digpoly-curvature-measures-cnc-3d.cpp

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#include <iostream>
#include <fstream>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/geometry/meshes/CorrectedNormalCurrentComputer.h"
#include "DGtal/helpers/Shortcuts.h"
#include "DGtal/helpers/ShortcutsGeometry.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/io/colormaps/GradientColorMap.h"
#include "DGtal/io/colormaps/QuantifiedColorMap.h"
 
DGtal::GradientColorMap< double >
makeColorMap( double min_value, double max_value )
{
  DGtal::GradientColorMap< double > gradcmap( min_value, max_value );
  gradcmap.addColor( DGtal::Color( 0, 0, 255 ) );
  gradcmap.addColor( DGtal::Color( 0, 255, 255 ) );
  gradcmap.addColor( DGtal::Color( 255, 255, 255 ) );
  gradcmap.addColor( DGtal::Color( 255, 255, 0 ) );
  gradcmap.addColor( DGtal::Color( 255, 0, 0 ) );
  return gradcmap;
}
 
void usage( int argc, char* argv[] )
{
  using namespace DGtal;
  using namespace DGtal::Z3i;
  typedef Shortcuts< KSpace >          SH;
  std::cout << "Usage: " << std::endl
            << "\t" << argv[ 0 ] << " <P> <B> <h> <R> <mode>" << std::endl
            << std::endl
            << "Computation of mean and Gaussian curvatures on an "      << std::endl
            << "digitized implicit shape using constant or "             << std::endl
            << "interpolated corrected curvature measures (based "       << std::endl
            << "on the theory of corrected normal currents)."            << std::endl
            << "- builds the surface mesh from polynomial <P>"           << std::endl
            << "- <B> defines the digitization space size [-B,B]^3"      << std::endl
            << "- <h> is the gridstep digitization"                      << std::endl
            << "- <R> is the radius of the measuring balls"              << std::endl
            << "- <mode> is either Const for constant corrected normal"  << std::endl
            << "  vector field or Interp for interpolated corrected"     << std::endl
            << "  normal vector field."                                  << std::endl
            << "It produces several OBJ files to display mean and"       << std::endl
            << "Gaussian curvature estimation results: `example-cnc-H.obj`" << std::endl
            << "and `example-cnc-G.obj` as well as the associated MTL file." << std::endl;
  std::cout << "You may either write your own polynomial as 3*x^2*y-z^2*x*y+1" << std::endl
            <<"or use a predefined polynomial in the following list:" << std::endl;
  auto L = SH::getPolynomialList();
  for ( const auto& p : L )
    std::cout << p.first << " : " << p.second << std::endl;
}
 
int main( int argc, char* argv[] )
{
  if ( argc <= 1 )
    {
      usage( argc, argv );
      return 0;
    }
  using namespace DGtal;
  using namespace DGtal::Z3i;
  typedef SurfaceMesh< RealPoint, RealVector >                    SM;
  typedef CorrectedNormalCurrentComputer< RealPoint, RealVector > CNC;
  typedef Shortcuts< KSpace >          SH;
  typedef ShortcutsGeometry< KSpace > SHG;
  std::string  poly = argv[ 1 ]; // polynomial
  const double    B = argc > 2 ? atof( argv[ 2 ] ) : 1.0; // max ||_oo bbox
  const double    h = argc > 3 ? atof( argv[ 3 ] ) : 1.0; // gridstep  
  const double    R = argc > 4 ? atof( argv[ 4 ] ) : 2.0; // radius of measuring ball
  std::string  mode = argc > 5 ? argv[ 5 ] : "Const"; // either Const or Interp
  bool interpolated = mode == "Interp";
  if ( interpolated )
    std::cout << "Using vertex-*Interpolated* Corrected Normal Current" << std::endl;
  else
    std::cout << "Using face-*Constant* Corrected Normal Current" << std::endl;
  // Read polynomial and build digital surface
  auto params = SH::defaultParameters() | SHG::defaultParameters();
  params( "t-ring", 3 )( "surfaceTraversal", "Default" );
  params( "polynomial", poly )( "gridstep", h ); 
  params( "minAABB", -B )( "maxAABB", B );
  params( "offset", 3.0 );
  auto shape       = SH::makeImplicitShape3D( params );
  auto K           = SH::getKSpace( params );
  auto dshape      = SH::makeDigitizedImplicitShape3D( shape, params );
  auto bimage      = SH::makeBinaryImage( dshape, params );
  if ( bimage == nullptr ) 
    {
      trace.error() <<  "Unable to read polynomial <"
                    << poly.c_str() << ">" << std::endl;
      return 1;
    }
  auto sembedder   = SH::getSCellEmbedder( K );
  auto embedder    = SH::getCellEmbedder( K );
  auto surface     = SH::makeDigitalSurface( bimage, K, params );
  auto surfels     = SH::getSurfelRange( surface, params );
  trace.info() << "- surface has " << surfels.size()<< " surfels." << std::endl;
 
