fullConvexitySphereGeodesics.cpp

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#include <iostream>
#include <queue>
#include "DGtal/base/Common.h"
#include "DGtal/shapes/Shapes.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/helpers/StdDefs.h"
#include "DGtal/helpers/Shortcuts.h"
#include "DGtal/images/ImageContainerBySTLVector.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/geometry/volumes/TangencyComputer.h"
 
 
using namespace std;
using namespace DGtal;
typedef Z3i::Space          Space;
typedef Z3i::KSpace         KSpace;
typedef Z3i::Domain         Domain;
typedef Z3i::SCell          SCell;
typedef Shortcuts< KSpace > SH3;
typedef Space::Point        Point;
typedef Space::RealPoint    RealPoint;
typedef Space::RealVector   RealVector;
typedef Space::Vector       Vector;
typedef SurfaceMesh< RealPoint, RealVector > SMesh;
typedef SurfaceMeshWriter< RealPoint, RealVector > SMeshWriter;
typedef SMesh::Index        Index;
typedef SMesh::Vertices     Vertices;
 
void saveToObj( const std::string& output,
                const SMesh& surfmesh,
                const std::vector< double >& vvalues,
                int nb_isolines_per_unit = 10,
                const double thickness = 0.1 )
{
  std::string cobjname = output;
  std::string cisoname = output + "-iso";
  auto quantify = [] ( double v, double m, double nb )
    { return round( v/m*nb )*m/nb; };
  trace.beginBlock( "Output Corrected HD OBJ files" );
  const auto fvalues = surfmesh.computeFaceValuesFromVertexValues( vvalues );
  double maxValue = * ( std::max_element( vvalues.cbegin(), vvalues.cend() ) );
  double minValue = * ( std::min_element( vvalues.cbegin(), vvalues.cend() ) );
  double maxDist  = maxValue - minValue;
  trace.info() << "Max distance is " << maxDist << std::endl;
  auto cmap = SH3::getColorMap( 0.0, maxDist );
  std::vector< Color > fcolors( surfmesh.nbFaces() );
  for ( Index f = 0; f < fvalues.size(); ++f )
    fcolors[ f ] = cmap( quantify( fvalues[ f ] - minValue, maxDist, 50 ) );
  SMeshWriter::writeOBJ( cobjname, surfmesh, fcolors );
  double unit = pow( 10.0, floor( log( maxDist ) / log( 10.0 ) ) - 1.0 );
  const int N = 10 * nb_isolines_per_unit;
  std::vector< double > isolines( N );
  std::vector< Color >  isocolors( N );
  for ( int i = 0; i < N; i++ )
    {
      isolines [ i ] = (double) i * 10.0 * unit / (double) nb_isolines_per_unit
        + minValue;
      isocolors[ i ] = ( i % nb_isolines_per_unit == 0 )
        ? Color::Red : Color::Black;
    }
  SMeshWriter::writeIsoLinesOBJ( cisoname, surfmesh, fvalues, vvalues,
                                 isolines, thickness, isocolors );
  trace.endBlock();
}
 
 
int main( int argc, char** argv )
{
  trace.info() << "Usage: " << argv[ 0 ] << " <h> <opt>" << std::endl;
  trace.info() << "\tComputes shortest paths to a source point on a sphere digitized with gridstep <h>." << std::endl;
  trace.info() << "\t- h [==1.0]: digitization gridstep" << std::endl;
  trace.info() << "\t- opt [==sqrt(3)]: >= sqrt(3): secure shortest paths, 0: fast" << std::endl;
  double      h = argc > 1 ? atof( argv[ 1 ] ) : 0.0625; //< exact (sqrt(3)) or inexact (0) computations
  double    opt = argc > 2 ? atof( argv[ 2 ] ) : sqrt(3.0); //< exact (sqrt(3)) or inexact (0) computations
 
  // Domain creation from two bounding points.
  trace.beginBlock( "Building sphere1 shape ... " );
  auto   params  = SH3::defaultParameters();
  params( "polynomial", "sphere1" )( "gridstep",  h );
  params( "minAABB", -2)( "maxAABB", 2)( "offset", 1.0 )( "closed", 1 );
  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,
                                           SH3::Domain(K.lowerBound(),K.upperBound()),
                                           params );
  trace.endBlock();
  
  trace.beginBlock( "Build mesh from primal surface" );
  // Compute surface
  auto surface = SH3::makeDigitalSurface( binary_image, K, params );
  // Build a mesh
  SMesh smesh;
  auto embedder = SH3::getCellEmbedder( K );
  std::vector< Point >    lattice_points;
  SH3::RealPoints         vertices;
  std::vector< Vertices > faces;
  SH3::Cell2Index         c2i;
  auto pointels = SH3::getPointelRange( c2i, surface );
  for ( auto p : pointels ) lattice_points.push_back( K.uCoords( p ) );
  trace.info() << "#surfels =" << surface->size() << std::endl;
  trace.info() << "#pointels=" << pointels.size() << std::endl;
  vertices = SH3::RealPoints( pointels.size() );
  std::transform( pointels.cbegin(), pointels.cend(), vertices.begin(),
                  [&] (const SH3::Cell& c) { return h * embedder( c ); } ); 
  // Build faces
  for ( auto&& surfel : *surface )
    {
      const auto primal_surfel_vtcs = SH3::getPointelRange( K, surfel );
      std::vector< Index > 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;
  trace.endBlock();
 
  // Find lowest and uppest point.
  const Index nb = lattice_points.size();
  Index   lowest = 0;
  Index   uppest = 0;
  for ( Index i = 1; i < nb; i++ )
    {
      if ( lattice_points[ i ] < lattice_points[ lowest ] ) lowest = i;
      if ( lattice_points[ uppest ] < lattice_points[ i ] ) uppest = i;
    }
  
  // Extracts shortest paths to a target
  typedef TangencyComputer< KSpace >::Index Index;
  trace.beginBlock( "Compute geodesics" );
  TangencyComputer< KSpace > TC( K );
  TC.init( lattice_points.cbegin(), lattice_points.cend() );
  auto SP = TC.makeShortestPaths( opt );
  SP.init( lowest ); //< set source
  double last_distance = 0.0;
  Index  last = 0;
  while ( ! SP.finished() )
    {
      last = std::get<0>( SP.current() );
      last_distance = std::get<2>( SP.current() );
      SP.expand();
    }
  double time = trace.endBlock();
  std::cout << "Max distance is " << last_distance*h << std::endl;
  std::cout << "Comput. time is " << time << std::endl;
  std::cout << "Last index is   " << last << std::endl;
  std::cout << "Uppest index is " << uppest << std::endl;
 
  // Export surface for display
  std::vector<double> distances = SP.distances();
  for ( Index i = 0; i < distances.size(); i++ )
    distances[ i ] *= h;
  saveToObj( "sphere1-geodesics", smesh, distances, 10, 0.1 );
  return 0;
}
//                                                                           //