dgtalCalculus-poisson.cpp File Reference

#include <iostream>
#include <DGtal/base/Common.h>
#include <DGtal/helpers/StdDefs.h>
#include <DGtal/helpers/Shortcuts.h>
#include <DGtal/helpers/ShortcutsGeometry.h>
#include <DGtal/shapes/SurfaceMesh.h>
#include <DGtal/geometry/surfaces/DigitalSurfaceRegularization.h>
#include <DGtal/dec/PolygonalCalculus.h>
#include <DGtal/math/linalg/DirichletConditions.h>
#include <polyscope/polyscope.h>
#include <polyscope/surface_mesh.h>
#include <polyscope/point_cloud.h>
#include <Eigen/Dense>
#include <Eigen/Sparse>

Include dependency graph for dgtalCalculus-poisson.cpp:

Go to the source code of this file.

Typedefs
typedef Shortcuts< Z3i::KSpace >	SH3
typedef ShortcutsGeometry< Z3i::KSpace >	SHG3
typedef SurfaceMesh< RealPoint, RealVector >	SurfMesh
typedef std::size_t	Index

Functions
void	computeLaplace ()
void	myCallback ()
int	main ()

Variables
polyscope::SurfaceMesh *	psMesh
SurfMesh	surfmesh
float	scale = 0.1

Detailed Description

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Author

David Coeurjolly (david.nosp@m..coe.nosp@m.urjol.nosp@m.ly@l.nosp@m.iris..nosp@m.cnrs.nosp@m..fr ) Laboratoire d'InfoRmatique en Image et Systemes d'information - LIRIS (CNRS, UMR 5205), CNRS, France

Date

2021/09/02

This file is part of the DGtal library.

Definition in file dgtalCalculus-poisson.cpp.

Typedef Documentation

Index

typedef std::size_t Index

Definition at line 52 of file dgtalCalculus-poisson.cpp.

SH3

typedef Shortcuts<Z3i::KSpace> SH3

Definition at line 48 of file dgtalCalculus-poisson.cpp.

SHG3

typedef ShortcutsGeometry<Z3i::KSpace> SHG3

Definition at line 49 of file dgtalCalculus-poisson.cpp.

SurfMesh

typedef SurfaceMesh< RealPoint, RealVector > SurfMesh

Definition at line 51 of file dgtalCalculus-poisson.cpp.

Function Documentation

computeLaplace()

void computeLaplace

(

)

[PolyDEC-init]

[PolyDEC-init]

Definition at line 58 of file dgtalCalculus-poisson.cpp.

{
  typedef PolygonalCalculus<SH3::RealPoint,SH3::RealVector> PolyDEC;
  typedef DirichletConditions< EigenLinearAlgebraBackend >  DC;
  PolyDEC calculus(surfmesh);
  PolyDEC::SparseMatrix L = calculus.globalLaplaceBeltrami();
  PolyDEC::Form g = calculus.form0();
  DC::IntegerVector b = DC::IntegerVector::Zero( g.rows() );
  
  //We set values on the boundary
  auto boundaryEdges = surfmesh.computeManifoldBoundaryEdges();
  std::cout<< "Number of boundary edges= "<<boundaryEdges.size()<<std::endl;
  
  auto pihVertex=[&](const SurfMesh::Vertex &v){return  cos(scale*(surfmesh.position(v)[0]))*(scale*surfmesh.position(v)[1]);};
  
  for(auto &e: boundaryEdges)
  {
    auto adjVertices = surfmesh.edgeVertices(e);
    g(adjVertices.first)  = pihVertex(adjVertices.first);
    g(adjVertices.second) = pihVertex(adjVertices.second);
    b(adjVertices.first)  = 1;
    b(adjVertices.second) = 1;
  }
 
  // Solve Δu=0 with g as boundary conditions
  PolyDEC::Solver solver;
  PolyDEC::SparseMatrix L_dirichlet = DC::dirichletOperator( L, b );
  solver.compute( L_dirichlet );
  ASSERT(solver.info()==Eigen::Success);
  PolyDEC::Form g_dirichlet = DC::dirichletVector( L, g, b, g );
  PolyDEC::Form x_dirichlet = solver.solve( g_dirichlet );
  PolyDEC::Form u = DC::dirichletSolution( x_dirichlet, b, g );
 
  psMesh->addVertexScalarQuantity("g", g);
  psMesh->addVertexScalarQuantity("u", u);
}

References calculus, DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryEdges(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeVertices(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::form0(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::globalLaplaceBeltrami(), DGtal::L, DGtal::SurfaceMesh< TRealPoint, TRealVector >::position(), psMesh, and surfmesh.

Referenced by myCallback().

main()

int main

(

void

)

Definition at line 104 of file dgtalCalculus-poisson.cpp.

{
  auto params = SH3::defaultParameters() | SHG3::defaultParameters() |  SHG3::parametersGeometryEstimation();
  
  auto h=.7   ; //gridstep
  params( "polynomial", "0.1*y*y -0.1*x*x - 2.0*z" )( "gridstep", h );
  auto implicit_shape  = SH3::makeImplicitShape3D  ( params );
  auto digitized_shape = SH3::makeDigitizedImplicitShape3D( implicit_shape, params );
  auto K               = SH3::getKSpace( params );
  auto binary_image    = SH3::makeBinaryImage( digitized_shape, params );
  auto surface         = SH3::makeDigitalSurface( binary_image, K, params );
  auto primalSurface   = SH3::makePrimalSurfaceMesh(surface);
  
  //Need to convert the faces
  std::vector<std::vector<SH3::SurfaceMesh::Vertex>> faces;
  std::vector<RealPoint> positions = primalSurface->positions();
  for(auto face= 0 ; face < primalSurface->nbFaces(); ++face)
    faces.push_back(primalSurface->incidentVertices( face ));
  
  surfmesh = SurfMesh(positions.begin(),
                      positions.end(),
                      faces.begin(),
                      faces.end());
  psMesh = polyscope::registerSurfaceMesh("digital surface", positions, faces);
 
  // Initialize polyscope
  polyscope::init();
 
  // Set the callback function
  polyscope::state::userCallback = myCallback;
  polyscope::show();
  return EXIT_SUCCESS;
}

References binary_image, init(), K, myCallback(), psMesh, surface, and surfmesh.

myCallback()

void myCallback

(

)

Definition at line 97 of file dgtalCalculus-poisson.cpp.

{
  ImGui::SliderFloat("Phi scale", &scale, 0., 10.);
  if(ImGui::Button("Compute Laplace problem"))
    computeLaplace();
}

References computeLaplace().

Referenced by main().

Variable Documentation

psMesh

polyscope::SurfaceMesh* psMesh

Definition at line 54 of file dgtalCalculus-poisson.cpp.

Referenced by computeLaplace(), and main().

scale

float scale = 0.1

Definition at line 56 of file dgtalCalculus-poisson.cpp.

surfmesh

SurfMesh surfmesh

Definition at line 55 of file dgtalCalculus-poisson.cpp.

Referenced by computeLaplace(), and main().