Ponca::SingularWeightKernel< _Scalar > Class Template Reference

Compact singular WeightKernel defined in \(\left]0 : 1\right]\). More...

#include <weightKernel.h>

Inheritance diagram for Ponca::SingularWeightKernel< _Scalar >:

Collaboration diagram for Ponca::SingularWeightKernel< _Scalar >:

Public Types
typedef _Scalar	Scalar
	Scalar type defined outside the class.

Public Member Functions
Scalar	f (const Scalar &_x) const
	Defines the Singular weighting function \( w(x) = 1 / (x^2) \).
Scalar	df (const Scalar &_x) const
	Defines the Singular first order weighting function \( \nabla w(x) = -2 / (x^3) \).
Scalar	ddf (const Scalar &_x) const
	Defines the Singular second order weighting function \( \nabla^2 w(x) = 6 / (x^4) \).

Static Public Attributes
static constexpr bool	isCompact = true
	The kernel is compact and shall not be evaluated outside of the scale bounds.
static constexpr bool	isDValid = true
	df is defined and valid on the definition interval
static constexpr bool	isDDValid = true
	ddf is defined and valid on the definition interval

Detailed Description

template<typename _Scalar>
class Ponca::SingularWeightKernel< _Scalar >

Compact singular WeightKernel defined in \(\left]0 : 1\right]\).

Weight function is an implementation of an unnumbered equation but defined in the Appendices in [1]

Definition at line 193 of file weightKernel.h.

Member Typedef Documentation

Scalar

template<typename _Scalar >

typedef _Scalar Ponca::SingularWeightKernel< _Scalar >::Scalar

Scalar type defined outside the class.

Definition at line 197 of file weightKernel.h.

Member Function Documentation

ddf()

template<typename _Scalar >

Scalar Ponca::SingularWeightKernel< _Scalar >::ddf ( const Scalar &  _x ) const

inline

Defines the Singular second order weighting function \( \nabla^2 w(x) = 6 / (x^4) \).

Definition at line 212 of file weightKernel.h.

df()

template<typename _Scalar >

Scalar Ponca::SingularWeightKernel< _Scalar >::df ( const Scalar &  _x ) const

inline

Defines the Singular first order weighting function \( \nabla w(x) = -2 / (x^3) \).

Definition at line 208 of file weightKernel.h.

f()

template<typename _Scalar >

Scalar Ponca::SingularWeightKernel< _Scalar >::f ( const Scalar &  _x ) const

inline

Defines the Singular weighting function \( w(x) = 1 / (x^2) \).

Definition at line 204 of file weightKernel.h.

Member Data Documentation

isCompact

template<typename _Scalar >

constexpr bool Ponca::SingularWeightKernel< _Scalar >::isCompact = true

staticconstexpr

The kernel is compact and shall not be evaluated outside of the scale bounds.

Definition at line 200 of file weightKernel.h.

isDDValid

template<typename _Scalar >

constexpr bool Ponca::SingularWeightKernel< _Scalar >::isDDValid = true

staticconstexpr

ddf is defined and valid on the definition interval

Definition at line 218 of file weightKernel.h.

isDValid

template<typename _Scalar >

constexpr bool Ponca::SingularWeightKernel< _Scalar >::isDValid = true

staticconstexpr

df is defined and valid on the definition interval

Definition at line 216 of file weightKernel.h.