GEO::VSDM Class Reference

Voronoi Square Distance Minimization. More...

#include <exploragram/optimal_transport/VSDM.h>

Public Member Functions
	VSDM (Mesh *S, Mesh *T)
	VSDM constructor.
virtual	~VSDM ()
	VSDM destructor.
void	set_affinity (double x)
	Sets the affinity.
void	optimize (index_t nb_iter)
	Optimizes the fitting.
void	set_progress (ProgressTask *progress)
	Sets an optional progress bar to track progress during calls of optimize()
void	set_subdivision_surface (Mesh *mesh, index_t nb_subdiv)
	Sets a subdivision surface.

Static Public Member Functions
static void	funcgrad_CB (index_t n, double *x, double &f, double *g)
	The callback to evaluate the objective function, used by the optimizer.
static void	newiteration_CB (index_t n, const double *x, double f, const double *g, double gnorm)
	The callback for each iteration of the optimizer.

Protected Member Functions
virtual void	funcgrad (index_t n, double *x, double &f, double *g)
	Evaluates the objective function and its gradient.
virtual void	newiteration ()
	Updates the progress bar (if specified) and graphics.
void	add_funcgrad_affinity (index_t n, double *x, double &f, double *g)
	Adds the value and gradient of the affinity to the currently evaluated objective function.

Static Protected Member Functions
static VSDM *	instance ()
	Gets the instance.
static void	compute_graph_Laplacian (Mesh *S, NLSparseMatrix *L)
	Computes the graph Laplacian of a surface mesh.

Protected Attributes
Delaunay_var	delaunay_
RestrictedVoronoiDiagram_var	RVD_
Mesh *	S_
Mesh *	T_
double	affinity_
double	affinity_scaling_
ProgressTask *	progress_
Optimizer_var	optimizer_
index_t	nb_iter_
index_t	cur_iter_
NLSparseMatrix	L_
vector< double >	temp_V1_
vector< double >	temp_V2_
NLMatrix	subd_matrix_
Mesh *	subd_
vector< double >	subd_g_

Static Protected Attributes
static VSDM *	instance_

Detailed Description

Voronoi Square Distance Minimization.

Fits a surface mesh to a target surface mesh. The algorithm is described in the following references:

• Fitting Polynomial Surfaces to Triangular Meshes with Voronoi Squared Distance Minimization, Vindent Nivolers, Dong-Ming Yan and Bruno Levy, Intl. Meshing Roundtable Conf. Proc., 2011
• Centroidal Voronoi Tessellation of Line Segments and Graphs, Lin Lu, Bruno Levy and Wenping Wang, Eurographics conf. Proc., 2012

Definition at line 66 of file VSDM.h.

Constructor & Destructor Documentation

VSDM()

GEO::VSDM::VSDM	(	Mesh *	S,
		Mesh *	T
	)

VSDM constructor.

Parameters

[in]	S	the surface mesh to be fitted.
[in]	T	the target surface mesh.

Member Function Documentation

add_funcgrad_affinity()

void GEO::VSDM::add_funcgrad_affinity ( index_t  n, double *  x, double &  f, double *  g  )

protected

Adds the value and gradient of the affinity to the currently evaluated objective function.

Parameters

[in]	n	dimension of the problem (here, three times the number of vertices of the surface S).
[in]	x	a pointer to the current vector of variables, of dimension n.
[in,out]	f	the value of the objective function.
[in,out]	g	a pointer to a vector of dimension n with the gradient of the objective function.

compute_graph_Laplacian()

static void GEO::VSDM::compute_graph_Laplacian ( Mesh *  S, NLSparseMatrix *  L  )

staticprotected

Computes the graph Laplacian of a surface mesh.

Parameters

[in]	S	a pointer to a surface mesh.
[out]	L	the graph Laplacian of S.

funcgrad()

virtual void GEO::VSDM::funcgrad ( index_t  n, double *  x, double &  f, double *  g  )

protectedvirtual

Evaluates the objective function and its gradient.

Parameters

[in]	n	dimension of the problem (here, three times the number of vertices of the surface S).
[in]	x	a pointer to the current vector of variables, of dimension n.
[out]	f	the value of the objective function.
[out]	g	a pointer to a vector of dimension n with the gradient of the objective function.

funcgrad_CB()

static void GEO::VSDM::funcgrad_CB ( index_t  n, double *  x, double &  f, double *  g  )

static

The callback to evaluate the objective function, used by the optimizer.

