Metric Class Reference

Class representing a metric on a manifold. More...

#include <geometry.h>

Inheritance diagram for Metric:

Public Member Functions
	Metric (int cS)
	Constructor. More...
virtual	~Metric ()
	Destructor.
double	g (int i, int j, Point p)
	Component of the metric. More...
double	invg (int i, int j, Point p)
	Component of the inverse metric. More...
double	christoffel (int i, int j, int k, Point p)
	Component of the Christoffel symbol. More...
double	g (vector4 u, vector4 v, Point p)
	Dot product. More...
vector4	christoffel (vector4 u, vector4 v, Point p)
	Christoffel symbol acting on two vectors. More...

Protected Member Functions
double	dg (int i, int j, int k, Point p)
	Partial derivative of the metric. More...
virtual double	_g (int i, int j, Point p)=0
	Component of the metric. More...
virtual double	_invg (int i, int j, Point p)=0
	Component of the inverse metric. More...
virtual double	_christoffel (int i, int j, int k, Point p)=0
	Component of the Christoffel symbol. More...

Protected Attributes
int	coordSystem

Detailed Description

Class representing a metric on a manifold.

This class represents the metric tensor on a manifold, expressed in some coordinate system.

Constructor & Destructor Documentation

Metric::Metric

(

int

cS

)

Constructor.

Parameters

cS	Coordinate system.

Member Function Documentation

virtual double Metric::_christoffel ( int  i, int  j, int  k, Point  p  )

protectedpure virtual

Component of the Christoffel symbol.

Function calculating a component of the Christoffel symbol.

Parameters

i	First index of the component
j	Second index of the component
k	Third index of the component
p	The point at which the component is evaluated

Returns

Gamma^i_jk(p)

Implemented in KerrNearPoleMetric, SchwNearPoleMetric, KerrEFMetric, and SchwEFMetric.

virtual double Metric::_g ( int  i, int  j, Point  p  )

protectedpure virtual

Component of the metric.

Function calculating a component of the metric.

Parameters

i	First index of the component
j	Second index of the component
p	The point at which the component is evaluated

Returns

g_ij(p)

Implemented in KerrNearPoleMetric, SchwNearPoleMetric, KerrEFMetric, and SchwEFMetric.

virtual double Metric::_invg ( int  i, int  j, Point  p  )

protectedpure virtual

Component of the inverse metric.

Function calculating a component of the inverse metric.

Parameters

i	First index of the component
j	Second index of the component
p	The point at which the component is evaluated

Returns

g^ij(p)

Implemented in KerrNearPoleMetric, SchwNearPoleMetric, KerrEFMetric, and SchwEFMetric.

double Metric::christoffel	(	int	i,
		int	j,
		int	k,
		Point	p
	)

Component of the Christoffel symbol.

Function returning a component of the Christoffel symbol Uses internal caching.

Parameters

i	First index of the component
j	Second index of the component
k	Third index of the component
p	The point at which the component is evaluated

Returns

Gamma^i_jk(p)

vector4 Metric::christoffel	(	vector4	u,
		vector4	v,
		Point	p
	)

Christoffel symbol acting on two vectors.

Function returning result of contraction of the Christoffel symbol with two vectors.

Parameters

u	First vector
v	Second vector
p	The point at which the dot product is evaluated

Returns

Gamma^i_jk(p) u^j v^k

double Metric::dg ( int  i, int  j, int  k, Point  p  )

protected

Partial derivative of the metric.

Returns partial derivative of a component of the metric with respect to some coordinate.

Parameters

i	First index of the component
j	Second index of the component
k	The index of the coordinate, with respect to which the derivative is calculated
p	The point at which the derivative is evaluated

Returns

dg_ij/dx^k(p)

double Metric::g	(	int	i,
		int	j,
		Point	p
	)

Component of the metric.

Function returning a component of the metric Uses internal caching.

Parameters

i	First index of the component
j	Second index of the component
p	The point at which the component is evaluated

Returns

g_ij(p)

double Metric::g	(	vector4	u,
		vector4	v,
		Point	p
	)

Dot product.

Function returning the dot product of two vectors.

Parameters

u	First vector
v	Second vector
p	The point at which the dot product is evaluated

Returns

g_ij(p) u^i v^j

double Metric::invg	(	int	i,
		int	j,
		Point	p
	)

Component of the inverse metric.

Function returning a component of the inverse metric Uses internal caching.

Parameters

i	First index of the component
j	Second index of the component
p	The point at which the component is evaluated

Returns

g^ij(p)

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

• engine/geometry.h
• engine/geometry.cpp