Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T > Class Template Reference

Inheritance diagram for Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >:

Collaboration diagram for Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >:

Public Types
using	Scalar = typename DataPoint::Scalar
	Alias to scalar type.
using	VectorType = typename Base::VectorType
	Alias to vector type.
using	WFunctor = typename Base::WFunctor
	Alias to weight function.
using	ScalarArray = typename Base::ScalarArray
	Alias to scalar derivatives array.
using	VectorArray = typename Base::VectorArray
	Alias to vector derivatives array.

Public Member Functions
MeanNormalDer< DataPoint, _WFunctor, DiffType, T > &	meanNormalDer ()
	Explicit conversion to MeanNormalDer , to access methods potentially hidden by heritage.
const MeanNormalDer< DataPoint, _WFunctor, DiffType, T > &	meanNormalDer () const
	Explicit conversion to MeanNormalDer , to access methods potentially hidden by heritage.
void	init (const VectorType &_evalPos)
	Set the evaluation position and reset the internal states.
bool	addLocalNeighbor (Scalar w, const VectorType &localQ, const DataPoint &attributes, ScalarArray &dw)
	Add a neighbor to perform the fit.
VectorArray	dMeanNormal () const
	Compute the derivative of the mean normal vector of the input points.

Protected Types
enum	{ Check , PROVIDES_MEAN_NORMAL_DERIVATIVE }
using	Base = T
	Base class of the procedure.

Protected Attributes
VectorArray	m_dSumN {VectorArray::Zero()}
	Derivatives of the input normals of the input points vectors.

Detailed Description

template<class DataPoint, class _WFunctor, int DiffType, typename T>
class Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >

Definition at line 149 of file mean.h.

Member Typedef Documentation

Base

template<class DataPoint , class _WFunctor , int DiffType, typename T >

using Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::Base = T

protected

Base class of the procedure.

Definition at line 150 of file mean.h.

Scalar

template<class DataPoint , class _WFunctor , int DiffType, typename T >

using Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::Scalar = typename DataPoint::Scalar

Alias to scalar type.

Definition at line 150 of file mean.h.

ScalarArray

template<class DataPoint , class _WFunctor , int DiffType, typename T >

using Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::ScalarArray = typename Base::ScalarArray

Alias to scalar derivatives array.

Definition at line 151 of file mean.h.

VectorArray

template<class DataPoint , class _WFunctor , int DiffType, typename T >

using Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::VectorArray = typename Base::VectorArray

Alias to vector derivatives array.

Definition at line 151 of file mean.h.

VectorType

template<class DataPoint , class _WFunctor , int DiffType, typename T >

using Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::VectorType = typename Base::VectorType

Alias to vector type.

Definition at line 150 of file mean.h.

WFunctor

template<class DataPoint , class _WFunctor , int DiffType, typename T >

using Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::WFunctor = typename Base::WFunctor

Alias to weight function.

Definition at line 150 of file mean.h.

Member Enumeration Documentation

anonymous enum

template<class DataPoint , class _WFunctor , int DiffType, typename T >

anonymous enum

protected

Enumerator
PROVIDES_MEAN_NORMAL_DERIVATIVE	Provides derivative of the mean normal.

Definition at line 154 of file mean.h.

Member Function Documentation

addLocalNeighbor()

template<class DataPoint , class _WFunctor , int DiffType, typename T >

bool MeanNormalDer::addLocalNeighbor ( Scalar  w, const VectorType &  localQ, const DataPoint &  attributes, ScalarArray &  dw  )

inline

Add a neighbor to perform the fit.

Returns

false if param nei is not a valid neighbour (weight = 0)

Definition at line 82 of file mean.hpp.

dMeanNormal()

template<class DataPoint , class _WFunctor , int DiffType, typename T >

VectorArray Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::dMeanNormal ( ) const

inline

Compute the derivative of the mean normal vector of the input points.

Step-by-step derivation of the mean normal :

Given the definition of the mean normal \( n(\mathbf{x}) = \frac{\sum_i w_\mathbf{x}(\mathbf{p_i}) \mathbf{n_i}}{\sum_i w_\mathbf{x}(\mathbf{p_i})} \), where \(\left[\mathbf{p_i}, \mathbf{n_i} \in \text{neighborhood}(\mathbf{x})\right]\) are all the point and normal samples in \(\mathbf{x}\)'s neighborhood.

We denote \( t(\mathbf{x}) = \sum_i w_\mathbf{x}(\mathbf{p_i}) \mathbf{n_i} \) and \( s(\mathbf{x}) = \sum_i w_\mathbf{x}(\mathbf{p_i})\), such that \( n(\mathbf{x}) = \frac{t(\mathbf{x})}{s(\mathbf{x})}\).

By definition, \( n'(\mathbf{x}) = \frac{s(\mathbf{x})t'(\mathbf{x}) - t(\mathbf{x})s'(\mathbf{x})}{s(\mathbf{x})^2}\).

Assuming the weight of each normal is dependent on the position, we have \( s'(\mathbf{x}) = \sum_i w'_\mathbf{x}(\mathbf{p_i}) \).

We rewrite \( t(\mathbf{x}) = \sum u(\mathbf{x})v(\mathbf{x}) \), with \( u(\mathbf{x}) = w_\mathbf{x}(\mathbf{p_i}) \) and \( v(\mathbf{x}) = \mathbf{n_i} \).

Assuming the normal vectors themselves do not change with position, \(v(\mathbf{x})\) is constant, its derivative is null, and so \( t'(\mathbf{x}) = \sum_i u'(\mathbf{x}) v(\mathbf{x}) = \sum_i w'_\mathbf{x}(\mathbf{n_i}) \mathbf{n_i} \).

Which leads to \( n'(\mathbf{x}) = \frac{\sum_i w'_\mathbf{x}(\mathbf{p_i}) \mathbf{n_i} - n(\mathbf{x})\sum_i w'_\mathbf{x}(\mathbf{p_i})}{\sum_i w_\mathbf{x}(\mathbf{p_i})} \).

Note

This code is not directly tested.

Definition at line 190 of file mean.h.

init()

template<class DataPoint , class _WFunctor , int DiffType, typename T >

void MeanNormalDer::init ( const VectorType &  _evalPos )

inline

Set the evaluation position and reset the internal states.

Warning

Must be called be for any computation (but after #setWeightFunc)

Definition at line 75 of file mean.hpp.

meanNormalDer() [1/2]

template<class DataPoint , class _WFunctor , int DiffType, typename T >

MeanNormalDer< DataPoint, _WFunctor, DiffType, T > & Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::meanNormalDer ( )

inline

Explicit conversion to MeanNormalDer , to access methods potentially hidden by heritage.

Definition at line 165 of file mean.h.

meanNormalDer() [2/2]

template<class DataPoint , class _WFunctor , int DiffType, typename T >

const MeanNormalDer< DataPoint, _WFunctor, DiffType, T > & Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::meanNormalDer ( ) const

inline

Explicit conversion to MeanNormalDer , to access methods potentially hidden by heritage.

Definition at line 165 of file mean.h.

Member Data Documentation

m_dSumN

template<class DataPoint , class _WFunctor , int DiffType, typename T >

VectorArray Ponca::MeanNormalDer< DataPoint, _WFunctor, DiffType, T >::m_dSumN {VectorArray::Zero()}

protected

Derivatives of the input normals of the input points vectors.

Definition at line 161 of file mean.h.