SimplexMeanRatio< N, T > Class Template Reference

Implements the mean ratio quality metric. More...

#include <SimplexMeanRatio.h>

Inheritance diagram for SimplexMeanRatio< N, T >:
SimplexJacQF< N, T > SimplexModMeanRatio< N, T >

List of all members.

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 $ |S|^2 $.

Detailed Description

template<int N, typename T = double>
class 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().

Member Function Documentation

template<int N, typename T = double>
void SimplexMeanRatio< N, T >::computeGradient ( Vertex *  gradient  )  const

Calculate the gradient of the mean ratio (eta) quality metric.

Precondition:
The Jacobian determinant must be positive.

Let $ S $ be the Jacobian matrix, $ \sigma $ be the Jacobian determinant and $ | \cdot | $ be the Frobenius norm. The eta function is

\[ \frac{ |S|^2 }{ N \sigma^{2/N} }. \]

Reimplemented in SimplexModMeanRatio< N, T >.

template<int N, typename T = double>
Number SimplexMeanRatio< N, T >::operator() ( const Simplex &  simplex  )  const [inline]

Return the mean ratio (eta) quality metric.

Precondition:
The Jacobian determinant must be positive.
Returns:
Let $ S $ be the Jacobian matrix, $ \sigma $ be the Jacobian determinant and $ | \cdot | $ be the Frobenius norm. Return

\[ \frac{ |S|^2 }{ N \sigma^{2/N} }. \]

Reimplemented in SimplexModMeanRatio< N, T >.

References SimplexMeanRatio< N, T >::operator()(), and SimplexJacQF< N, T >::setFunction().

template<int N, typename T = double>
Number SimplexMeanRatio< N, T >::operator() (  )  const

Return the mean ratio (eta) quality metric.

Precondition:
The Jacobian determinant must be positive.
Returns:
Let $ S $ be the Jacobian matrix, $ \sigma $ be the Jacobian determinant and $ | \cdot | $ be the Frobenius norm. Return

\[ \frac{ |S|^2 }{ N \sigma^{2/N} }. \]

Reimplemented in SimplexModMeanRatio< N, T >.

Referenced by SimplexMeanRatio< N, T >::operator()().

The documentation for this class was generated from the following file:
Generated on Thu Jun 30 02:14:58 2016 for Computational Geometry Package by  doxygen 1.6.3