DECHelpers.h

 
#pragma once

 
#if defined(DECHelpers_RECURSES)
#error Recursive header files inclusion detected in DECHelpers.h
#else // defined(DECHelpers_RECURSES)
#define DECHelpers_RECURSES
 
#if !defined DECHelpers_h
#define DECHelpers_h

// Inclusions
#include <iostream>
#include "DGtal/base/Common.h"
#include "DGtal/dec/Duality.h"
#include "DGtal/dec/DiscreteExteriorCalculus.h"
 
namespace DGtal
{
  namespace dec_helper
  {

    template <typename Calculus, DGtal::Dimension dim, DGtal::Duality duality>
    DGtal::LinearOperator<Calculus, dim, duality, dim, duality>
    diagonal(const DGtal::KForm<Calculus, dim, duality>& kform)
    {
      typedef DGtal::LinearOperator<Calculus,dim, duality, dim, duality> Operator;
      typedef typename Calculus::LinearAlgebraBackend::Triplet Triplet;
      typedef typename Calculus::Index Index;
      typedef std::vector<Triplet> Triplets;
 
      Triplets triplets;
      for (Index index=0; index<kform.length(); index++)
        triplets.emplace_back( index, index, kform.myContainer(index) );
      Operator ope(kform.myCalculus);
      ope.myContainer.setFromTriplets(triplets.begin(), triplets.end());
 
      return ope;
    }

    template <typename Calculus>
    DGtal::LinearOperator<Calculus, 0, DGtal::PRIMAL, 1, DGtal::PRIMAL>
    averageOperator01(const Calculus& calculus)
    {
      auto M01        = calculus.template derivative<0,DGtal::PRIMAL>();
      M01.myContainer = 0.5 * M01.myContainer.cwiseAbs();
      return M01;
    }

    template <typename Calculus>
    DGtal::LinearOperator<Calculus, 1, DGtal::PRIMAL, 2, DGtal::PRIMAL>
    averageOperator01(const Calculus& calculus)
    {
      auto M12        = calculus.template derivative<1,DGtal::PRIMAL>();
      M12.myContainer = 0.25 * M12.myContainer.cwiseAbs();
      return M12;
    }

    template <typename Calculus>
    DGtal::LinearOperator<Calculus, 2, DGtal::PRIMAL, 0, DGtal::PRIMAL>
    averageOperator20(const Calculus& calculus)
    {
      BOOST_STATIC_ASSERT( Calculus::dimensionEmbedded == 2 );
      BOOST_STATIC_ASSERT( Calculus::dimensionAmbient == 3 );
      using DGtal::PRIMAL;
      using DGtal::DUAL;
 
      typedef typename Calculus::LinearAlgebraBackend::SparseMatrix SparseMatrix;
      typedef typename Calculus::LinearAlgebraBackend::Triplet Triplet;
      typedef typename Calculus::KSpace KSpace;
      typedef typename Calculus::Index Index;
      typedef typename Calculus::Cell Cell;
      typedef typename Calculus::Scalar Scalar;
      typedef typename Calculus::Point Point;
      typedef DGtal::LinearOperator<Calculus, 2, DGtal::PRIMAL, 0, DGtal::PRIMAL>
        Operator;
 
      const KSpace& kspace = calculus.myKSpace;
 
      const std::vector<Point> deltas = {
        Point(0,1,1), Point(0,-1,1), Point(0,-1,-1), Point(0,1,-1),
        Point(1,0,1), Point(-1,0,1), Point(-1,0,-1), Point(1,0,-1),
        Point(1,1,0), Point(-1,1,0), Point(-1,-1,0), Point(1,-1,0)
      };
 
      std::vector<Triplet> triplets;
      for (Index index_point=0; index_point<calculus.kFormLength(0,PRIMAL); index_point++)
        {
          const Cell point = kspace.unsigns(calculus.getSCell(0, PRIMAL, index_point));
          ASSERT( kspace.uDim(point) == 0 );
 
          std::vector<Index> indexes_surfel;
          for (const Point delta : deltas)
            {
              const Cell surfel = kspace.uCell((kspace.uKCoords(point)+delta));
              ASSERT( kspace.uDim(surfel) == 2 );
              if (calculus.containsCell(surfel))
                indexes_surfel.push_back(calculus.getCellIndex(surfel));
            }
          ASSERT( indexes_surfel.size() > 2 );
 
          const double weight = 1/static_cast<Scalar>(indexes_surfel.size());
          for (const Index index_surfel : indexes_surfel)
            triplets.emplace_back( index_point, index_surfel, weight );
        }
 
      SparseMatrix matrix( calculus.kFormLength(0, DGtal::PRIMAL),
                           calculus.kFormLength(2, DGtal::PRIMAL) );
      matrix.setFromTriplets(triplets.begin(), triplets.end());
 
      return Operator(calculus, matrix);
    }
 
  } // namespace dec_helper
 
} // namespace DGtal
 
 
//                                                                           //
 
#endif // !defined DECHelpers_h
 
#undef DECHelpers_RECURSES
#endif // else defined(DECHelpers_RECURSES)