp.

unsigned GeographicLib::SphericalHarmonic1::_norm
private

Definition at line 58 of file SphericalHarmonic1.hpp.


The documentation for this class was generated from the following file:


gtsam
Author(s):
autogenerated on Sat May 8 2021 02:58:00