  SM smesh;
  std::vector< SM::Vertices > faces;
  SH::Cell2Index c2i;
  auto pointels = SH::getPointelRange( c2i, surface );
  auto vertices = SH::RealPoints( pointels.size() );
  std::transform( pointels.cbegin(), pointels.cend(), vertices.begin(),
                  [&] (const SH::Cell& c) { return h * embedder( c ); } ); 
  for ( auto&& surfel : *surface )
    {
      const auto primal_surfel_vtcs = SH::getPointelRange( K, surfel );
      SM::Vertices face;              
      for ( auto&& primal_vtx : primal_surfel_vtcs )
        face.push_back( c2i[ primal_vtx ] );
      faces.push_back( face );
    }
  smesh.init( vertices.cbegin(), vertices.cend(),
              faces.cbegin(),    faces.cend() );
  trace.info() << smesh << std::endl;
 
  auto exp_H = SHG::getMeanCurvatures( shape, K, surfels, params );
  auto exp_G = SHG::getGaussianCurvatures( shape, K, surfels, params );
 
  // Builds a CorrectedNormalCurrentComputer object onto the SurfaceMesh object
  CNC cnc( smesh );
  // Estimates normal vectors using Convolved Trivial Normal estimator 
  auto face_normals = SHG::getCTrivialNormalVectors( surface, surfels, params );
  // Set corrected face normals => Corrected Normal Current with
  // constant per face corrected vector field.
  smesh.setFaceNormals( face_normals.cbegin(), face_normals.cend() ); // CCNC
  // Set corrected vertex normals => Corrected Normal Current with
  // smooth linearly interpolated per face corrected vector field.
  if ( interpolated ) smesh.computeVertexNormalsFromFaceNormals();    // ICNC
  // computes area, mean and Gaussian curvature measures
  auto mu0 = cnc.computeMu0();
  auto mu1 = cnc.computeMu1();
  auto mu2 = cnc.computeMu2();
 
  // estimates mean (H) and Gaussian (G) curvatures by measure normalization.
  std::vector< double > H( smesh.nbFaces() );
  std::vector< double > G( smesh.nbFaces() );
  for ( auto f = 0; f < smesh.nbFaces(); ++f )
    {
      const auto b    = smesh.faceCentroid( f );
      const auto area = mu0.measure( b, R, f );
      H[ f ] = cnc.meanCurvature    ( area, mu1.measure( b, R, f ) );
      G[ f ] = cnc.GaussianCurvature( area, mu2.measure( b, R, f ) );
    }
 
  auto H_min_max = std::minmax_element( H.cbegin(), H.cend() );
  auto G_min_max = std::minmax_element( G.cbegin(), G.cend() );
  auto exp_H_min_max = std::minmax_element( exp_H.cbegin(), exp_H.cend() );
  auto exp_G_min_max = std::minmax_element( exp_G.cbegin(), exp_G.cend() );
  std::cout << "Expected mean curvatures:"
            << " min=" << *exp_H_min_max.first << " max=" << *exp_H_min_max.second
            << std::endl;
  std::cout << "Computed mean curvatures:"
            << " min=" << *H_min_max.first << " max=" << *H_min_max.second
            << std::endl;
  std::cout << "Expected Gaussian curvatures:"
            << " min=" << *exp_G_min_max.first << " max=" << *exp_G_min_max.second
            << std::endl;
  std::cout << "Computed Gaussian curvatures:"
            << " min=" << *G_min_max.first << " max=" << *G_min_max.second
            << std::endl;
  const auto      error_H = SHG::getScalarsAbsoluteDifference( H, exp_H );
  const auto stat_error_H = SHG::getStatistic( error_H );
  const auto   error_H_l2 = SHG::getScalarsNormL2( H, exp_H );
  trace.info() << "|H-H_CNC|_oo = " << stat_error_H.max() << std::endl;
  trace.info() << "|H-H_CNC|_2  = " << error_H_l2 << std::endl;
  const auto      error_G = SHG::getScalarsAbsoluteDifference( G, exp_G );
  const auto stat_error_G = SHG::getStatistic( error_G );
  const auto   error_G_l2 = SHG::getScalarsNormL2( G, exp_G );
  trace.info() << "|G-G_CNC|_oo = " << stat_error_G.max() << std::endl;
  trace.info() << "|G-G_CNC|_2  = " << error_G_l2 << std::endl;
 
  // Remove normals for better blocky display.
  smesh.vertexNormals() = SH::RealVectors();
  smesh.faceNormals()   = SH::RealVectors();
  typedef SurfaceMeshWriter< RealPoint, RealVector > SMW;
  const double    Hmax = std::max( fabs( *exp_H_min_max.first ),
                                   fabs( *exp_H_min_max.second ) );
  const double    Gmax = std::max( fabs( *exp_G_min_max.first ),
                                   fabs( *exp_G_min_max.second ) );
  const auto colormapH = makeQuantifiedColorMap( makeColorMap( -Hmax, Hmax ) );
  const auto colormapG = makeQuantifiedColorMap( makeColorMap( -Gmax, Gmax ) );
  auto colorsH = SMW::Colors( smesh.nbFaces() );
  auto colorsG = SMW::Colors( smesh.nbFaces() );
  for ( auto i = 0; i < smesh.nbFaces(); i++ )
    {
      colorsH[ i ] = colormapH( H[ i ] );
      colorsG[ i ] = colormapG( G[ i ] );
    }
  SMW::writeOBJ( "example-cnc-H", smesh, colorsH );
  SMW::writeOBJ( "example-cnc-G", smesh, colorsG );
  return 0;
}