Weight neighbors according to the euclidean distance between a query and a reference position. More...

#include <weightFunc.h>

Inheritance diagram for Ponca::DistWeightFunc< DataPoint, WeightKernel >:

Collaboration diagram for Ponca::DistWeightFunc< DataPoint, WeightKernel >:

Public Types
using	Scalar = typename DataPoint::Scalar
	Scalar type from DataPoint.

using	VectorType = typename DataPoint::VectorType
	Vector type from DataPoint.

using	MatrixType = typename DataPoint::MatrixType
	Matrix type from DataPoint.

using	WeightReturnType = std::pair< Scalar, VectorType >
	Return type of the method #w()

using	NeighborhoodFrame = CenteredNeighborhoodFrame< DataPoint >
	Frame used to express the neighbors locally.

Public Types inherited from Ponca::CenteredNeighborhoodFrame< DataPoint >
using	Scalar = typename DataPoint::Scalar
	Scalar type from DataPoint.

using	VectorType = typename DataPoint::VectorType
	Vector type from DataPoint.

Public Member Functions
	DistWeightFunc (const VectorType &_evalPos=VectorType::Zero(), const Scalar &_t=Scalar(1.))
	Constructor that defines the current evaluation scale.

WeightReturnType	operator() (const DataPoint &q) const
	Compute the weight of the given query with respect to its coordinates.

VectorType	spacedw (const VectorType &_q, const DataPoint &) const
	First order derivative in space (for each spatial dimension \(\mathsf{x})\).

MatrixType	spaced2w (const VectorType &_q, const DataPoint &) const
	Second order derivative in space (for each spatial dimension \(\mathsf{x})\).

Scalar	scaledw (const VectorType &_q, const DataPoint &) const
	First order derivative in scale \(t\).

Scalar	scaled2w (const VectorType &_q, const DataPoint &) const
	Second order derivative in scale \(t\).

VectorType	scaleSpaced2w (const VectorType &_q, const DataPoint &) const
	Cross derivative in scale \(t\) and in space (for each spatial dimension \(\mathsf{x})\).

Scalar	evalScale () const
	Access to the evaluation scale set during the initialization.

Public Member Functions inherited from Ponca::CenteredNeighborhoodFrame< DataPoint >
	CenteredNeighborhoodFrame (const VectorType &_evalPos=VectorType::Zero())

void	changeNeighborhoodFrame (const VectorType &_newEvalPos)
	Change neighborhood frame (move basis center)

VectorType	convertToGlobalBasis (const VectorType &_q) const
	Convert query from local to global coordinate system, such as \(\mathbf{x}=\mathbf{x}'+\mathbf{p}\).

VectorType	convertToLocalBasis (const VectorType &_q) const
	Convert query from global to local coordinate system, such as \(\mathbf{x}'=\mathbf{x}-\mathbf{p}\).

VectorType	evalPos () const
	Get access to the stored points of evaluation.

Static Public Attributes
static constexpr bool	isCompact = WeightKernel::isCompact
	Flag indicating if the weighting kernel is compact of not.

Static Public Attributes inherited from Ponca::CenteredNeighborhoodFrame< DataPoint >
static constexpr bool	hasLocalFrame = true
	Flag indicating that this class modifies the coordinates when passing from global to local.

Protected Attributes
Scalar	m_t
	Evaluation scale.

WeightKernel	m_wk
	1D function applied to weight queries

Detailed Description

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

Weight neighbors according to the euclidean distance between a query and a reference position.

The evaluation position is set in the constructor. All the queries are expressed in global system, and converted internally to relatively to the evaluation position using CenteredNeighborhoodFrame.

Template Parameters

DataPoint	Type of input points.
WeightKernel	1d function used to compute the weight depending on the distance between query point and the basis center. If `WeightKernel::isCompact == true`, the distance to the basis center is checked against the scale parameter, and any point whose distance is larger than the scale will be assigned with a weight of \(0\). For non-compact (ie. global) kernels, the weights are computed for all points.

