.NET wrapper for GeographicLib::SphericalHarmonic2. More...

#include <SphericalHarmonic2.h>

Public Types
enum	Normalization { Normalization::FULL, Normalization::SCHMIDT }

Public Member Functions
CircularEngine	Circle (double tau1, double tau2, double p, double z, bool gradp)

SphericalCoefficients	Coefficients ()

SphericalCoefficients	Coefficients1 ()

SphericalCoefficients	Coefficients2 ()

double	HarmonicSum (double tau1, double tau2, double x, double y, double z)

double	HarmonicSum (double tau1, double tau2, double x, double y, double z, [System::Runtime::InteropServices::Out] double%gradx, [System::Runtime::InteropServices::Out] double%grady, [System::Runtime::InteropServices::Out] double%gradz)

	SphericalHarmonic2 (array< double >^C, array< double >^S, int N, array< double >^C1, array< double >^S1, int N1, array< double >^C2, array< double >^S2, int N2, double a, Normalization norm)

	SphericalHarmonic2 (array< double >^C, array< double >^S, int N, int nmx, int mmx, array< double >^C1, array< double >^S1, int N1, int nmx1, int mmx1, array< double >^C2, array< double >^S2, int N2, int nmx2, int mmx2, double a, Normalization norm)

	~SphericalHarmonic2 ()

Private Member Functions
	!SphericalHarmonic2 (void)

Private Attributes
std::vector< double > **	m_C

const GeographicLib::SphericalHarmonic2 *	m_pSphericalHarmonic2

std::vector< double > **	m_S

Static Private Attributes
static const int	m_numCoeffVectors = 3

Detailed Description

.NET wrapper for GeographicLib::SphericalHarmonic2.

This class allows .NET applications to access GeographicLib::SphericalHarmonic2.

This class is similar to SphericalHarmonic, except that the coefficients C_nm are replaced by C_nm + tau' C'_nm + tau'' C''_nm (and similarly for S_nm).

C# Example:

using System;
using NETGeographicLib;
namespace example_SphericalHarmonic2
{
    class Program
    {
        static void Main(string[] args)
        {
            try
            {
                int N = 3, N1 = 2, N2 = 1;                     // The maximum degrees
                double[] ca = { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }; // cosine coefficients
                double[] sa = { 6, 5, 4, 3, 2, 1 }; // sine coefficients
                double[] cb = { 1, 2, 3, 4, 5, 6 };
                double[] sb = { 3, 2, 1 };
                double[] cc = { 2, 1 };
                double[] S2 = { 0 };
                double a = 1;
                SphericalHarmonic2 h = new SphericalHarmonic2(
                                        ca, sa, N, N, N, cb, sb, N1, N1, N1,
                                        cc, S2, N2, N2, 0, a,
                                        SphericalHarmonic2.Normalization.SCHMIDT);
                double tau1 = 0.1, tau2 = 0.05, x = 2, y = 3, z = 1;
                double v, vx, vy, vz;
                v = h.HarmonicSum(tau1, tau2, x, y, z, out vx, out vy, out vz);
                Console.WriteLine(String.Format("{0} {1} {2} {3}", v, vx, vy, vz));
            }
            catch (GeographicErr e)
            {
                Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
            }
        }
    }
}

Managed C++ Example:

// Example of using the GeographicLib::SphericalHarmonic2 class
#include <iostream>
#include <exception>
#include <vector>
#include <GeographicLib/SphericalHarmonic2.hpp>
using namespace std;
using namespace GeographicLib;
int main() {
  try {
    int N = 3, N1 = 2, N2 = 1;                     // 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 cc[] = {2, 1};
    vector<double> C2(cc, cc + (N2 + 1));
    vector<double> S2;
    double a = 1;
    SphericalHarmonic2 h(C, S, N, N, N, C1, S1, N1, N1, N1,
                         C2, S2, N2, N2, 0, a);
    double tau1 = 0.1, tau2 = 0.05, x = 2, y = 3, z = 1;
    double v, vx, vy, vz;
    v = h(tau1, tau2, x, y, z, vx, vy, vz);
    cout << v << " " << vx << " " << vy << " " << vz << "\n";
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

Visual Basic Example:

