geom::SimplexMeanRatio< N, T > Class Template Reference

Implements the mean ratio quality metric. More...

#include <SimplexMeanRatio.h>

Inheritance diagram for geom::SimplexMeanRatio< N, T >:


Public Types
typedef T	Number
	The number type.
typedef Base::Vertex	Vertex
	The class for a vertex.
typedef Base::Simplex	Simplex
	The simplex type.
typedef Base::Matrix	Matrix
	An NxN matrix.
Public Member Functions
Constructors etc.
	SimplexMeanRatio ()
	Default constructor. Un-initialized memory.
	SimplexMeanRatio (const SimplexMeanRatio &other)
	Copy constructor.
	SimplexMeanRatio (const Simplex &s)
	Construct from a simplex.
SimplexMeanRatio &	operator= (const SimplexMeanRatio &other)
	Assignment operator.
	~SimplexMeanRatio ()
	Trivial destructor.
Mathematical functions
Number	operator() () const
	Return the mean ratio (eta) quality metric.
Number	operator() (const Simplex &simplex) const
	Return the mean ratio (eta) quality metric.
void	computeGradient (Vertex *gradient) const
	Calculate the gradient of the mean ratio (eta) quality metric.
Protected Member Functions
Number	computeFunctionGivenS2 (Number s2) const
	Return the eta quality metric given .

Detailed Description

template<int N, typename T = double>
class geom::SimplexMeanRatio< N, T >

Implements the mean ratio quality metric.

Parameters:

	N	is the dimension.
	T	is the number type. By default it is double.

This class implements the mean ratio quality metric. Let $ S $

be the Jacobian matrix, $\sigma$ be the Jacobian determinant and $| \cdot |$ be the Frobenius norm. The operator() member function returns the mean ratio quality metric:

$\eta = \frac{ |S|^2 }{ N \sigma^{2/N} }.$

This quality metric is only defined for simplices with positive content. (The Jacobian determinant must be positive.)

computeGradient() calculates the gradient of the mean ratio metric.

Before evaluating the mean ratio metric, you must set the Jacobian matrix with setFunction() or set(). Before evaluating the gradient of the metric, you must set the Jacobian matrix and its gradient with set().