.NET wrapper for GeographicLib::SphericalHarmonic1. More...

#include <SphericalHarmonic1.h>

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

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

SphericalCoefficients	Coefficients ()

SphericalCoefficients	Coefficients1 ()

double	HarmonicSum (double tau, double x, double y, double z)

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

	SphericalHarmonic1 (array< double >^ C, array< double >^ S, int N, array< double >^ C1, array< double >^ S1, int N1, double a, Normalization norm)

	SphericalHarmonic1 (array< double >^ C, array< double >^ S, int N, int nmx, int mmx, array< double >^ C1, array< double >^ S1, int N1, int nmx1, int mmx1, double a, Normalization norm)

	~SphericalHarmonic1 ()

Private Member Functions
	!SphericalHarmonic1 (void)

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

const GeographicLib::SphericalHarmonic1 *	m_pSphericalHarmonic1

std::vector< double > **	m_S

Static Private Attributes
static const int	m_numCoeffVectors = 2

Detailed Description

.NET wrapper for GeographicLib::SphericalHarmonic1.

This class allows .NET applications to access GeographicLib::SphericalHarmonic1.

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

C# Example:

using System;
using NETGeographicLib;
 
namespace example_SphericalHarmonic1
{
    class Program
    {
        static void Main(string[] args)
        {
            try {
                int N = 3, N1 = 2;                  // 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 a = 1;
                SphericalHarmonic1 h = new SphericalHarmonic1(ca, sa, N, cb, sb, N1, a, SphericalHarmonic1.Normalization.SCHMIDT);
                double tau = 0.1, x = 2, y = 3, z = 1;
                double v, vx, vy, vz;
                v = h.HarmonicSum(tau, 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::SphericalHarmonic1 class
 
#include <iostream>
#include <exception>
#include <vector>
#include <GeographicLib/SphericalHarmonic1.hpp>
 
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;
  }
}

Visual Basic Example:

Imports NETGeographicLib
 
Module example_SphericalHarmonic1
    Sub Main()
        Try
            Dim N As Integer = 3, N1 = 2                  ' 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 a As Double = 1
            Dim h As SphericalHarmonic1 = New SphericalHarmonic1(ca, sa, N, cb, sb, N1, a, SphericalHarmonic1.Normalization.SCHMIDT)
            Dim tau As Double = 0.1, x = 2, y = 3, z = 1
            Dim vx, vy, vz As Double
            Dim v As Double = h.HarmonicSum(tau, 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 returns a SphericalCoefficients object.

Definition at line 38 of file SphericalHarmonic1.h.

Member Enumeration Documentation

◆ Normalization

enum NETGeographicLib::SphericalHarmonic1::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 56 of file SphericalHarmonic1.h.

Constructor & Destructor Documentation

◆ !SphericalHarmonic1()

SphericalHarmonic1::!SphericalHarmonic1 ( void )

private

Definition at line 23 of file SphericalHarmonic1.cpp.

◆ SphericalHarmonic1() [1/2]

SphericalHarmonic1::SphericalHarmonic1	(	array< double >^	C,
		array< double >^	S,
		int	N,
		array< double >^	C1,
		array< double >^	S1,
		int	N1,
		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 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 SphericalHarmonic1::FULL (the default) or SphericalHarmonic1::SCHMIDT.

Exceptions

GeographicErr	if N and N1 do not satisfy N ≥ N1 ≥ −1.
GeographicErr	if 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 51 of file SphericalHarmonic1.cpp.

◆ SphericalHarmonic1() [2/2]

SphericalHarmonic1::SphericalHarmonic1	(	array< double >^	C,
		array< double >^	S,
		int	N,
		int	nmx,
		int	mmx,
		array< double >^	C1,
		array< double >^	S1,
		int	N1,
		int	nmx1,
		int	mmx1,
		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]	a	the reference radius appearing in the definition of the sum.
[in]	norm	the normalization for the associated Legendre polynomials, either SphericalHarmonic1::FULL (the default) or SphericalHarmonic1::SCHMIDT.

Exceptions

GeographicErr	if the parameters do not satisfy N ≥ nmx ≥ mmx ≥ −1; N1 ≥ nmx1 ≥ mmx1 ≥ −1; N ≥ N1; nmx ≥ nmx1; mmx ≥ mmx1.
GeographicErr	if 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 88 of file SphericalHarmonic1.cpp.

◆ ~SphericalHarmonic1()

NETGeographicLib::SphericalHarmonic1::~SphericalHarmonic1 ( )

inline

The destructor calls the finalizer.

Definition at line 151 of file SphericalHarmonic1.h.

Member Function Documentation

◆ Circle()

CircularEngine SphericalHarmonic1::Circle	(	double	tau,
		double	p,
		double	z,
		bool	gradp
	)

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

Parameters

[in]	tau	the multiplier for the correction coefficients.
[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.

SphericalHarmonic1::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}. 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 146 of file SphericalHarmonic1.cpp.

◆ Coefficients()

SphericalCoefficients SphericalHarmonic1::Coefficients ( )

Returns: the zeroth SphericalCoefficients object.

Definition at line 159 of file SphericalHarmonic1.cpp.

◆ Coefficients1()

SphericalCoefficients SphericalHarmonic1::Coefficients1 ( )

Returns: the first SphericalCoefficients object.

Definition at line 165 of file SphericalHarmonic1.cpp.

◆ HarmonicSum() [1/2]

double SphericalHarmonic1::HarmonicSum	(	double	tau,
		double	x,
		double	y,
		double	z
	)

Compute a spherical harmonic sum with a correction term.

Parameters

[in]	tau	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 126 of file SphericalHarmonic1.cpp.

◆ HarmonicSum() [2/2]

double SphericalHarmonic1::HarmonicSum	(	double	tau,
		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 a correction term and its gradient.

Parameters

[in]	tau	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 132 of file SphericalHarmonic1.cpp.

Member Data Documentation

◆ m_C

std::vector<double>** NETGeographicLib::SphericalHarmonic1::m_C

private

Definition at line 51 of file SphericalHarmonic1.h.

◆ m_numCoeffVectors

const int NETGeographicLib::SphericalHarmonic1::m_numCoeffVectors = 2

staticprivate

Definition at line 47 of file SphericalHarmonic1.h.

◆ m_pSphericalHarmonic1

const GeographicLib::SphericalHarmonic1* NETGeographicLib::SphericalHarmonic1::m_pSphericalHarmonic1

private

Definition at line 42 of file SphericalHarmonic1.h.

◆ m_S

std::vector<double> ** NETGeographicLib::SphericalHarmonic1::m_S

private

Definition at line 51 of file SphericalHarmonic1.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

◆ Normalization

Constructor & Destructor Documentation

◆ !SphericalHarmonic1()

◆ SphericalHarmonic1() [1/2]

◆ SphericalHarmonic1() [2/2]

◆ ~SphericalHarmonic1()

Member Function Documentation

◆ Circle()

◆ Coefficients()

◆ Coefficients1()

◆ HarmonicSum() [1/2]

◆ HarmonicSum() [2/2]

Member Data Documentation

◆ m_C

◆ m_numCoeffVectors

◆ m_pSphericalHarmonic1

◆ m_S