Imports NETGeographicLib
Module example_SphericalHarmonic2
    Sub Main()
        Try
            Dim N As Integer = 3, N1 = 2, N2 = 1 ' The maximum degrees
            Dim ca As Double() = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1} ' cosine coefficients
            Dim sa As Double() = {6, 5, 4, 3, 2, 1} ' sine coefficients
            Dim cb As Double() = {1, 2, 3, 4, 5, 6}
            Dim sb As Double() = {3, 2, 1}
            Dim cc As Double() = {2, 1}
            Dim S2 As Double() = {0}
            Dim a As Double = 1
            Dim h As SphericalHarmonic2 = New SphericalHarmonic2(
                                    ca, sa, N, N, N, cb, sb, N1, N1, N1,
                                    cc, S2, N2, N2, 0, a,
                                    SphericalHarmonic2.Normalization.SCHMIDT)
            Dim tau1 As Double = 0.1, tau2 = 0.05, x = 2, y = 3, z = 1
            Dim vx, vy, vz As Double
            Dim v As Double = h.HarmonicSum(tau1, tau2, x, y, z, vx, vy, vz)
            Console.WriteLine(String.Format("{0} {1} {2} {3}", v, vx, vy, vz))
        Catch ex As GeographicErr
            Console.WriteLine(String.Format("Caught exception: {0}", ex.Message))
        End Try
    End Sub
End Module

INTERFACE DIFFERENCES:
This class replaces the () operator with HarmonicSum().

Coefficients, Coefficients1, and Coefficients2 return a SphericalCoefficients object.

Definition at line 40 of file SphericalHarmonic2.h.

Member Enumeration Documentation

enum NETGeographicLib::SphericalHarmonic2::Normalization

strong

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 57 of file SphericalHarmonic2.h.

Constructor & Destructor Documentation

SphericalHarmonic2::!SphericalHarmonic2 ( void )

private

Definition at line 23 of file SphericalHarmonic2.cpp.

SphericalHarmonic2::SphericalHarmonic2	(	array< double >^	C,
		array< double >^	S,
		int	N,
		array< double >^	C1,
		array< double >^	S1,
		int	N1,
		array< double >^	C2,
		array< double >^	S2,
		int	N2,
		double	a,
		Normalization	norm
	)

Constructor with a full set of coefficients specified.

Parameters

[in]	C	the coefficients C_nm.
[in]	S	the coefficients S_nm.
[in]	N	the maximum degree and order of the sum
[in]	C1	the coefficients C'_nm.
[in]	S1	the coefficients S'_nm.
[in]	N1	the maximum degree and order of the first correction coefficients C'_nm and S'_nm.
[in]	C2	the coefficients C''_nm.
[in]	S2	the coefficients S''_nm.
[in]	N2	the maximum degree and order of the second correction coefficients C'_nm and S'_nm.
[in]	a	the reference radius appearing in the definition of the sum.
[in]	norm	the normalization for the associated Legendre polynomials, either SphericalHarmonic2::FULL (the default) or SphericalHarmonic2::SCHMIDT.

Exceptions

GeographicErr	if N and N1 do not satisfy N ≥ N1 ≥ −1, and similarly for N2.
GeographicErr	if any of the vectors of coefficients is not large enough.

See SphericalHarmonic for the way the coefficients should be stored. N1 and N2 should satisfy N1 ≤ N and N2 ≤ N.

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

Definition at line 51 of file SphericalHarmonic2.cpp.

SphericalHarmonic2::SphericalHarmonic2	(	array< double >^	C,
		array< double >^	S,
		int	N,
		int	nmx,
		int	mmx,
		array< double >^	C1,
		array< double >^	S1,
		int	N1,
		int	nmx1,
		int	mmx1,
		array< double >^	C2,
		array< double >^	S2,
		int	N2,
		int	nmx2,
		int	mmx2,
		double	a,
		Normalization	norm
	)

Constructor with a subset of coefficients specified.

Parameters

[in]	C	the coefficients C_nm.
[in]	S	the coefficients S_nm.
[in]	N	the degree used to determine the layout of C and S.
[in]	nmx	the maximum degree used in the sum. The sum over n is from 0 thru nmx.
[in]	mmx	the maximum order used in the sum. The sum over m is from 0 thru min(n, mmx).
[in]	C1	the coefficients C'_nm.
[in]	S1	the coefficients S'_nm.
[in]	N1	the degree used to determine the layout of C' and S'.
[in]	nmx1	the maximum degree used for C' and S'.
[in]	mmx1	the maximum order used for C' and S'.
[in]	C2	the coefficients C''_nm.
[in]	S2	the coefficients S''_nm.
[in]	N2	the degree used to determine the layout of C'' and S''.
[in]	nmx2	the maximum degree used for C'' and S''.
[in]	mmx2	the maximum order used for C'' and S''.
[in]	a	the reference radius appearing in the definition of the sum.
[in]	norm	the normalization for the associated Legendre polynomials, either SphericalHarmonic2::FULL (the default) or SphericalHarmonic2::SCHMIDT.