Parameters

[in]	n	dimension of the problem (here, three times the number of vertices of the surface S).
[in]	x	a pointer to the current vector of variables, of dimension n.
[out]	f	the value of the objective function.
[out]	g	a pointer to a vector of dimension n with the gradient of the objective function.

instance()

static VSDM * GEO::VSDM::instance ( )

inlinestaticprotected

Gets the instance.

Returns

a pointer to the current VSDM instance.

Definition at line 148 of file VSDM.h.

newiteration()

virtual void GEO::VSDM::newiteration ( )

protectedvirtual

Updates the progress bar (if specified) and graphics.

This function is called after each iteration of the optimizer.

newiteration_CB()

static void GEO::VSDM::newiteration_CB ( index_t  n, const double *  x, double  f, const double *  g, double  gnorm  )

static

The callback for each iteration of the optimizer.

Parameters

[in]	n	dimension of the problem (here, three times the number of vertices of the surface S).
[in]	x	a pointer to the current vector of variables, of dimension n.
[in]	f	the current value of the objective function.
[in]	g	a pointer to a vector of dimension n with the gradient of the objective function.
[in]	gnorm	the norm of the gradient.

optimize()

void GEO::VSDM::optimize

(

index_t

nb_iter

)

Optimizes the fitting.

Parameters

[in]

nb_iter

maximum number of iterations.

set_affinity()

void GEO::VSDM::set_affinity ( double  x )

inline

Sets the affinity.

Parameters

[in]

x

the affinity, the higher the smoother. Default value is 1.0.

Definition at line 85 of file VSDM.h.

set_progress()

void GEO::VSDM::set_progress ( ProgressTask *  progress )

inline

Sets an optional progress bar to track progress during calls of optimize()

Parameters

[in]

progress

a pointer to a ProgressTask.

Definition at line 100 of file VSDM.h.

set_subdivision_surface()

void GEO::VSDM::set_subdivision_surface	(	Mesh *	mesh,
		index_t	nb_subdiv
	)

Sets a subdivision surface.

If this function is called, then the S mesh passed to the constructor is considered as the control mesh of a subdivision surface.

Parameters

[in]	mesh	a pointer to the mesh that will store the subdivision surface.
[in]	nb_subdiv	the number of Catmull-Clark subdivisions.

Member Data Documentation

affinity_

double GEO::VSDM::affinity_

protected

Definition at line 196 of file VSDM.h.

affinity_scaling_

double GEO::VSDM::affinity_scaling_

protected

Definition at line 197 of file VSDM.h.

cur_iter_

index_t GEO::VSDM::cur_iter_

protected

Definition at line 202 of file VSDM.h.

delaunay_

Delaunay_var GEO::VSDM::delaunay_

protected

Definition at line 192 of file VSDM.h.

instance_

VSDM* GEO::VSDM::instance_

staticprotected

Definition at line 199 of file VSDM.h.

L_

NLSparseMatrix GEO::VSDM::L_

protected

Definition at line 204 of file VSDM.h.

nb_iter_

index_t GEO::VSDM::nb_iter_

protected

Definition at line 201 of file VSDM.h.

optimizer_

Optimizer_var GEO::VSDM::optimizer_

protected

Definition at line 200 of file VSDM.h.

progress_

ProgressTask* GEO::VSDM::progress_

protected

Definition at line 198 of file VSDM.h.

RVD_

RestrictedVoronoiDiagram_var GEO::VSDM::RVD_

protected

Definition at line 193 of file VSDM.h.

S_

Mesh* GEO::VSDM::S_

protected

Definition at line 194 of file VSDM.h.

subd_

Mesh* GEO::VSDM::subd_

protected

Definition at line 209 of file VSDM.h.

subd_g_

vector<double> GEO::VSDM::subd_g_

protected

Definition at line 210 of file VSDM.h.

subd_matrix_

NLMatrix GEO::VSDM::subd_matrix_

protected

Definition at line 208 of file VSDM.h.

T_

Mesh* GEO::VSDM::T_

protected

Definition at line 195 of file VSDM.h.

temp_V1_

vector<double> GEO::VSDM::temp_V1_

protected

Definition at line 205 of file VSDM.h.

temp_V2_

vector<double> GEO::VSDM::temp_V2_

protected

Definition at line 206 of file VSDM.h.

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The documentation for this class was generated from the following file:

• exploragram/optimal_transport/VSDM.h