MathTL::LinearBezierMapping Class Reference

#include <chart.h>

Inheritance diagram for MathTL::LinearBezierMapping:

List of all members.

Public Member Functions
	LinearBezierMapping ()
	LinearBezierMapping (const LinearBezierMapping &)
	LinearBezierMapping (const Point< 2 > &, const Point< 2 > &, const Point< 2 > &, const Point< 2 > &)
	~LinearBezierMapping ()
LinearBezierMapping &	operator= (const LinearBezierMapping &x)
void	setup ()
const Point< 2 > &	get_b_00 () const
const Point< 2 > &	get_b_01 () const
const Point< 2 > &	get_b_10 () const
const Point< 2 > &	get_b_11 () const
void	map_point (const Point< 2 > &, Point< 2 > &) const
double	map_point (const double, const int) const
void	map_point_inv (const Point< 2 > &, Point< 2 > &) const
double	map_point_inv (const double, const int) const
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
const bool	in_patch (const Point< 2 > &x) const
const double	a_i (const int i) const
const string	to_string () const
Public Attributes
Point< 2 >	b_00
Point< 2 >	b_01
Point< 2 >	b_10
Point< 2 >	b_11
Static Public Attributes
static const string	className = "LinearBezierMapping"

---

Detailed Description

This class models parametrizations for arbitrary quadrangles in R^2. It's crucial functionality is to map a single point, lying in (0,1)^2 to a point in the quadrangle and vice versa. The involved mapping explicitely looks like:

k(s,t) := (1-s)*(1-t)b_00 + s*(1-t)b_10 + (1-s)*t*b_01 + s*t*b_11,

where the b_ij are the vertices of the qudrangle at hand.

---

Constructor & Destructor Documentation

MathTL::LinearBezierMapping::LinearBezierMapping

(

)

[inline]

default constructor:

MathTL::LinearBezierMapping::LinearBezierMapping

(

const LinearBezierMapping &

kappa

)

[inline]

copy constructor

MathTL::LinearBezierMapping::LinearBezierMapping	(	const Point< 2 > &	_b_00,
		const Point< 2 > &	_b_01,
		const Point< 2 > &	_b_10,
		const Point< 2 > &	_b_11
	)		[inline]

constructor for initialization of the four vertices

MathTL::LinearBezierMapping::~LinearBezierMapping

(

)

[inline]

virtual destructor

---

Member Function Documentation

const double MathTL::LinearBezierMapping::a_i

(

const int

i

)

const [inline, 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

Implements MathTL::Chart< 2, 2 >.

const Point< 2 > & MathTL::LinearBezierMapping::get_b_00

(

)

const [inline]

access to vertices

double MathTL::LinearBezierMapping::map_point	(	const double	,
		const int
	)		const [inline, virtual]

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

Implements MathTL::Chart< 2, 2 >.

double MathTL::LinearBezierMapping::map_point_inv	(	const double	,
		const int
	)		const [inline, virtual]

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

Implements MathTL::Chart< 2, 2 >.

LinearBezierMapping& MathTL::LinearBezierMapping::operator=

(

const LinearBezierMapping &

x

)

assignment operator

void MathTL::LinearBezierMapping::setup

(

)

[inline]

setup routine, called by preceding constructor, sets up generic qudrangle, needed for beeingable to invert the mapping. idea: by appropriate shifting rotation and shearing, the qudrangle can be transformed into another qudrangle for which it is clear how its parametrization be inverted.

const string MathTL::LinearBezierMapping::to_string

(

)

const [virtual]

returns a string representation of this object

Implements MathTL::Chart< 2, 2 >.

---

Member Data Documentation

const string MathTL::LinearBezierMapping::className = "LinearBezierMapping" [static]

static field to store the name of the class

---

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

• geometry/chart.h
• geometry/chart.cpp