AMP::DelaunayTessellation Namespace Reference

Classes
class	FaceList

Functions
double	calc_volume (int ndim, const double x[])
	Function to calculate the volume of a simplex.
template<class TYPE >
bool	collinear (const Array< TYPE > &x)
	Check if.
void	compute_Barycentric (const int ndim, const double *x, const double *xi, double *L)
	Subroutine to compute the Barycentric coordinates.
template<class TYPE >
std::tuple< AMP::Array< int >, AMP::Array< int > >	create_tessellation (const Array< TYPE > &x)
	Function that creates the Delaunay Tessellation.
template<int NDIM, class TYPE >
void	get_circumsphere (const std::array< TYPE, NDIM > x0[], double &R, double *center)
	Function to return the circumsphere containing a simplex.
template<int NDIM, class TYPE >
int	test_in_circumsphere (const std::array< TYPE, NDIM > x[], const std::array< TYPE, NDIM > &xi, double TOL_VOL)
	Function to check if a point is inside the circumsphere of a simplex.

Function Documentation

calc_volume()

double AMP::DelaunayTessellation::calc_volume	(	int	ndim,
		const double	x[]
	)

Function to calculate the volume of a simplex.

This function calculates the volume of a N-dimensional simplex Note: the sign of the volume depends on the order of the points. It will be positive for points stored in a clockwise mannor. Note: If the volume is zero, then the simplex is invalid. Eg. a line in 2D or a plane in 3D.

Parameters

ndim	The number of dimensions (currently only 2D and 3D are supported)
x	The coordinates of the vertices of the simplex ( NDIM x NDIM+1 )

collinear()

template<class TYPE >

bool AMP::DelaunayTessellation::collinear

(

const Array< TYPE > &

x

)

Check if.

Check if the points are collinear

This function will check if all the points in a set are collinear

Parameters

x	The coordinates of the vertices (ndim x N)

Returns

Returns true if the points are collinear

compute_Barycentric()

void AMP::DelaunayTessellation::compute_Barycentric	(	const int	ndim,
		const double *	x,
		const double *	xi,
		double *	L
	)

Subroutine to compute the Barycentric coordinates.

This function computes the Barycentric coordinates.

Parameters

[in]	ndim	The number of dimensions
	x	Coordinates of the triangle vertices ( NDIM x NDIM+1 )
	xi	Coordinates of the desired point ( NDIM )
	L	(output) The Barycentric coordinates of the point ( NDIM+1 )

create_tessellation()

template<class TYPE >

std::tuple< AMP::Array< int >, AMP::Array< int > > AMP::DelaunayTessellation::create_tessellation

(

const Array< TYPE > &

x

)

Function that creates the Delaunay Tessellation.

This function will create a valid Delaunay Tessellation in multiple dimensions. Currently only 2D and 3D are supported. If successful, it will return the number of triangles, if unsuccessful it will throw a std::exception. Additionally, there are several optional stuctures.

Parameters

x	The coordinates of the vertices (ndim x N)

Returns

Returns the triangles and triangle neighbors <tri,tri_nab> tri - The returned pointer where the triangles are stored (ndim+1,N) tri_nab - The returned pointer where the triangle neighbors are stored (ndim+1,N)

get_circumsphere()

template<int NDIM, class TYPE >

void AMP::DelaunayTessellation::get_circumsphere	(	const std::array< TYPE, NDIM >	x0[],
		double &	R,
		double *	center
	)

Function to return the circumsphere containing a simplex.

This function computes the circumsphere that contains a simplex

Parameters

[in]	x0	The coordinates of the vertices of the simplex
[out]	R	The radius of the circumsphere
[out]	center	The center of the circumsphere

test_in_circumsphere()

template<int NDIM, class TYPE >

int AMP::DelaunayTessellation::test_in_circumsphere	(	const std::array< TYPE, NDIM >	x[],
		const std::array< TYPE, NDIM > &	xi,
		double	TOL_VOL
	)

Function to check if a point is inside the circumsphere of a simplex.

This function checks if a point is inside the circumsphere of a simplex. It returns -1 if the point is outside the circumsphere, 1 if it is inside the sphere, and 0 if it is within the tolerance of the sphere. Note: For this function to work properly, the volume of the simplex (as computed by calc_volume) must be positive. Note: If we are checking the surface between 2 simplicies and they are both valid (have a positive, non-zero volume), it is suffcient to check the vertix of 1 volume against the circumcircle of the other. We do not need to perform both checks.

Parameters

x	The coordinates of the vertices of the simplex
xi	The coordinates of the vertex to check
TOL_VOL	A tolerance on the volume to use