NETGeographicLib::SphericalHarmonic2 Class Reference

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

#include <NETGeographicLib/SphericalHarmonic2.h>

List of all members.

Public Types

enum  Normalization { FULL, SCHMIDT }

Public Member Functions

 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 ()
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)
CircularEngineCircle (double tau1, double tau2, double p, double z, bool gradp)
SphericalCoefficientsCoefficients ()
SphericalCoefficientsCoefficients1 ()
SphericalCoefficientsCoefficients2 ()

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 Cnm are replaced by Cnm + tau' C'nm + tau'' C''nm (and similarly for Snm).

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:

using namespace System;
using namespace NETGeographicLib;

int main(array<System::String ^> ^/*args*/)
{
    try
    {
        int N = 3, N1 = 2, N2 = 1;                     // The maximum degrees
        array<double>^ ca = { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }; // cosine coefficients
        array<double>^ sa = { 6, 5, 4, 3, 2, 1 }; // sine coefficients
        array<double>^ cb = { 1, 2, 3, 4, 5, 6 };
        array<double>^ sb = { 3, 2, 1 };
        array<double>^ cc = { 2, 1 };
        array<double>^ S2 = { 0 };
        double a = 1;
        SphericalHarmonic2^ h = gcnew 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, vx, vy, 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));
        return -1;
    }
    return 0;
}

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

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

NETGeographicLib::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 Cnm.
[in] S the coefficients Snm.
[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.

Referenced by ~SphericalHarmonic2().

NETGeographicLib::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 Cnm.
[in] S the coefficients Snm.
[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.

NETGeographicLib::SphericalHarmonic2::~SphericalHarmonic2 (  )  [inline]

The destructor calls the finalizer.

Definition at line 170 of file SphericalHarmonic2.h.

References SphericalHarmonic2().


Member Function Documentation

double NETGeographicLib::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.

double NETGeographicLib::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.

CircularEngine ^ NETGeographicLib::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.

SphericalCoefficients ^ NETGeographicLib::SphericalHarmonic2::Coefficients (  ) 
Returns:
the zeroth SphericalCoefficients object.
SphericalCoefficients ^ NETGeographicLib::SphericalHarmonic2::Coefficients1 (  ) 
Returns:
the first SphericalCoefficients object.
SphericalCoefficients ^ NETGeographicLib::SphericalHarmonic2::Coefficients2 (  ) 
Returns:
the second SphericalCoefficients object.

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