Ponca::SmoothWeightKernel< _Scalar > Class Template Reference

Smooth WeightKernel of 2nd degree, defined in \(\left[0 : 1\right]\) Special case of PolynomialSmoothWeightKernel<Scalar, 2, 2> More...

#include <weightKernel.h>

Inheritance diagram for Ponca::SmoothWeightKernel< _Scalar >:

Collaboration diagram for Ponca::SmoothWeightKernel< _Scalar >:

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

Public Member Functions
Scalar	f (const Scalar &_x) const
	Defines the smooth weighting function \( w(x) = (x^2-1)^2 \).
Scalar	df (const Scalar &_x) const
	Defines the smooth first order weighting function \( \nabla w(x) = 4x(x^2-1) \).
Scalar	ddf (const Scalar &_x) const
	Defines the smooth second order weighting function \( \nabla^2 w(x) = 12x^2-4 \).

Static Public Attributes
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::SmoothWeightKernel< _Scalar >

Smooth WeightKernel of 2nd degree, defined in \(\left[0 : 1\right]\) Special case of PolynomialSmoothWeightKernel<Scalar, 2, 2>

Definition at line 60 of file weightKernel.h.

Member Typedef Documentation

Scalar

template<typename _Scalar >

typedef _Scalar Ponca::SmoothWeightKernel< _Scalar >::Scalar

Scalar type defined outside the class.

Definition at line 64 of file weightKernel.h.

Member Function Documentation

ddf()

template<typename _Scalar >

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

inline

Defines the smooth second order weighting function \( \nabla^2 w(x) = 12x^2-4 \).

Definition at line 72 of file weightKernel.h.

df()

template<typename _Scalar >

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

inline

Defines the smooth first order weighting function \( \nabla w(x) = 4x(x^2-1) \).

Definition at line 70 of file weightKernel.h.

f()

template<typename _Scalar >

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

inline

Defines the smooth weighting function \( w(x) = (x^2-1)^2 \).

Definition at line 68 of file weightKernel.h.

Member Data Documentation

isDDValid

template<typename _Scalar >

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

staticconstexpr

ddf is defined and valid on the definition interval

Definition at line 76 of file weightKernel.h.

isDValid

template<typename _Scalar >

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

staticconstexpr

df is defined and valid on the definition interval

Definition at line 74 of file weightKernel.h.