DGtal  1.4.beta
Public Types | Public Member Functions | Private Attributes
DGtal::VectorsInHeat< TPolygonalCalculus > Class Template Reference

This class implements [109] 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< LinAlgBackendConditions
 
typedef Conditions::IntegerVector IntegerVector
 

Public Member Functions

 VectorsInHeat ()=delete
 
 VectorsInHeat (ConstAlias< PolygonalCalculus > calculus)
 
 ~VectorsInHeat ()=default
 
 VectorsInHeat (const VectorsInHeat &other)=delete
 
 VectorsInHeat (VectorsInHeat &&other)=delete
 
VectorsInHeatoperator= (const VectorsInHeat &other)=delete
 
VectorsInHeatoperator= (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 More...
 
Vector intrinsicVectorSourceAtVertex (const Vertex aV)
 intrinsicVectorSourceAtVertex get intrinsic source at vertex More...
 
std::vector< Vectorcompute () const
 
bool isValid () const
 

Private Attributes

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

Detailed Description

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

This class implements [109] 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
amodel 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
calculusa instance of PolygonalCalculus

Definition at line 84 of file VectorsInHeat.h.

84  : myCalculus(&calculus)
85  {
86  myIsInit=false;
87  }

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
otherthe object to clone.

◆ VectorsInHeat() [4/4]

template<typename TPolygonalCalculus >
DGtal::VectorsInHeat< TPolygonalCalculus >::VectorsInHeat ( VectorsInHeat< TPolygonalCalculus > &&  other)
delete

Move constructor.

Parameters
otherthe 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
aVthe Vertex
evthe extrinsic R3 vector to add (only keeps the tangential part)

Definition at line 182 of file VectorsInHeat.h.

183  {
184  ASSERT_MSG(aV < myCalculus->nbVertices(), "Vertex is not in the surface mesh vertex range");
185  Vector v = myCalculus->Tv(aV).transpose()*ev;
186  v = v.normalized()*ev.norm();
187  myVectorSource( 2*aV ) = v(0);
188  myVectorSource( 2*aV+1 ) = v(1);
189  myScalarSource( aV ) = v.norm();
190  myDiracSource( aV ) = 1;
191  }

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

◆ 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.

238  {
239  FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
240  //Heat diffusion
241  Vector vectorHeatDiffusion = myVectorHeatSolver.solve(myVectorSource);
242  Vector scalarHeatDiffusion = myScalarHeatSolver.solve(myScalarSource);
243  Vector diracHeatDiffusion = myScalarHeatSolver.solve(myDiracSource);
244  auto surfmesh = myCalculus->getSurfaceMeshPtr();
245 
246 
247  // Take care of boundaries
248  if ( myManageBoundary )
249  {
250  Vector bValues = Vector::Zero( myCalculus->nbVertices() );
252  myBoundary, bValues );
253  Vector bSol = myHeatDirichletSolver.solve( bNormSources );
254  Vector heatDiffusionDirichlet
255  = Conditions::dirichletSolution( bSol, myBoundary, bValues );
256  scalarHeatDiffusion = 0.5 * ( scalarHeatDiffusion + heatDiffusionDirichlet );
257  }
258 
259  std::vector<Vector> result(surfmesh->nbVertices());
260 
261  for (auto v = 0;v<surfmesh->nbVertices();v++){
262  Vector Y(2);
263  Y(0) = vectorHeatDiffusion(2*v);
264  Y(1) = vectorHeatDiffusion(2*v+1);
265  Y = Y.normalized()*(scalarHeatDiffusion(v)/diracHeatDiffusion(v));
266  result[v] = myCalculus->toExtrinsicVector(v,Y);
267  }
268 
269  return result;
270  }

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 DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbVertices().

◆ extrinsicVectorSourceAtVertex()

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

extrinsicVectorSourceAtVertex get extrinsic source at vertex

Parameters
aVthe vertex
Returns
3D source vector

Definition at line 216 of file VectorsInHeat.h.

216  {
217  FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
218  return myCalculus->toExtrinsicVector(aV,intrinsicVectorSourceAtVertex(aV));
219  }

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
dttimestep
lambda
boundary_with_mixed_solutionwhen '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.

136  {
137  myIsInit=true;
138 
139  SparseMatrix laplacian = myCalculus->globalLaplaceBeltrami( lambda );
140 
141  SparseMatrix connectionLaplacian = myCalculus->globalConnectionLaplace( lambda );
142 
143  SparseMatrix mass = myCalculus->globalLumpedMassMatrix();
144  SparseMatrix mass2= myCalculus->doubledGlobalLumpedMassMatrix();
145  myScalarHeatOpe = mass - dt*laplacian;
146  myVectorHeatOpe = mass2 - dt*connectionLaplacian;
147 
148  //Prefactorizing
151 
152  //empty sources
153  myVectorSource = Vector::Zero(2*myCalculus->nbVertices());
154  myScalarSource = Vector::Zero(myCalculus->nbVertices());
155  myDiracSource = Vector::Zero(myCalculus->nbVertices());
156 
157  // Manage boundaries
158  myManageBoundary = false;
159  if ( ! boundary_with_mixed_solution ) return;
160  myBoundary = IntegerVector::Zero(myCalculus->nbVertices());
161  const auto surfmesh = myCalculus->getSurfaceMeshPtr();
162  const auto edges = surfmesh->computeManifoldBoundaryEdges();
163  for ( auto e : edges )
164  {
165  const auto vtcs = surfmesh->edgeVertices( e );
166  myBoundary[ vtcs.first ] = 1;
167  myBoundary[ vtcs.second ] = 1;
168  }
169  myManageBoundary = ! edges.empty();
170  if ( ! myManageBoundary ) return;
171  // Prepare solver for a problem with Dirichlet conditions.
173  // Prefactoring
174  myHeatDirichletSolver.compute( heatOpe_d );
175  }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryEdges(), DGtal::DirichletConditions< TLinearAlgebraBackend >::dirichletOperator(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeVertices(), 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, and DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource.