See also: operator()

Warning: DistWeightFunc assumes that the evaluation scale t is strictly positive, but the valus is not checked

Definition at line 126 of file weightFunc.h.

Member Typedef Documentation

◆ MatrixType

template<class DataPoint , class WeightKernel >

using Ponca::DistWeightFunc< DataPoint, WeightKernel >::MatrixType = typename DataPoint::MatrixType

Matrix type from DataPoint.

Definition at line 134 of file weightFunc.h.

◆ NeighborhoodFrame

template<class DataPoint , class WeightKernel >

using Ponca::DistWeightFunc< DataPoint, WeightKernel >::NeighborhoodFrame = CenteredNeighborhoodFrame<DataPoint>

Frame used to express the neighbors locally.

Definition at line 138 of file weightFunc.h.

◆ Scalar

template<class DataPoint , class WeightKernel >

using Ponca::DistWeightFunc< DataPoint, WeightKernel >::Scalar = typename DataPoint::Scalar

Scalar type from DataPoint.

Definition at line 130 of file weightFunc.h.

◆ VectorType

template<class DataPoint , class WeightKernel >

using Ponca::DistWeightFunc< DataPoint, WeightKernel >::VectorType = typename DataPoint::VectorType

Vector type from DataPoint.

Definition at line 132 of file weightFunc.h.

◆ WeightReturnType

template<class DataPoint , class WeightKernel >

using Ponca::DistWeightFunc< DataPoint, WeightKernel >::WeightReturnType = std:: pair <Scalar, VectorType>

Return type of the method #w()

Definition at line 136 of file weightFunc.h.

Constructor & Destructor Documentation

◆ DistWeightFunc()

template<class DataPoint , class WeightKernel >

Ponca::DistWeightFunc< DataPoint, WeightKernel >::DistWeightFunc	(	const VectorType &	_evalPos = `VectorType::Zero()`,
		const Scalar &	_t = `Scalar(1.)`
	)

inline

Constructor that defines the current evaluation scale.

Warning: t > 0

Definition at line 146 of file weightFunc.h.

Member Function Documentation

◆ evalScale()

template<class DataPoint , class WeightKernel >

Scalar Ponca::DistWeightFunc< DataPoint, WeightKernel >::evalScale ( ) const

inline

Access to the evaluation scale set during the initialization.

Definition at line 274 of file weightFunc.h.

◆ operator()()

template<class DataPoint , class WeightKernel >

DistWeightFunc< DataPoint, WeightKernel >::WeightReturnType DistWeightFunc::operator() ( const DataPoint & q ) const

inline

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

Parameters

_q	Query in global coordinate system

As the query \(\mathbf{q}\) is expressed in global coordinate, it is first converted to the centered basis. Then, the WeightKernel is directly applied to the norm of its coordinates with respect to the current scale \( t \) :

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

See also: convertToLocalBasis

Returns: The computed weight + the point expressed in local basis

Definition at line 11 of file weightFunc.hpp.

◆ scaled2w()

template<class DataPoint , class WeightKernel >

DistWeightFunc< DataPoint, WeightKernel >::Scalar DistWeightFunc::scaled2w	(	const VectorType &	_q,
		const DataPoint &
	)		const

inline

Second order derivative in scale \(t\).

Parameters

_q	Query in global coordinate system

\( \frac{\delta^2 \frac{\left|\mathbf{q}\right|}{t}}{\delta t^2} \nabla w(\frac{\left|\mathbf{q}\right|}{t}) + \left(\frac{\delta \frac{\left|\mathbf{q}\right|}{t}}{\delta t}\right)^2 \nabla^2 w(\frac{\left|\mathbf{q}\right|}{t}) = \frac{2\left|\mathbf{q}\right|}{t^3} \nabla{w(\frac{\left|\mathbf{q}\right|}{t})} + \frac{\left|\mathbf{q}\right|^2}{t^4} \nabla^2{w(\frac{\left|\mathbf{q}\right|}{t})} \)

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

Warning: Requires \(\nabla^2 w(x)\) to be valid

Definition at line 66 of file weightFunc.hpp.

