DGtal::VectorsInHeat< TPolygonalCalculus > Class Template Reference

This class implements [111] on polygonal surfaces (using Discrete differential calculus on polygonal surfaces). More...

#include <DGtal/dec/VectorsInHeat.h>

Public Types
typedef TPolygonalCalculus	PolygonalCalculus
typedef PolygonalCalculus::SparseMatrix	SparseMatrix
typedef PolygonalCalculus::DenseMatrix	DenseMatrix
typedef PolygonalCalculus::Solver	Solver
typedef PolygonalCalculus::Vector	Vector
typedef PolygonalCalculus::Vertex	Vertex
typedef PolygonalCalculus::LinAlg	LinAlgBackend
typedef DirichletConditions< LinAlgBackend >	Conditions
typedef Conditions::IntegerVector	IntegerVector

Public Member Functions
	VectorsInHeat ()=delete
	VectorsInHeat (ConstAlias< PolygonalCalculus > calculus)
	~VectorsInHeat ()=default
	VectorsInHeat (const VectorsInHeat &other)=delete
	VectorsInHeat (VectorsInHeat &&other)=delete
VectorsInHeat &	operator= (const VectorsInHeat &other)=delete
VectorsInHeat &	operator= (VectorsInHeat &&other)=delete
void	init (double dt, double lambda=1.0, bool boundary_with_mixed_solution=false)
void	addSource (const Vertex aV, const Vector &ev)
void	clearSource ()
Vector	vectorSource () const
Vector	extrinsicVectorSourceAtVertex (const Vertex aV)
	extrinsicVectorSourceAtVertex get extrinsic source at vertex
Vector	intrinsicVectorSourceAtVertex (const Vertex aV)
	intrinsicVectorSourceAtVertex get intrinsic source at vertex
std::vector< Vector >	compute () const
bool	isValid () const

Private Attributes
const PolygonalCalculus *	myCalculus
	The underlying PolygonalCalculus instance.
SparseMatrix	myScalarHeatOpe
	The operators for heat diffusion.
SparseMatrix	myVectorHeatOpe
Solver	myScalarHeatSolver
	Heat solvers.
Solver	myVectorHeatSolver
Vector	myScalarSource
	Source vectors.
Vector	myDiracSource
Vector	myVectorSource
bool	myManageBoundary
IntegerVector	myBoundary
	The boundary characteristic vector.
bool	myIsInit
	Validitate flag.
Solver	myHeatDirichletSolver
	Heat solver with Dirichlet boundary conditions.

Detailed Description

template<typename TPolygonalCalculus>
class DGtal::VectorsInHeat< TPolygonalCalculus >

This class implements [111] on polygonal surfaces (using Discrete differential calculus on polygonal surfaces).

Description of template class 'VectorsInHeat'

see Vector Heat Method using discrete polygonal calculus for details and examples.

Template Parameters

a	model of PolygonalCalculus.

Definition at line 62 of file VectorsInHeat.h.

Member Typedef Documentation

Conditions

template<typename TPolygonalCalculus >

typedef DirichletConditions< LinAlgBackend > DGtal::VectorsInHeat< TPolygonalCalculus >::Conditions

Definition at line 74 of file VectorsInHeat.h.

DenseMatrix

template<typename TPolygonalCalculus >

typedef PolygonalCalculus::DenseMatrix DGtal::VectorsInHeat< TPolygonalCalculus >::DenseMatrix

Definition at line 69 of file VectorsInHeat.h.

IntegerVector

template<typename TPolygonalCalculus >

typedef Conditions::IntegerVector DGtal::VectorsInHeat< TPolygonalCalculus >::IntegerVector

Definition at line 75 of file VectorsInHeat.h.

LinAlgBackend

template<typename TPolygonalCalculus >

typedef PolygonalCalculus::LinAlg DGtal::VectorsInHeat< TPolygonalCalculus >::LinAlgBackend

Definition at line 73 of file VectorsInHeat.h.

PolygonalCalculus

template<typename TPolygonalCalculus >

typedef TPolygonalCalculus DGtal::VectorsInHeat< TPolygonalCalculus >::PolygonalCalculus

Definition at line 67 of file VectorsInHeat.h.

