MathTL::RingChart Class Reference

#include <ring_chart.h>

Inheritance diagram for MathTL::RingChart:

List of all members.

Public Member Functions
	RingChart (const double r0, const double r1)
	constructor from two radii
virtual	~RingChart ()
	virtual destructor
void	map_point (const Point< 2 > &x, Point< 2 > &y) const
	map a point (forward) y = kappa(x)
double	map_point (const double, const int) const
	dummy 1D relict
void	map_point_inv (const Point< 2 > &x, Point< 2 > &y) const
	inverse mapping y = kappa^{-1}(x)
double	map_point_inv (const double, const int) const
	dummy 1D relict
const double	Gram_factor (const Point< 2 > &x) const
const double	Gram_D_factor (const unsigned int i, const Point< 2 > &x) const
const double	Dkappa_inv (const unsigned int i, const unsigned int j, const Point< 2 > &x) const
	(i,j)-th element of (D (kappa^{-1}))(x)
const bool	in_patch (const Point< 2 > &x) const
	checks whether a special point x lies in the patch represented by this parametrization
const double	a_i (const int i) const
	dummy
const string	to_string () const
	returns a string representation of this object
Protected Attributes
double	r0_
double	r1_

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Detailed Description

A parametrization of the ring-shaped domain R = {(x,y) : r_0 <= ||(x,y)|| <= r_1 } by kappa: (0,1)^2 -> R, kappa(s,phi) = r(s)(cos(2*pi*phi),sin(2*pi*phi)) with r(s) = r_0+s*(r_1-r_0).

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Member Function Documentation

const double MathTL::RingChart::Gram_D_factor	(	const unsigned int	i,
		const Point< 2 > &	x
	)		const

i-th partial derivative of Gram factor (additional factor for integration over first derivatives)

const double MathTL::RingChart::Gram_factor

(

const Point< 2 > &

x

)

const [inline]

square root of the Gram determinant sqrt(det(Dkappa(x)^T * Dkappa(x))) (additional factor for integration over "plain" functions)

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

• geometry/ring_chart.h
• geometry/ring_chart.cpp