GeographicLib::CircularEngine Class Reference

Spherical harmonic sums for a circle. More...

#include <GeographicLib/CircularEngine.hpp>

Public Member Functions
	CircularEngine ()
Math::real	operator() (real sinlon, real coslon) const
Math::real	operator() (real lon) const
Math::real	operator() (real sinlon, real coslon, real &gradx, real &grady, real &gradz) const
Math::real	operator() (real lon, real &gradx, real &grady, real &gradz) const

Friends
class	SphericalEngine

Detailed Description

Spherical harmonic sums for a circle.

The class is a companion to SphericalEngine. If the results of a spherical harmonic sum are needed for several points on a circle of constant latitude lat and height h, then SphericalEngine::Circle can compute the inner sum, which is independent of longitude lon, and produce a CircularEngine object. CircularEngine::operator()() can then be used to perform the outer sum for particular vales of lon. This can lead to substantial improvements in computational speed for high degree sum (approximately by a factor of N / 2 where N is the maximum degree).

CircularEngine is tightly linked to the internals of SphericalEngine. For that reason, the constructor for this class is private. Use SphericalHarmonic::Circle, SphericalHarmonic1::Circle, and SphericalHarmonic2::Circle to create instances of this class.

CircularEngine stores the coefficients needed to allow the summation over order to be performed in 2 or 6 vectors of length M + 1 (depending on whether gradients are to be calculated). For this reason the constructor may throw a std::bad_alloc exception.

Example of use:

// Example of using the GeographicLib::CircularEngine class
 
#include <iostream>
#include <exception>
#include <vector>
#include <GeographicLib/CircularEngine.hpp>
#include <GeographicLib/SphericalHarmonic.hpp>
 
using namespace std;
using namespace GeographicLib;
 
int main() {
  // This computes the same value as example-SphericalHarmonic.cpp using a
  // CircularEngine (which will be faster if many values on a circle of
  // latitude are to be found).
  try {
    using std::hypot;
    int N = 3;                  // The maxium degree
    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 a = 1;
    SphericalHarmonic h(C, S, N, a);
    double x = 2, y = 3, z = 1, p = hypot(x, y);
    CircularEngine circ = h.Circle(p, z, true);
    double v, vx, vy, vz;
    v = circ(x/p, y/p, vx, vy, vz);
    cout << v << " " << vx << " " << vy << " " << vz << "\n";
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

Definition at line 52 of file CircularEngine.hpp.

Constructor & Destructor Documentation

CircularEngine()

GeographicLib::CircularEngine::CircularEngine ( )

inline

A default constructor. CircularEngine::operator()() on the resulting object returns zero. The resulting object can be assigned to the result of SphericalHarmonic::Circle.

Definition at line 110 of file CircularEngine.hpp.

Member Function Documentation

operator()() [1/4]

Math::real GeographicLib::CircularEngine::operator() ( real  sinlon, real  coslon  ) const

inline

Evaluate the sum for a particular longitude given in terms of its sine and cosine.

Parameters

[in]	sinlon	the sine of the longitude.
[in]	coslon	the cosine of the longitude.

Returns

V the value of the sum.

The arguments must satisfy sinlon² + coslon² = 1.

Definition at line 128 of file CircularEngine.hpp.

operator()() [2/4]

Math::real GeographicLib::CircularEngine::operator() ( real  lon ) const

inline

Evaluate the sum for a particular longitude.

Parameters

[in]

lon

the longitude (degrees).

Returns

V the value of the sum.

Definition at line 139 of file CircularEngine.hpp.

References GeographicLib::Math::sincosd().

operator()() [3/4]

Math::real GeographicLib::CircularEngine::operator() ( real  sinlon, real  coslon, real &  gradx, real &  grady, real &  gradz  ) const

inline

Evaluate the sum and its gradient for a particular longitude given in terms of its sine and cosine.

Parameters

[in]	sinlon	the sine of the longitude.
[in]	coslon	the cosine of the longitude.
[out]	gradx	x component of the gradient.
[out]	grady	y component of the gradient.
[out]	gradz	z component of the gradient.

Returns

V the value of the sum.

The gradients will only be computed if the CircularEngine object was created with this capability (e.g., via gradp = true in SphericalHarmonic::Circle). If not, gradx, etc., will not be touched. The arguments must satisfy sinlon² + coslon² = 1.

Definition at line 162 of file CircularEngine.hpp.

operator()() [4/4]

Math::real GeographicLib::CircularEngine::operator() ( real  lon, real &  gradx, real &  grady, real &  gradz  ) const

inline

Evaluate the sum and its gradient for a particular longitude.

Parameters

[in]	lon	the longitude (degrees).
[out]	gradx	x component of the gradient.
[out]	grady	y component of the gradient.
[out]	gradz	z component of the gradient.

Returns

V the value of the sum.

The gradients will only be computed if the CircularEngine object was created with this capability (e.g., via gradp = true in SphericalHarmonic::Circle). If not, gradx, etc., will not be touched.

Definition at line 181 of file CircularEngine.hpp.

References GeographicLib::Math::sincosd().

Friends And Related Function Documentation

SphericalEngine

friend class SphericalEngine

friend

Definition at line 69 of file CircularEngine.hpp.

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

• CircularEngine.hpp
• CircularEngine.cpp