Solver

template<typename TPolygonalCalculus >

typedef PolygonalCalculus::Solver DGtal::VectorsInHeat< TPolygonalCalculus >::Solver

Definition at line 70 of file VectorsInHeat.h.

SparseMatrix

template<typename TPolygonalCalculus >

typedef PolygonalCalculus::SparseMatrix DGtal::VectorsInHeat< TPolygonalCalculus >::SparseMatrix

Definition at line 68 of file VectorsInHeat.h.

Vector

template<typename TPolygonalCalculus >

typedef PolygonalCalculus::Vector DGtal::VectorsInHeat< TPolygonalCalculus >::Vector

Definition at line 71 of file VectorsInHeat.h.

Vertex

template<typename TPolygonalCalculus >

typedef PolygonalCalculus::Vertex DGtal::VectorsInHeat< TPolygonalCalculus >::Vertex

Definition at line 72 of file VectorsInHeat.h.

Constructor & Destructor Documentation

VectorsInHeat() [1/4]

template<typename TPolygonalCalculus >

DGtal::VectorsInHeat< TPolygonalCalculus >::VectorsInHeat ( )

delete

Default constructor.

VectorsInHeat() [2/4]

template<typename TPolygonalCalculus >

DGtal::VectorsInHeat< TPolygonalCalculus >::VectorsInHeat ( ConstAlias< PolygonalCalculus > calculus )

inline

Constructor from an existing polygonal calculus. T

Parameters

calculus

a instance of PolygonalCalculus

Definition at line 84 of file VectorsInHeat.h.

                                                         : myCalculus(&calculus)
    {
        myIsInit=false;
    }

References DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit.

~VectorsInHeat()

template<typename TPolygonalCalculus >

DGtal::VectorsInHeat< TPolygonalCalculus >::~VectorsInHeat ( )

default

Destructor.

VectorsInHeat() [3/4]

template<typename TPolygonalCalculus >

DGtal::VectorsInHeat< TPolygonalCalculus >::VectorsInHeat ( const VectorsInHeat< TPolygonalCalculus > & other )

delete

Copy constructor.

Parameters

other

the object to clone.

VectorsInHeat() [4/4]

template<typename TPolygonalCalculus >

DGtal::VectorsInHeat< TPolygonalCalculus >::VectorsInHeat ( VectorsInHeat< TPolygonalCalculus > && other )

delete

Move constructor.

Parameters

other

the object to move.

Member Function Documentation

addSource()

template<typename TPolygonalCalculus >

void DGtal::VectorsInHeat< TPolygonalCalculus >::addSource ( const Vertex aV, const Vector & ev )

inline

Adds a source vector (3D extrinsic) at a vertex aV the vector gets projected to the tangent space

Parameters

aV	the Vertex
ev	the extrinsic R3 vector to add (only keeps the tangential part)

Definition at line 182 of file VectorsInHeat.h.

    {
        ASSERT_MSG(aV < myCalculus->nbVertices(), "Vertex is not in the surface mesh vertex range");
        Vector v = myCalculus->Tv(aV).transpose()*ev;
        v = v.normalized()*ev.norm();
        myVectorSource( 2*aV ) = v(0);
        myVectorSource( 2*aV+1 ) = v(1);
        myScalarSource( aV ) = v.norm();
        myDiracSource( aV ) = 1;
    }

References DGtal::VectorsInHeat< TPolygonalCalculus >::myCalculus, DGtal::VectorsInHeat< TPolygonalCalculus >::myDiracSource, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarSource, and DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource.

clearSource()

template<typename TPolygonalCalculus >

void DGtal::VectorsInHeat< TPolygonalCalculus >::clearSource ( )

inline

Clears all sources

Definition at line 195 of file VectorsInHeat.h.