◆ scaledw()

template<class DataPoint , class WeightKernel >

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

inline

First order derivative in scale \(t\).

Parameters

_q	Query in global coordinate system

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

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

Warning: Requires \(\nabla w(x)\) to be valid

Definition at line 56 of file weightFunc.hpp.

◆ scaleSpaced2w()

template<class DataPoint , class WeightKernel >

DistWeightFunc< DataPoint, WeightKernel >::VectorType DistWeightFunc::scaleSpaced2w	(	const VectorType &	_q,
		const DataPoint &
	)		const

inline

Cross derivative in scale \(t\) and in space (for each spatial dimension \(\mathsf{x})\).

Parameters

_q	Query in global coordinate system

\( \frac{\delta^2 \frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}}{\delta t\ \delta \mathsf{x}} \nabla w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) + \frac{\delta \frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}}{\delta \mathsf{x}} \frac{\delta \frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}}{\delta t} \nabla^2 w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) = -\frac{\mathbf{q}_\mathsf{x}}{t^2} \left( \frac{1}{\left|\mathbf{q}_\mathsf{x}\right|}\nabla w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) + \frac{1}{t}\nabla^2 w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) \right)\)

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

Warning: Requires \(\nabla^2 w(x)\) to be valid

Definition at line 78 of file weightFunc.hpp.

◆ spaced2w()

template<class DataPoint , class WeightKernel >

DistWeightFunc< DataPoint, WeightKernel >::MatrixType DistWeightFunc::spaced2w	(	const VectorType &	_q,
		const DataPoint &
	)		const

inline

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

Parameters

_q	Query in global coordinate system

\( \frac{\delta^2 \frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}}{\delta \mathsf{x}^2} \nabla w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) + \left(\frac{\delta \frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}}{\delta \mathsf{x}}\right)^2 \nabla^2 w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) = \frac{1}{t\left|\mathbf{q}_\mathsf{x}\right|} \left( I_d - \frac{\mathbf{q}_\mathsf{x}\mathbf{q}_\mathsf{x}^T}{\left|\mathbf{q}_\mathsf{x}\right|^2}\right) \nabla w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) + \frac{\mathbf{q}_\mathsf{x}\mathbf{q}_\mathsf{x}^T}{t^2\left|\mathbf{q}_\mathsf{x}\right|^2} \nabla^2 w(\frac{\left|\mathbf{q}_\mathsf{x}\right|}{t}) \)

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

Warning: Requires \(\nabla^2 w(x)\) to be valid

Definition at line 37 of file weightFunc.hpp.

◆ spacedw()

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 \(\mathsf{x})\).

Parameters

_q	Query in global coordinate system

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

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

Warning: Requires \(\nabla w(x)\) to be valid

Definition at line 23 of file weightFunc.hpp.

Member Data Documentation

◆ isCompact

template<class DataPoint , class WeightKernel >

constexpr bool Ponca::DistWeightFunc< DataPoint, WeightKernel >::isCompact = WeightKernel::isCompact

staticconstexpr

Flag indicating if the weighting kernel is compact of not.

Definition at line 140 of file weightFunc.h.

◆ m_t

template<class DataPoint , class WeightKernel >

Scalar Ponca::DistWeightFunc< DataPoint, WeightKernel >::m_t

protected

Evaluation scale.

Definition at line 277 of file weightFunc.h.

◆ m_wk

template<class DataPoint , class WeightKernel >

WeightKernel Ponca::DistWeightFunc< DataPoint, WeightKernel >::m_wk

protected

1D function applied to weight queries

Definition at line 278 of file weightFunc.h.

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ MatrixType

◆ NeighborhoodFrame

◆ Scalar

◆ VectorType

◆ WeightReturnType

Constructor & Destructor Documentation

◆ DistWeightFunc()

Member Function Documentation

◆ evalScale()

◆ operator()()

◆ scaled2w()

◆ scaledw()

◆ scaleSpaced2w()

◆ spaced2w()

◆ spacedw()

Member Data Documentation

◆ isCompact

◆ m_t

◆ m_wk