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SphericalHarmonic2.hpp
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/**
* \file SphericalHarmonic2.hpp
* \brief Header for GeographicLib::SphericalHarmonic2 class
*
* Copyright (c) Charles Karney (2011-2012) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP)
#define GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP 1
#include <vector>
#include <GeographicLib/Constants.hpp>
#include <GeographicLib/SphericalEngine.hpp>
#include <GeographicLib/CircularEngine.hpp>
namespace GeographicLib {
/**
* \brief Spherical harmonic series with two corrections to the coefficients
*
* This classes is similar to SphericalHarmonic, except that the coefficients
* <i>C</i><sub><i>nm</i></sub> are replaced by
* <i>C</i><sub><i>nm</i></sub> + \e tau' <i>C'</i><sub><i>nm</i></sub> + \e
* tau'' <i>C''</i><sub><i>nm</i></sub> (and similarly for
* <i>S</i><sub><i>nm</i></sub>).
*
* Example of use:
* \include example-SphericalHarmonic2.cpp
**********************************************************************/
// Don't include the GEOGRPAHIC_EXPORT because this header-only class isn't
// used by any other classes in the library.
class /*GEOGRAPHICLIB_EXPORT*/ SphericalHarmonic2 {
public:
/**
* Supported normalizations for associate Legendre polynomials.
**********************************************************************/
enum normalization {
/**
* Fully normalized associated Legendre polynomials. See
* SphericalHarmonic::FULL for documentation.
*
* @hideinitializer
**********************************************************************/
FULL = SphericalEngine::FULL,
/**
* Schmidt semi-normalized associated Legendre polynomials. See
* SphericalHarmonic::SCHMIDT for documentation.
*
* @hideinitializer
**********************************************************************/
SCHMIDT = SphericalEngine::SCHMIDT,
};
private:
typedef Math::real real;
SphericalEngine::coeff _c[3];
real _a;
unsigned _norm;
public:
/**
* Constructor with a full set of coefficients specified.
*
* @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
* @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
* @param[in] N the maximum degree and order of the sum
* @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
* @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
* @param[in] N1 the maximum degree and order of the first correction
* coefficients <i>C'</i><sub><i>nm</i></sub> and
* <i>S'</i><sub><i>nm</i></sub>.
* @param[in] C2 the coefficients <i>C''</i><sub><i>nm</i></sub>.
* @param[in] S2 the coefficients <i>S''</i><sub><i>nm</i></sub>.
* @param[in] N2 the maximum degree and order of the second correction
* coefficients <i>C'</i><sub><i>nm</i></sub> and
* <i>S'</i><sub><i>nm</i></sub>.
* @param[in] a the reference radius appearing in the definition of the
* sum.
* @param[in] norm the normalization for the associated Legendre
* polynomials, either SphericalHarmonic2::FULL (the default) or
* SphericalHarmonic2::SCHMIDT.
* @exception GeographicErr if \e N and \e N1 do not satisfy \e N &ge;
* \e N1 &ge; &minus;1, and similarly for \e N2.
* @exception GeographicErr if any of the vectors of coefficients is not
* large enough.
*
* See SphericalHarmonic for the way the coefficients should be stored. \e
* N1 and \e N2 should satisfy \e N1 &le; \e N and \e N2 &le; \e N.
*
* The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
* C', \e S', \e C'', and \e S''. These arrays should not be altered or
* destroyed during the lifetime of a SphericalHarmonic object.
**********************************************************************/
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)
: _a(a)
, _norm(norm) {
if (!(N1 <= N && N2 <= N))
throw GeographicErr("N1 and N2 cannot be larger that N");
_c[0] = SphericalEngine::coeff(C, S, N);
_c[1] = SphericalEngine::coeff(C1, S1, N1);
_c[2] = SphericalEngine::coeff(C2, S2, N2);
}
/**
* Constructor with a subset of coefficients specified.
*
* @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
* @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
* @param[in] N the degree used to determine the layout of \e C and \e S.
* @param[in] nmx the maximum degree used in the sum. The sum over \e n is
* from 0 thru \e nmx.
* @param[in] mmx the maximum order used in the sum. The sum over \e m is
* from 0 thru min(\e n, \e mmx).
* @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
* @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
* @param[in] N1 the degree used to determine the layout of \e C' and \e
* S'.
* @param[in] nmx1 the maximum degree used for \e C' and \e S'.
* @param[in] mmx1 the maximum order used for \e C' and \e S'.
* @param[in] C2 the coefficients <i>C''</i><sub><i>nm</i></sub>.
* @param[in] S2 the coefficients <i>S''</i><sub><i>nm</i></sub>.
* @param[in] N2 the degree used to determine the layout of \e C'' and \e
* S''.
* @param[in] nmx2 the maximum degree used for \e C'' and \e S''.