    {
      myVectorSource            = Vector::Zero(2*myCalculus->nbVertices());
      myScalarSource            = Vector::Zero(myCalculus->nbVertices());
      myDiracSource             = Vector::Zero(myCalculus->nbVertices());
    }

References DGtal::VectorsInHeat< TPolygonalCalculus >::myCalculus, DGtal::VectorsInHeat< TPolygonalCalculus >::myDiracSource, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarSource, and DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource.

compute()

template<typename TPolygonalCalculus >

std::vector< Vector > DGtal::VectorsInHeat< TPolygonalCalculus >::compute ( ) const

inline

Main computation of the Vectors In Heat

Returns

the estimated heat diffused vectors from the sources expressed

Definition at line 237 of file VectorsInHeat.h.

    {
        FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
        //Heat diffusion
        Vector vectorHeatDiffusion = myVectorHeatSolver.solve(myVectorSource);
        Vector scalarHeatDiffusion = myScalarHeatSolver.solve(myScalarSource);
        Vector diracHeatDiffusion = myScalarHeatSolver.solve(myDiracSource);
        auto surfmesh = myCalculus->getSurfaceMeshPtr();
 
 
        // Take care of boundaries
        if ( myManageBoundary )
        {
          Vector bValues  = Vector::Zero( myCalculus->nbVertices() );
          Vector bNormSources = Conditions::dirichletVector( myScalarHeatOpe, myScalarSource,
                                                         myBoundary, bValues );
          Vector bSol     = myHeatDirichletSolver.solve( bNormSources );
          Vector heatDiffusionDirichlet
                          = Conditions::dirichletSolution( bSol, myBoundary, bValues );
          scalarHeatDiffusion = 0.5 * ( scalarHeatDiffusion + heatDiffusionDirichlet );
        }
 
        std::vector<Vector> result(surfmesh->nbVertices());
 
        for (typename PolygonalCalculus::MySurfaceMesh::Index v = 0;v<surfmesh->nbVertices();v++){
            Vector Y(2);
            Y(0) = vectorHeatDiffusion(2*v);
            Y(1) = vectorHeatDiffusion(2*v+1);
            Y = Y.normalized()*(scalarHeatDiffusion(v)/diracHeatDiffusion(v));
            result[v] = myCalculus->toExtrinsicVector(v,Y);
        }
 
        return result;
    }

References DGtal::DirichletConditions< TLinearAlgebraBackend >::dirichletSolution(), DGtal::DirichletConditions< TLinearAlgebraBackend >::dirichletVector(), DGtal::VectorsInHeat< TPolygonalCalculus >::myBoundary, DGtal::VectorsInHeat< TPolygonalCalculus >::myCalculus, DGtal::VectorsInHeat< TPolygonalCalculus >::myDiracSource, DGtal::VectorsInHeat< TPolygonalCalculus >::myHeatDirichletSolver, DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit, DGtal::VectorsInHeat< TPolygonalCalculus >::myManageBoundary, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarHeatOpe, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarHeatSolver, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarSource, DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorHeatSolver, DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource, and surfmesh.

extrinsicVectorSourceAtVertex()

template<typename TPolygonalCalculus >

Vector DGtal::VectorsInHeat< TPolygonalCalculus >::extrinsicVectorSourceAtVertex ( const Vertex aV )

inline

extrinsicVectorSourceAtVertex get extrinsic source at vertex

Parameters

aV	the vertex

Returns

3D source vector

Definition at line 216 of file VectorsInHeat.h.

                                                         {
        FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
        return myCalculus->toExtrinsicVector(aV,intrinsicVectorSourceAtVertex(aV));
    }

References DGtal::VectorsInHeat< TPolygonalCalculus >::intrinsicVectorSourceAtVertex(), DGtal::VectorsInHeat< TPolygonalCalculus >::myCalculus, and DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit.

init()

template<typename TPolygonalCalculus >

void DGtal::VectorsInHeat< TPolygonalCalculus >::init ( double dt, double lambda = 1.0, bool boundary_with_mixed_solution = false )

inline

Initialize the solvers with dt as timestep for the heat diffusion and lambda parameter for the polygonal calculus, which guarantee definiteness for positive lambda.

Parameters

dt	timestep
lambda
boundary_with_mixed_solution	when 'true' and when the surface has boundaries, mix two solutions of the heat diffusion operation (Neumann and Dirichlet null conditions on boundary).

Definition at line 134 of file VectorsInHeat.h.