Exceptions

GeographicErr	if the parameters do not satisfy N ≥ nmx ≥ mmx ≥ −1; N1 ≥ nmx1 ≥ mmx1 ≥ −1; N ≥ N1; nmx ≥ nmx1; mmx ≥ mmx1; and similarly for N2, nmx2, and mmx2.
GeographicErr	if any of the vectors of coefficients is not large enough.

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

Definition at line 93 of file SphericalHarmonic2.cpp.

NETGeographicLib::SphericalHarmonic2::~SphericalHarmonic2 ( )

inline

The destructor calls the finalizer.

Definition at line 170 of file SphericalHarmonic2.h.

Member Function Documentation

CircularEngine SphericalHarmonic2::Circle	(	double	tau1,
		double	tau2,
		double	p,
		double	z,
		bool	gradp
	)

Create a CircularEngine to allow the efficient evaluation of several points on a circle of latitude at fixed values of tau1 and tau2.

Parameters

[in]	tau1	multiplier for correction coefficients C' and S'.
[in]	tau2	multiplier for correction coefficients C'' and S''.
[in]	p	the radius of the circle.
[in]	z	the height of the circle above the equatorial plane.
[in]	gradp	if true the returned object will be able to compute the gradient of the sum.

Exceptions

std::bad_alloc if the memory for the CircularEngine can't be allocated.

Returns: the CircularEngine object.

SphericalHarmonic2::operator()() exchanges the order of the sums in the definition, i.e., ∑_{n = 0..N} ∑_{m = 0..n} becomes ∑_{m = 0..N} ∑_{n = m..N}.. SphericalHarmonic2::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 157 of file SphericalHarmonic2.cpp.

SphericalCoefficients SphericalHarmonic2::Coefficients ( )

Returns: the zeroth SphericalCoefficients object.

Definition at line 171 of file SphericalHarmonic2.cpp.

SphericalCoefficients SphericalHarmonic2::Coefficients1 ( )

Returns: the first SphericalCoefficients object.

Definition at line 177 of file SphericalHarmonic2.cpp.

SphericalCoefficients SphericalHarmonic2::Coefficients2 ( )

Returns: the second SphericalCoefficients object.

Definition at line 183 of file SphericalHarmonic2.cpp.

double SphericalHarmonic2::HarmonicSum	(	double	tau1,
		double	tau2,
		double	x,
		double	y,
		double	z
	)

Compute a spherical harmonic sum with two correction terms.

Parameters

[in]	tau1	multiplier for correction coefficients C' and S'.
[in]	tau2	multiplier for correction coefficients C'' and S''.
[in]	x	cartesian coordinate.
[in]	y	cartesian coordinate.
[in]	z	cartesian coordinate.

Returns: V the spherical harmonic sum.

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

Definition at line 136 of file SphericalHarmonic2.cpp.

double SphericalHarmonic2::HarmonicSum	(	double	tau1,
		double	tau2,
		double	x,
		double	y,
		double	z,
		[System::Runtime::InteropServices::Out] double%	gradx,
		[System::Runtime::InteropServices::Out] double%	grady,
		[System::Runtime::InteropServices::Out] double%	gradz
	)

Compute a spherical harmonic sum with two correction terms and its gradient.

Parameters

[in]	tau1	multiplier for correction coefficients C' and S'.
[in]	tau2	multiplier for correction coefficients C'' and S''.
[in]	x	cartesian coordinate.
[in]	y	cartesian coordinate.
[in]	z	cartesian coordinate.
[out]	gradx	x component of the gradient
[out]	grady	y component of the gradient
[out]	gradz	z 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 142 of file SphericalHarmonic2.cpp.

Member Data Documentation

std::vector<double>** NETGeographicLib::SphericalHarmonic2::m_C

private

Definition at line 52 of file SphericalHarmonic2.h.

const int NETGeographicLib::SphericalHarmonic2::m_numCoeffVectors = 3

staticprivate

Definition at line 48 of file SphericalHarmonic2.h.

const GeographicLib::SphericalHarmonic2* NETGeographicLib::SphericalHarmonic2::m_pSphericalHarmonic2

private

Definition at line 44 of file SphericalHarmonic2.h.

std::vector<double> ** NETGeographicLib::SphericalHarmonic2::m_S

private

Definition at line 52 of file SphericalHarmonic2.h.

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

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation