dgtalCalculus-poisson.cpp

 
#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>
 
using namespace DGtal;
using namespace Z3i;
 
// Using standard 3D digital space.
typedef Shortcuts<Z3i::KSpace>         SH3;
typedef ShortcutsGeometry<Z3i::KSpace> SHG3;
// The following typedefs are useful
typedef SurfaceMesh< RealPoint, RealVector >  SurfMesh;
typedef std::size_t             Index;
//Polyscope global
polyscope::SurfaceMesh *psMesh;
SurfMesh surfmesh;
float scale = 0.1;
 
void computeLaplace()
{
  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);
}
 
void myCallback()
{
  ImGui::SliderFloat("Phi scale", &scale, 0., 10.);
  if(ImGui::Button("Compute Laplace problem"))
    computeLaplace();
}
 
int main()
{
  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;
}