    {
        myIsInit=true;
 
        SparseMatrix laplacian = myCalculus->globalLaplaceBeltrami( lambda );
 
        SparseMatrix connectionLaplacian = myCalculus->globalConnectionLaplace( lambda );
 
        SparseMatrix mass = myCalculus->globalLumpedMassMatrix();
        SparseMatrix mass2= myCalculus->doubledGlobalLumpedMassMatrix();
        myScalarHeatOpe   =  mass - dt*laplacian;
        myVectorHeatOpe   =  mass2 - dt*connectionLaplacian;
 
        //Prefactorizing
        myScalarHeatSolver.compute(myScalarHeatOpe);
        myVectorHeatSolver.compute(myVectorHeatOpe);
 
        //empty sources
        myVectorSource          = Vector::Zero(2*myCalculus->nbVertices());
        myScalarSource          = Vector::Zero(myCalculus->nbVertices());
        myDiracSource           = Vector::Zero(myCalculus->nbVertices());
 
        // Manage boundaries
        myManageBoundary = false;
        if ( ! boundary_with_mixed_solution ) return;
        myBoundary = IntegerVector::Zero(myCalculus->nbVertices());
        const auto surfmesh = myCalculus->getSurfaceMeshPtr();
        const auto edges    = surfmesh->computeManifoldBoundaryEdges();
        for ( auto e : edges )
          {
            const auto vtcs = surfmesh->edgeVertices( e );
            myBoundary[ vtcs.first  ] = 1;
            myBoundary[ vtcs.second ] = 1;
          }
        myManageBoundary = ! edges.empty();
        if ( ! myManageBoundary ) return;
        // Prepare solver for a problem with Dirichlet conditions.
        SparseMatrix heatOpe_d = Conditions::dirichletOperator( myScalarHeatOpe, myBoundary );
        // Prefactoring
        myHeatDirichletSolver.compute( heatOpe_d );
    }

References DGtal::DirichletConditions< TLinearAlgebraBackend >::dirichletOperator(), dt, laplacian(), DGtal::VectorsInHeat< TPolygonalCalculus >::myBoundary, DGtal::VectorsInHeat< TPolygonalCalculus >::myCalculus, DGtal::VectorsInHeat< TPolygonalCalculus >::myDiracSource, DGtal::VectorsInHeat< TPolygonalCalculus >::myHeatDirichletSolver, DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit, DGtal::VectorsInHeat< TPolygonalCalculus >::myManageBoundary, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarHeatOpe, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarHeatSolver, DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarSource, DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorHeatOpe, DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorHeatSolver, DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource, and surfmesh.

intrinsicVectorSourceAtVertex()

template<typename TPolygonalCalculus >

Vector DGtal::VectorsInHeat< TPolygonalCalculus >::intrinsicVectorSourceAtVertex ( const Vertex aV )

inline

intrinsicVectorSourceAtVertex get intrinsic source at vertex

Parameters

aV	the vertex

Returns

2D vector expressed in aV tangent frame

Definition at line 226 of file VectorsInHeat.h.

                                                         {
        FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
        Vector s(2);
        s(0) = myVectorSource(2*aV);
        s(1) = myVectorSource(2*aV+1);
        return s;
    }

References DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit, and DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::extrinsicVectorSourceAtVertex().

isValid()

template<typename TPolygonalCalculus >

bool DGtal::VectorsInHeat< TPolygonalCalculus >::isValid ( ) const

inline

Returns

true if the calculus is valid.

Definition at line 274 of file VectorsInHeat.h.

    {
        return myIsInit && myCalculus->isValid();
    }

References DGtal::VectorsInHeat< TPolygonalCalculus >::myCalculus, and DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit.

operator=() [1/2]

template<typename TPolygonalCalculus >

VectorsInHeat & DGtal::VectorsInHeat< TPolygonalCalculus >::operator= ( const VectorsInHeat< TPolygonalCalculus > & other )

delete

Copy assignment operator.

Parameters

other

the object to copy.

Returns

a reference on 'this'.

operator=() [2/2]

template<typename TPolygonalCalculus >

VectorsInHeat & DGtal::VectorsInHeat< TPolygonalCalculus >::operator= ( VectorsInHeat< TPolygonalCalculus > && other )

delete

Move assignment operator.

