OpenMD::TriangleQuadrature< NumericReturnType, T > Class Template Reference

A class for integrating a function using numerical quadrature over triangular domains. More...

#include <TriangleQuadrature.hpp>

Static Public Member Functions
static NumericReturnType	Integrate (const std::function< NumericReturnType(const Vector< T, 2 > &)> &f, const TriangleQuadratureRule &rule, const T &area)
	Numerically integrates the function f over a triangle using the given quadrature rule and the initial value.
static NumericReturnType	Integrate (const std::function< NumericReturnType(const Vector< T, 3 > &)> &f, const TriangleQuadratureRule &rule, const T &area)
	Alternative signature for Integrate() that uses three-dimensional barycentric coordinates.

Detailed Description

template<typename NumericReturnType, typename T>
class OpenMD::TriangleQuadrature< NumericReturnType, T >

A class for integrating a function using numerical quadrature over triangular domains.

Template Parameters

NumericReturnType	the output type of the function being integrated. Commonly will be a IEEE floating point scalar (e.g., double), but could be a VectorXd, or any other numeric type that supports both scalar multiplication (i.e., operator*(const NumericReturnType&, double) and addition with another of the same type (i.e., operator+(const NumericReturnType&, const NumericReturnType&)).
T	the scalar type of the function being integrated over. Supported types are currently only IEEE floating point scalars.

Definition at line 35 of file TriangleQuadrature.hpp.

Member Function Documentation

Integrate() [1/2]

template<typename NumericReturnType , typename T >

NumericReturnType OpenMD::TriangleQuadrature< NumericReturnType, T >::Integrate ( const std::function< NumericReturnType(const Vector< T, 2 > &)> & f, const TriangleQuadratureRule & rule, const T & area )

static

Numerically integrates the function f over a triangle using the given quadrature rule and the initial value.

Parameters

f(p)	a function that returns a numerical value for point p in the domain of the triangle, specified in barycentric coordinates. The barycentric coordinates are given by (p[0], p[1], 1 - p[0] - p[1]).
area	the area of the triangle.

Definition at line 61 of file TriangleQuadrature.hpp.

References OpenMD::TriangleQuadratureRule::quadrature_points(), and OpenMD::TriangleQuadratureRule::weights().

Integrate() [2/2]

template<typename NumericReturnType , typename T >

NumericReturnType OpenMD::TriangleQuadrature< NumericReturnType, T >::Integrate ( const std::function< NumericReturnType(const Vector< T, 3 > &)> & f, const TriangleQuadratureRule & rule, const T & area )

static

Alternative signature for Integrate() that uses three-dimensional barycentric coordinates.

Parameters

f(p)	a function that returns a numerical value for point p in the domain of the triangle, specified in barycentric coordinates. The barycentric coordinates are given by (p[0], p[1], p[2]).
area	the area of the triangle.

Definition at line 88 of file TriangleQuadrature.hpp.

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

• math/integration/TriangleQuadrature.hpp