Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n > Class Template Reference

Compact generalised version of SmoothWeightKernel with arbitrary degrees : \( w(x)=(x^n-1)^m \). More...

#include <weightKernel.h>

Inheritance diagram for Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >:

Collaboration diagram for Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >:

Public Types
using	Scalar = _Scalar
	Scalar type defined outside the class.

Public Member Functions
Scalar	f (const Scalar &_x) const
	Defines the smooth weighting function \( w(x)=(x^n-1)^m \).
Scalar	df (const Scalar &_x) const
	Defines the smooth first order weighting function \( \nabla w(x) = m n x^{n-1} \left(x^n-1\right)^{m-1} \).
Scalar	ddf (const Scalar &_x) const
	Defines the smooth second order weighting function \( \nabla^2 w(x) = (m-1) m n^2 x^{2 n-2} \left(x^n-1\right)^{m-2}+m (n-1) n x^{n-2} \left(x^n-1\right)^{m-1} \).

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, int m, int n>
class Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >

Compact generalised version of SmoothWeightKernel with arbitrary degrees : \( w(x)=(x^n-1)^m \).

Definition at line 101 of file weightKernel.h.

Member Typedef Documentation

Scalar

template<typename _Scalar , int m, int n>

using Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >::Scalar = _Scalar

Scalar type defined outside the class.

Definition at line 105 of file weightKernel.h.

Member Function Documentation

ddf()

template<typename _Scalar , int m, int n>

Scalar Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >::ddf ( const Scalar &  _x ) const

inline

Defines the smooth second order weighting function \( \nabla^2 w(x) = (m-1) m n^2 x^{2 n-2} \left(x^n-1\right)^{m-2}+m (n-1) n x^{n-2} \left(x^n-1\right)^{m-1} \).

Definition at line 126 of file weightKernel.h.

df()

template<typename _Scalar , int m, int n>

Scalar Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >::df ( const Scalar &  _x ) const

inline

Defines the smooth first order weighting function \( \nabla w(x) = m n x^{n-1} \left(x^n-1\right)^{m-1} \).

Definition at line 119 of file weightKernel.h.

f()

template<typename _Scalar , int m, int n>

Scalar Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >::f ( const Scalar &  _x ) const

inline

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

Definition at line 112 of file weightKernel.h.

Member Data Documentation

isCompact

template<typename _Scalar , int m, int n>

constexpr bool Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >::isCompact = true

staticconstexpr

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

Definition at line 108 of file weightKernel.h.

isDDValid

template<typename _Scalar , int m, int n>

constexpr bool Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >::isDDValid = true

staticconstexpr

ddf is defined and valid on the definition interval

Definition at line 137 of file weightKernel.h.

isDValid

template<typename _Scalar , int m, int n>

constexpr bool Ponca::PolynomialSmoothWeightKernel< _Scalar, m, n >::isDValid = true

staticconstexpr

df is defined and valid on the definition interval

Definition at line 135 of file weightKernel.h.