Ponca::WendlandWeightKernel< _Scalar > Class Template Reference

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

#include <weightKernel.h>

Inheritance diagram for Ponca::WendlandWeightKernel< _Scalar >:

Collaboration diagram for Ponca::WendlandWeightKernel< _Scalar >:

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

Public Member Functions
Scalar	f (const Scalar &_x) const
	Defines the Wendland weighting function \( w(x) = (1-x)^4(4x+1) \).
Scalar	df (const Scalar &_x) const
	Defines the Wendland first order weighting function \( \nabla w(x) = 20x * (x−1)^3 \).
Scalar	ddf (const Scalar &_x) const
	Defines the Wendland second order weighting function \( \nabla^2 w(x) = (x−1)^2 * (80x−20) \).

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::WendlandWeightKernel< _Scalar >

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

Weight function is an implementation of equation 2 in [1]

Definition at line 152 of file weightKernel.h.

Member Typedef Documentation

Scalar

template<typename _Scalar >

typedef _Scalar Ponca::WendlandWeightKernel< _Scalar >::Scalar

Scalar type defined outside the class.

Definition at line 156 of file weightKernel.h.

Member Function Documentation

ddf()

template<typename _Scalar >

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

inline

Defines the Wendland second order weighting function \( \nabla^2 w(x) = (x−1)^2 * (80x−20) \).

Definition at line 173 of file weightKernel.h.

df()

template<typename _Scalar >

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

inline

Defines the Wendland first order weighting function \( \nabla w(x) = 20x * (x−1)^3 \).

Definition at line 168 of file weightKernel.h.

f()

template<typename _Scalar >

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

inline

Defines the Wendland weighting function \( w(x) = (1-x)^4(4x+1) \).

Definition at line 163 of file weightKernel.h.

Member Data Documentation

isCompact

template<typename _Scalar >

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

staticconstexpr

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

Definition at line 159 of file weightKernel.h.

isDDValid

template<typename _Scalar >

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

staticconstexpr

ddf is defined and valid on the definition interval

Definition at line 180 of file weightKernel.h.

isDValid

template<typename _Scalar >

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

staticconstexpr

df is defined and valid on the definition interval

Definition at line 178 of file weightKernel.h.