MathTL::Chart< DIM_d, DIM_m > Class Template Reference

#include <chart.h>

List of all members.

Public Member Functions
virtual	~Chart ()
	virtual destructor
virtual void	map_point (const Point< DIM_d > &x, Point< DIM_m > &y) const =0
virtual double	map_point (const double, const int) const =0
virtual void	map_point_inv (const Point< DIM_m > &x, Point< DIM_d > &y) const =0
virtual double	map_point_inv (const double, const int) const =0
virtual const double	Gram_factor (const Point< DIM_d > &x) const =0
virtual const double	Gram_D_factor (const unsigned int i, const Point< DIM_d > &x) const =0
virtual const double	Dkappa_inv (const unsigned int i, const unsigned int j, const Point< DIM_d > &x) const =0
virtual const double	a_i (const int i) const =0
virtual const bool	in_patch (const Point< DIM_m > &x) const =0
virtual const string	to_string () const =0

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Detailed Description

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>
class MathTL::Chart< DIM_d, DIM_m >

Abstract base class for smooth parametrizations kappa: (0,1)^d -> R^m of single "patches" in R^m.

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Member Function Documentation

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual const double MathTL::Chart< DIM_d, DIM_m >::a_i

(

const int

i

)

const [pure virtual]

return the i-th diagonal element in the case of kappa not depending on x TODO: shift this virtual method into a subclass of Chart

Implemented in MathTL::LinearBezierMapping, MathTL::SimpleAffineLinearMapping< DIM >, MathTL::AffineLinearMapping< DIM >, and MathTL::RingChart.

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual const double MathTL::Chart< DIM_d, DIM_m >::Dkappa_inv	(	const unsigned int	i,
		const unsigned int	j,
		const Point< DIM_d > &	x
	)		const [pure virtual]

(i,j)-th element of (D (kappa^{-1}))(x)

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual const double MathTL::Chart< DIM_d, DIM_m >::Gram_D_factor	(	const unsigned int	i,
		const Point< DIM_d > &	x
	)		const [pure virtual]

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

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual const double MathTL::Chart< DIM_d, DIM_m >::Gram_factor

(

const Point< DIM_d > &

x

)

const [pure virtual]

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

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual const bool MathTL::Chart< DIM_d, DIM_m >::in_patch

(

const Point< DIM_m > &

x

)

const [pure virtual]

checks whether a special point x lies in the patch represented by this parametrization

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual void MathTL::Chart< DIM_d, DIM_m >::map_point	(	const Point< DIM_d > &	x,
		Point< DIM_m > &	y
	)		const [pure virtual]

map a point (forward) y = kappa(x)

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual double MathTL::Chart< DIM_d, DIM_m >::map_point	(	const double	,
		const int
	)		const [pure virtual]

special 1D version TODO: remove this member in this generic branch!

Implemented in MathTL::LinearBezierMapping, MathTL::SimpleAffineLinearMapping< DIM >, MathTL::AffineLinearMapping< DIM >, and MathTL::RingChart.

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual void MathTL::Chart< DIM_d, DIM_m >::map_point_inv	(	const Point< DIM_m > &	x,
		Point< DIM_d > &	y
	)		const [pure virtual]

inverse mapping y = kappa^{-1}(x)

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual double MathTL::Chart< DIM_d, DIM_m >::map_point_inv	(	const double	,
		const int
	)		const [pure virtual]

special 1D version TODO: remove this member in this generic branch!

Implemented in MathTL::LinearBezierMapping, MathTL::SimpleAffineLinearMapping< DIM >, MathTL::AffineLinearMapping< DIM >, and MathTL::RingChart.

template<unsigned int DIM_d, unsigned int DIM_m = DIM_d>

virtual const string MathTL::Chart< DIM_d, DIM_m >::to_string

(

)

const [pure virtual]

returns a string representation of this object

Implemented in MathTL::LinearBezierMapping, MathTL::SimpleAffineLinearMapping< DIM >, MathTL::AffineLinearMapping< DIM >, and MathTL::RingChart.

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

• geometry/chart.h