◆ intrinsicVectorSourceAtVertex()

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

intrinsicVectorSourceAtVertex get intrinsic source at vertex

Parameters
aVthe vertex
Returns
2D vector expressed in aV tangent frame

Definition at line 226 of file VectorsInHeat.h.

226  {
227  FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
228  Vector s(2);
229  s(0) = myVectorSource(2*aV);
230  s(1) = myVectorSource(2*aV+1);
231  return s;
232  }

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.

275  {
276  return myIsInit && myCalculus->isValid();
277  }

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
otherthe 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
otherthe 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.

206  {
207  FATAL_ERROR_MSG(myIsInit, "init() method must be called first");
208  return myVectorSource;
209  }

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

◆ myDiracSource

template<typename TPolygonalCalculus >
Vector DGtal::VectorsInHeat< TPolygonalCalculus >::myDiracSource
private

◆ 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

◆ 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

◆ myScalarSource

template<typename TPolygonalCalculus >
Vector DGtal::VectorsInHeat< TPolygonalCalculus >::myScalarSource
private

◆ 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

◆ myVectorSource

template<typename TPolygonalCalculus >
Vector DGtal::VectorsInHeat< TPolygonalCalculus >::myVectorSource
private

The documentation for this class was generated from the following file:
DGtal::VectorsInHeat::myManageBoundary
bool myManageBoundary
Definition: VectorsInHeat.h:301
DGtal::VectorsInHeat::myVectorHeatOpe
SparseMatrix myVectorHeatOpe
Definition: VectorsInHeat.h:288
DGtal::DirichletConditions::dirichletVector
static DenseVector dirichletVector(const SparseMatrix &A, const DenseVector &b, const IntegerVector &p, const DenseVector &u)
Definition: DirichletConditions.h:170
DGtal::VectorsInHeat::myHeatDirichletSolver
Solver myHeatDirichletSolver
Heat solver with Dirichlet boundary conditions.
Definition: VectorsInHeat.h:310
boost::edges
std::pair< typename graph_traits< DGtal::DigitalSurface< TDigitalSurfaceContainer > >::edge_iterator, typename graph_traits< DGtal::DigitalSurface< TDigitalSurfaceContainer > >::edge_iterator > edges(const DGtal::DigitalSurface< TDigitalSurfaceContainer > &digSurf)
Definition: DigitalSurfaceBoostGraphInterface.h:503
DGtal::VectorsInHeat::myDiracSource
Vector myDiracSource
Definition: VectorsInHeat.h:296
DGtal::VectorsInHeat::myScalarHeatSolver
Solver myScalarHeatSolver
Heat solvers.
Definition: VectorsInHeat.h:291
DGtal::SurfaceMesh::computeManifoldBoundaryEdges
Edges computeManifoldBoundaryEdges() const
DGtal::DirichletConditions::dirichletSolution
static DenseVector dirichletSolution(const DenseVector &xd, const IntegerVector &p, const DenseVector &u)
Definition: DirichletConditions.h:203
DGtal::DirichletConditions::dirichletOperator
static SparseMatrix dirichletOperator(const SparseMatrix &A, const IntegerVector &p)
Definition: DirichletConditions.h:130
DGtal::VectorsInHeat::intrinsicVectorSourceAtVertex
Vector intrinsicVectorSourceAtVertex(const Vertex aV)
intrinsicVectorSourceAtVertex get intrinsic source at vertex
Definition: VectorsInHeat.h:226
DGtal::SurfaceMesh::nbVertices
Size nbVertices() const
Definition: SurfaceMesh.h:280
SparseMatrix
EigenLinearAlgebraBackend::SparseMatrix SparseMatrix
Definition: testHeatLaplace.cpp:50
laplacian
void laplacian(Shape &shape, const Options &options, std::function< double(const RealPoint3D &)> input_function, std::function< double(const RealPoint3D &)> target_function, int argc, char **argv)
Definition: sphereCotangentLaplaceOperator.cpp:87
DGtal::VectorsInHeat::myScalarHeatOpe
SparseMatrix myScalarHeatOpe
The operators for heat diffusion.
Definition: VectorsInHeat.h:287
DGtal::VectorsInHeat::myBoundary
IntegerVector myBoundary
The boundary characteristic vector.
Definition: VectorsInHeat.h:304
DGtal::SurfaceMesh::edgeVertices
const VertexPair & edgeVertices(Edge e) const
Definition: SurfaceMesh.h:329
DGtal::VectorsInHeat::myIsInit
bool myIsInit
Validitate flag.
Definition: VectorsInHeat.h:307
DGtal::VectorsInHeat::myCalculus
const PolygonalCalculus * myCalculus
The underlying PolygonalCalculus instance.
Definition: VectorsInHeat.h:284
DGtal::VectorsInHeat::myVectorSource
Vector myVectorSource
Definition: VectorsInHeat.h:297
Vector
FreemanChain< int >::Vector Vector
Definition: testCombinDSS.cpp:60
DGtal::VectorsInHeat::myVectorHeatSolver
Solver myVectorHeatSolver
Definition: VectorsInHeat.h:292
DGtal::VectorsInHeat::myScalarSource
Vector myScalarSource
Source vectors.
Definition: VectorsInHeat.h:295