* @param[in] mmx2 the maximum order used for \e C'' and \e S''.
* @param[in] a the reference radius appearing in the definition of the
* sum.
* @param[in] norm the normalization for the associated Legendre
* polynomials, either SphericalHarmonic2::FULL (the default) or
* SphericalHarmonic2::SCHMIDT.
* @exception GeographicErr if the parameters do not satisfy \e N &ge; \e
* nmx &ge; \e mmx &ge; &minus;1; \e N1 &ge; \e nmx1 &ge; \e mmx1 &ge;
* &minus;1; \e N &ge; \e N1; \e nmx &ge; \e nmx1; \e mmx &ge; \e mmx1;
* and similarly for \e N2, \e nmx2, and \e mmx2.
* @exception GeographicErr if any of the vectors of coefficients is not
* large enough.
*
* The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
* C', \e S', \e C'', and \e S''. These arrays should not be altered or
* destroyed during the lifetime of a SphericalHarmonic object.
**********************************************************************/
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)
: _a(a)
, _norm(norm) {
if (!(nmx1 <= nmx && nmx2 <= nmx))
throw GeographicErr("nmx1 and nmx2 cannot be larger that nmx");
if (!(mmx1 <= mmx && mmx2 <= mmx))
throw GeographicErr("mmx1 and mmx2 cannot be larger that mmx");
_c[0] = SphericalEngine::coeff(C, S, N, nmx, mmx);
_c[1] = SphericalEngine::coeff(C1, S1, N1, nmx1, mmx1);
_c[2] = SphericalEngine::coeff(C2, S2, N2, nmx2, mmx2);
}
/**
* 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.
**********************************************************************/
SphericalHarmonic2() {}
/**
* Compute a spherical harmonic sum with two correction terms.
*
* @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
* @param[in] tau2 multiplier for correction coefficients \e C'' and \e
* S''.
* @param[in] x cartesian coordinate.
* @param[in] y cartesian coordinate.
* @param[in] z cartesian coordinate.
* @return \e V the spherical harmonic sum.
*
* This routine requires constant memory and thus never throws an
* exception.
**********************************************************************/
Math::real operator()(real tau1, real tau2, real x, real y, real z)
const {
real f[] = {1, tau1, tau2};
real v = 0;
real dummy;
switch (_norm) {
case FULL:
v = SphericalEngine::Value<false, SphericalEngine::FULL, 3>
(_c, f, x, y, z, _a, dummy, dummy, dummy);
break;
case SCHMIDT:
default: // To avoid compiler warnings
v = SphericalEngine::Value<false, SphericalEngine::SCHMIDT, 3>
(_c, f, x, y, z, _a, dummy, dummy, dummy);
break;
}
return v;
}
/**
* Compute a spherical harmonic sum with two correction terms and its
* gradient.
*
* @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
* @param[in] tau2 multiplier for correction coefficients \e C'' and \e
* S''.
* @param[in] x cartesian coordinate.
* @param[in] y cartesian coordinate.
* @param[in] z cartesian coordinate.
* @param[out] gradx \e x component of the gradient
* @param[out] grady \e y component of the gradient
* @param[out] gradz \e z component of the gradient
* @return \e 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 \e x, \e y, and \e z directions are
* computed. This routine requires constant memory and thus never throws
* an exception.
**********************************************************************/
Math::real operator()(real tau1, real tau2, real x, real y, real z,
real& gradx, real& grady, real& gradz) const {
real f[] = {1, tau1, tau2};
real v = 0;
switch (_norm) {
case FULL:
v = SphericalEngine::Value<true, SphericalEngine::FULL, 3>
(_c, f, x, y, z, _a, gradx, grady, gradz);
break;
case SCHMIDT:
default: // To avoid compiler warnings
v = SphericalEngine::Value<true, SphericalEngine::SCHMIDT, 3>
(_c, f, x, y, z, _a, gradx, grady, gradz);
break;
}
return v;
}
/**
* Create a CircularEngine to allow the efficient evaluation of several
* points on a circle of latitude at fixed values of \e tau1 and \e tau2.
*
* @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
* @param[in] tau2 multiplier for correction coefficients \e C'' and \e
* S''.
* @param[in] p the radius of the circle.
* @param[in] z the height of the circle above the equatorial plane.
* @param[in] gradp if true the returned object will be able to compute the
* gradient of the sum.
* @exception std::bad_alloc if the memory for the CircularEngine can't be
* allocated.
* @return the CircularEngine object.
*
* SphericalHarmonic2::operator()() exchanges the order of the sums in the
* definition, i.e., &sum;<sub><i>n</i> = 0..<i>N</i></sub>
* &sum;<sub><i>m</i> = 0..<i>n</i></sub> becomes &sum;<sub><i>m</i> =
* 0..<i>N</i></sub> &sum;<sub><i>n</i> = <i>m</i>..<i>N</i></sub>..
