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Public Member Functions | Private Attributes

qc::Isotropy< RealType > Class Template Reference

#include <anisotropies.h>

Inheritance diagram for qc::Isotropy< RealType >:
qc::Anisotropy3dGraphInterface< RealType, Isotropy< RealType > >

List of all members.

Public Member Functions

 Isotropy (RealType eps)
void implicitPart (const aol::Vec2< RealType > &, const aol::Vec2< RealType > &z, aol::Matrix22< RealType > &mat) const
void explicitPart (const aol::Vec2< RealType > &, const aol::Vec2< RealType > &z, aol::Matrix22< RealType > &mat) const
void implicitPart (const aol::Vec2< RealType > &z, aol::Matrix22< RealType > &mat) const
 second derivative, implicit part of the p-regularized willmore flow (graph case)
void explicitPart (const aol::Vec2< RealType > &z, aol::Matrix22< RealType > &mat) const
 second derivative, explicit part of the p-regularized willmore flow (graph case)
void gammaFirstDerivative (const aol::Vec2< RealType > &, const aol::Vec2< RealType > &z, aol::Vec2< RealType > &v) const
void gammaFirstDerivative (const aol::Vec2< RealType > &z, aol::Vec2< RealType > &v) const
RealType gammaNorm (const aol::Vec2< RealType > &z) const

Private Attributes

RealType _epsilon

Detailed Description

template<typename RealType>
class qc::Isotropy< RealType >

Definition at line 1960 of file anisotropies.h.


Constructor & Destructor Documentation

template<typename RealType >
qc::Isotropy< RealType >::Isotropy ( RealType  eps  )  [inline]

Definition at line 1970 of file anisotropies.h.

: Anisotropy3dGraphInterface<RealType, Isotropy<RealType> > ( ), _epsilon ( eps ) { }


Member Function Documentation

template<typename RealType >
void qc::Isotropy< RealType >::explicitPart ( const aol::Vec2< RealType > &  ,
const aol::Vec2< RealType > &  z,
aol::Matrix22< RealType > &  mat 
) const [inline]

Reimplemented from qc::Anisotropy3dGraphInterface< RealType, Isotropy< RealType > >.

Definition at line 1976 of file anisotropies.h.

                                                                                                                {
    explicitPart ( z, mat );
  }

template<typename RealType >
void qc::Isotropy< RealType >::explicitPart ( const aol::Vec2< RealType > &  z,
aol::Matrix22< RealType > &  mat 
) const [inline]

second derivative, explicit part of the p-regularized willmore flow (graph case)

Reimplemented from qc::Anisotropy3dGraphInterface< RealType, Isotropy< RealType > >.

Definition at line 1986 of file anisotropies.h.

References qc::Isotropy< RealType >::_epsilon, and aol::Sqr().

                                                                                     {
    for ( int i = 0; i < 2; i++ ) for ( int j = 0; j < 2; j++ ) mat[i][j] = z[i] * z[j];
    mat /= pow ( sqrt ( aol::Sqr ( z[0] ) + aol::Sqr ( z[1] ) + aol::Sqr ( _epsilon ) ), 3. ) ;
  }

template<typename RealType >
void qc::Isotropy< RealType >::gammaFirstDerivative ( const aol::Vec2< RealType > &  ,
const aol::Vec2< RealType > &  z,
aol::Vec2< RealType > &  v 
) const [inline]
template<typename RealType >
void qc::Isotropy< RealType >::gammaFirstDerivative ( const aol::Vec2< RealType > &  z,
aol::Vec2< RealType > &  v 
) const [inline]

This method is for the graph-case. Here the normal is (-grad u, 1). Notice: To use this method you have to set the graph-flag before!!

Reimplemented from qc::Anisotropy3dGraphInterface< RealType, Isotropy< RealType > >.

Definition at line 1996 of file anisotropies.h.

References qc::Isotropy< RealType >::gammaNorm().

                                                                                       {
    v = z;
    v /= gammaNorm ( z );
  }

template<typename RealType >
RealType qc::Isotropy< RealType >::gammaNorm ( const aol::Vec2< RealType > &  z  )  const [inline]

This method is for the graph-case. Here the normal is (-grad u, 1). Notice: To use this method you have to set the graph-flag before!!

Reimplemented from qc::Anisotropy3dGraphInterface< RealType, Isotropy< RealType > >.

Definition at line 2001 of file anisotropies.h.

References qc::Isotropy< RealType >::_epsilon, and aol::Sqr().

Referenced by qc::Isotropy< RealType >::gammaFirstDerivative().

                                                          {
    return sqrt ( aol::Sqr ( z[0] ) + aol::Sqr ( z[1] ) + aol::Sqr ( _epsilon ) ) ;
  }

template<typename RealType >
void qc::Isotropy< RealType >::implicitPart ( const aol::Vec2< RealType > &  z,
aol::Matrix22< RealType > &  mat 
) const [inline]

second derivative, implicit part of the p-regularized willmore flow (graph case)

Reimplemented from qc::Anisotropy3dGraphInterface< RealType, Isotropy< RealType > >.

Definition at line 1980 of file anisotropies.h.

References qc::Isotropy< RealType >::_epsilon, and aol::Sqr().

                                                                                     {
    mat[0][0] = mat[1][1] = 1.;
    mat[1][0] = mat[0][1] = 0.;
    mat /= sqrt ( aol::Sqr ( z[0] ) + aol::Sqr ( z[1] ) + aol::Sqr ( _epsilon ) ) ;
  }

template<typename RealType >
void qc::Isotropy< RealType >::implicitPart ( const aol::Vec2< RealType > &  ,
const aol::Vec2< RealType > &  z,
aol::Matrix22< RealType > &  mat 
) const [inline]

Reimplemented from qc::Anisotropy3dGraphInterface< RealType, Isotropy< RealType > >.

Definition at line 1972 of file anisotropies.h.

                                                                                                                {
    implicitPart ( z, mat );
  }


Member Data Documentation

template<typename RealType >
RealType qc::Isotropy< RealType >::_epsilon [private]

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

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