Grenaille::DistWeightFunc< DataPoint, WeightKernel > Class Template Reference

Inherits Grenaille::Concept::WeightFuncConcept< Point >.

Detailed Description

template<class DataPoint, class WeightKernel>
class Grenaille::DistWeightFunc< DataPoint, WeightKernel >

Weighting function based on the euclidean distance between a query and a reference position.

The query is assumed to be expressed in centered coordinates (ie. relatively to the evaluation position).

This class inherits BaseWeightFunc. It can be specialized for any DataPoint, and uses a generic 1D BaseWeightKernel.

Warning

it assumes that the evaluation scale t is strictly positive

Public Types
typedef DataPoint::Scalar	Scalar
	Scalar type from DataPoint.
typedef DataPoint::VectorType	VectorType
	Vector type from DataPoint.
Public Types inherited from Grenaille::Concept::WeightFuncConcept< Point >
typedef DataPoint::Scalar	Scalar
typedef DataPoint::VectorType	VectorType

Public Member Functions
	DistWeightFunc (const Scalar &_t=Scalar(1.))
	Constructor that defines the current evaluation scale. More...
Scalar	w (const VectorType &_q, const DataPoint &) const
	Compute the weight of the given query with respect to its coordinates. More...
VectorType	spacedw (const VectorType &_q, const DataPoint &) const
	First order derivative in space (for each spatial dimension \(\mathsf{x})\). More...
Scalar	scaledw (const VectorType &_q, const DataPoint &) const
	First order derivative in scale \(t\). More...
Scalar	evalScale () const
	Access to the evaluation scale set during the initialization.
Public Member Functions inherited from Grenaille::Concept::WeightFuncConcept< Point >
Scalar	w (const VectorType &relativeQuery, const DataPoint &attributes) const
	Apply the weight function to a query.
VectorType	spacedw (const VectorType &relativeQuery, const DataPoint &attributes) const
	Apply the weight function differenciated in space to a query.
Scalar	scaledw (const VectorType &relativeQuery, const DataPoint &attributes) const
	Apply the weight function differenciated in scale to a query.
Scalar	evalScale () const
	Read access to the evaluation scale.

Protected Attributes
Scalar	m_t
	Evaluation scale.
WeightKernel	m_wk
	1D function applied to weight queries

Constructor & Destructor Documentation

template<class DataPoint , class WeightKernel >

Grenaille::DistWeightFunc< DataPoint, WeightKernel >::DistWeightFunc ( const Scalar &  _t = Scalar(1.) )

inline

Constructor that defines the current evaluation scale.

Warning

t > 0

Member Function Documentation

template<class DataPoint , class WeightKernel >

DistWeightFunc< DataPoint, WeightKernel >::Scalar DistWeightFunc::scaledw ( const VectorType &  _q, const DataPoint &    ) const

inline

First order derivative in scale \(t\).

\( \frac{\delta \frac{\left|\mathbf{q}\right|}{t}}{\delta t} \nabla w(\frac{\left|\mathbf{q}\right|}{t}) = - \frac{\left|\mathbf{q}\right|}{t^2} \nabla{w(\frac{\left|\mathbf{q}\right|}{t})} \)

where \( \left|\mathbf{q}\right| \) represents the norm of the query coordinates expressed in centered basis.

template<class DataPoint , class WeightKernel >

DistWeightFunc< DataPoint, WeightKernel >::VectorType DistWeightFunc::spacedw ( const VectorType &  _q, const DataPoint &    ) const

inline

First order derivative in space (for each spatial dimension \(\mathsf{x})\).

\( \frac{\delta \frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}}{\delta \mathsf{x}} \nabla w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) = \frac{ \nabla{w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t})}}{t} \)

where \( \left|\mathbf{q}_\mathsf{x}\right| \) represents the norm of the query coordinates expressed in centered basis, for each spatial dimensions \( \mathsf{x}\).

template<class DataPoint , class WeightKernel >

DistWeightFunc< DataPoint, WeightKernel >::Scalar DistWeightFunc::w ( const VectorType &  _q, const DataPoint &    ) const

inline

Compute the weight of the given query with respect to its coordinates.

As the query \(\mathbf{q}\) is expressed in a centered basis, the WeightKernel is directly applied to the norm of its coordinates with respect to the current scale \( t \) :

\( w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) \)