ISOP Namespace Reference

ISOP namespace is for functions related to isoparametric interpolation. More...

Namespaces
namespace	Rules
	Quadrature rules. Must be of the closed type.

Classes
struct	isop_map
	Functor to transparently map [-1,1]x[-1,1] to interpolation space. More...
struct	quadrature_result
	Result of numerical integration. More...

Functions
double	isop (const double nodes[], double xi, double eta)
	Do the isoparametric interpolation given a list of 8 nodes. See notes for isop_render().
template<typename Function>
isop_map< Function >	make_isop_map (Function f, const double *x, const double *y)
	Creates an isoparametric mapping functor.
double	isop_render (Source &source, const double nodx[], const double nody[], double a_xi, double b_xi, double a_eta, double b_eta)
	Integrate source flux using the isoparameterized lens.
template<typename Rule, typename Function>
quadrature_result	quadrature (Function f, double a0, double b0, double a1, double b1, double pg, double ag)

Detailed Description

ISOP namespace is for functions related to isoparametric interpolation.

Function Documentation

isop()

double ISOP::isop ( const double nodes[], double xi, double eta )

inline

Do the isoparametric interpolation given a list of 8 nodes. See notes for isop_render().

Parameters

nodes	values of interpolated quantity (ie kappa, y coordinate) for the 8 border points
xi	x position where interpolate is wanted in [-1,1 units
eta	y position where interpolate is wanted in [-1,1 units

isop_render()

double ISOP::isop_render	(	Source &	source,
		const double	nodx[],
		const double	nody[],
		double	a_xi,
		double	b_xi,
		double	a_eta,
		double	b_eta )

Integrate source flux using the isoparameterized lens.

Integrate the surface brightness of a source using the isoparametric representation of the lens mapping.

The isoparametric representation is defined by the 8 nodes on the border of a [-1,1]x[-1,1] square. The first node (index 0) is in the bottom-left corner, and then nodes are counted counter-clockwise:

* 6 -- 5 -- 4
* |         |
* 7         3
* |         |
* 0 -- 1 -- 2
* 

The positions of the nodes in the isoparametric space are

* (-1, 1) -- ( 0, 1) -- ( 1, 1)
*    |                     |
* (-1, 0)               ( 1, 0)
*    |                     |
* (-1,-1) -- ( 0,-1) -- ( 1,-1)
* 

The interval to be integrated is given in terms of the isoparametric coordinates xi and eta.

Parameters

source	Source to be integrated
nodx	Source plane x coordinates of 8 nodes.
nody	Source plane y coordinates of 8 nodes.
a_xi	Lower bound of xi integration.
b_xi	Upper bound of xi integration.
a_eta	Lower bound of eta integration.
b_eta	Upper bound of eta integration.