* SphericalHarmonic2::Circle performs the inner sum over degree \e n
* (which entails about <i>N</i><sup>2</sup> operations). Calling
* CircularEngine::operator()() on the returned object performs the outer
* sum over the order \e m (about \e N operations).
*
* See SphericalHarmonic::Circle for an example of its use.
**********************************************************************/
CircularEngine Circle(real tau1, real tau2, real p, real z, bool gradp)
const {
real f[] = {1, tau1, tau2};
switch (_norm) {
case FULL:
return gradp ?
SphericalEngine::Circle<true, SphericalEngine::FULL, 3>
(_c, f, p, z, _a) :
SphericalEngine::Circle<false, SphericalEngine::FULL, 3>
(_c, f, p, z, _a);
break;
case SCHMIDT:
default: // To avoid compiler warnings
return gradp ?
SphericalEngine::Circle<true, SphericalEngine::SCHMIDT, 3>
(_c, f, p, z, _a) :
SphericalEngine::Circle<false, SphericalEngine::SCHMIDT, 3>
(_c, f, p, z, _a);
break;
}
}
/**
* @return the zeroth SphericalEngine::coeff object.
**********************************************************************/
const SphericalEngine::coeff& Coefficients() const
{ return _c[0]; }
/**
* @return the first SphericalEngine::coeff object.
**********************************************************************/
const SphericalEngine::coeff& Coefficients1() const
{ return _c[1]; }
/**
* @return the second SphericalEngine::coeff object.
**********************************************************************/
const SphericalEngine::coeff& Coefficients2() const
{ return _c[2]; }
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP
CircularEngine.hpp
Header for GeographicLib::CircularEngine class.
Constants.hpp
Header for GeographicLib::Constants class.
real
GeographicLib::Math::real real
Definition Geod3Solve.cpp:25
SphericalEngine.hpp
Header for GeographicLib::SphericalEngine class.
GeographicLib::CircularEngine
Spherical harmonic sums for a circle.
Definition CircularEngine.hpp:52
GeographicLib::GeographicErr
Exception handling for GeographicLib.
Definition Constants.hpp:344
GeographicLib::Math::real
double real
Definition Math.hpp:115
GeographicLib::SphericalEngine::coeff
Package up coefficients for SphericalEngine.
Definition SphericalEngine.hpp:99
GeographicLib::SphericalEngine::Value
static Math::real Value(const coeff c[], const real f[], real x, real y, real z, real a, real &gradx, real &grady, real &gradz)
Definition SphericalEngine.cpp:152
GeographicLib::SphericalEngine::SCHMIDT
@ SCHMIDT
Definition SphericalEngine.hpp:84
GeographicLib::SphericalEngine::FULL
@ FULL
Definition SphericalEngine.hpp:77
GeographicLib::SphericalEngine::Circle
static CircularEngine Circle(const coeff c[], const real f[], real p, real z, real a)
Definition SphericalEngine.cpp:296
GeographicLib::SphericalHarmonic2::Coefficients2
const SphericalEngine::coeff & Coefficients2() const
Definition SphericalHarmonic2.hpp:314
GeographicLib::SphericalHarmonic2::SphericalHarmonic2
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)
Definition SphericalHarmonic2.hpp:154
GeographicLib::SphericalHarmonic2::SphericalHarmonic2
SphericalHarmonic2()
Definition SphericalHarmonic2.hpp:180
GeographicLib::SphericalHarmonic2::Circle
CircularEngine Circle(real tau1, real tau2, real p, real z, bool gradp) const
Definition SphericalHarmonic2.hpp:279
GeographicLib::SphericalHarmonic2::Coefficients
const SphericalEngine::coeff & Coefficients() const
Definition SphericalHarmonic2.hpp:304
GeographicLib::SphericalHarmonic2::SphericalHarmonic2
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)
Definition SphericalHarmonic2.hpp:97
GeographicLib::SphericalHarmonic2::Coefficients1
const SphericalEngine::coeff & Coefficients1() const
Definition SphericalHarmonic2.hpp:309
GeographicLib::SphericalHarmonic2::operator()
Math::real operator()(real tau1, real tau2, real x, real y, real z) const
Definition SphericalHarmonic2.hpp:196
GeographicLib::SphericalHarmonic2::normalization
normalization
Definition SphericalHarmonic2.hpp:40
GeographicLib::SphericalHarmonic2::SCHMIDT
@ SCHMIDT
Definition SphericalHarmonic2.hpp:54
GeographicLib::SphericalHarmonic2::FULL
@ FULL
Definition SphericalHarmonic2.hpp:47
GeographicLib::SphericalHarmonic2::operator()
Math::real operator()(real tau1, real tau2, real x, real y, real z, real &gradx, real &grady, real &gradz) const
Definition SphericalHarmonic2.hpp:235
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12