Parameters

other

the object to move.

Returns

a reference on 'this'.

vectorSource()

template<typename TPolygonalCalculus >

Vector DGtal::VectorsInHeat< TPolygonalCalculus >::vectorSource ( ) const

inline

Returns

the source points vector.

Definition at line 205 of file VectorsInHeat.h.

    {
        FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
        return myVectorSource;
    }

References DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit, and DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource.

Field Documentation

myBoundary

template<typename TPolygonalCalculus >

IntegerVector DGtal::VectorsInHeat< TPolygonalCalculus >::myBoundary

private

The boundary characteristic vector.

Definition at line 304 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myCalculus

template<typename TPolygonalCalculus >

const PolygonalCalculus* DGtal::VectorsInHeat< TPolygonalCalculus >::myCalculus

private

The underlying PolygonalCalculus instance.

Definition at line 284 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::addSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::clearSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), DGtal::VectorsInHeat< TPolygonalCalculus >::extrinsicVectorSourceAtVertex(), DGtal::VectorsInHeat< TPolygonalCalculus >::init(), and DGtal::VectorsInHeat< TPolygonalCalculus >::isValid().

myDiracSource

template<typename TPolygonalCalculus >

Vector DGtal::VectorsInHeat< TPolygonalCalculus >::myDiracSource

private

Definition at line 296 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::addSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::clearSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myHeatDirichletSolver

template<typename TPolygonalCalculus >

Solver DGtal::VectorsInHeat< TPolygonalCalculus >::myHeatDirichletSolver

private

Heat solver with Dirichlet boundary conditions.

Definition at line 310 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myIsInit

template<typename TPolygonalCalculus >

bool DGtal::VectorsInHeat< TPolygonalCalculus >::myIsInit

private

Validitate flag.

Definition at line 307 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), DGtal::VectorsInHeat< TPolygonalCalculus >::extrinsicVectorSourceAtVertex(), DGtal::VectorsInHeat< TPolygonalCalculus >::init(), DGtal::VectorsInHeat< TPolygonalCalculus >::intrinsicVectorSourceAtVertex(), DGtal::VectorsInHeat< TPolygonalCalculus >::isValid(), DGtal::VectorsInHeat< TPolygonalCalculus >::VectorsInHeat(), and DGtal::VectorsInHeat< TPolygonalCalculus >::vectorSource().

myManageBoundary

template<typename TPolygonalCalculus >

bool DGtal::VectorsInHeat< TPolygonalCalculus >::myManageBoundary

private

When 'true', manage boundaries with a mixed solution of Neumann and Dirichlet conditions.

Definition at line 301 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myScalarHeatOpe

template<typename TPolygonalCalculus >

SparseMatrix DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarHeatOpe

private

The operators for heat diffusion.

Definition at line 287 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myScalarHeatSolver

template<typename TPolygonalCalculus >

Solver DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarHeatSolver

private

Heat solvers.

Definition at line 291 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myScalarSource

template<typename TPolygonalCalculus >

Vector DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarSource

private

Source vectors.

Definition at line 295 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::addSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::clearSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myVectorHeatOpe

template<typename TPolygonalCalculus >

SparseMatrix DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorHeatOpe

private

Definition at line 288 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myVectorHeatSolver

template<typename TPolygonalCalculus >

Solver DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorHeatSolver

private

Definition at line 292 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), and DGtal::VectorsInHeat< TPolygonalCalculus >::init().

myVectorSource

template<typename TPolygonalCalculus >

Vector DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource

private

Definition at line 297 of file VectorsInHeat.h.

Referenced by DGtal::VectorsInHeat< TPolygonalCalculus >::addSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::clearSource(), DGtal::VectorsInHeat< TPolygonalCalculus >::compute(), DGtal::VectorsInHeat< TPolygonalCalculus >::init(), DGtal::VectorsInHeat< TPolygonalCalculus >::intrinsicVectorSourceAtVertex(), and DGtal::VectorsInHeat< TPolygonalCalculus >::vectorSource().

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

• VectorsInHeat.h