geometry/volumes/checkFullConvexityTheorems.cpp

This example shows how to use the fully convex envelope to build a digital polyhedron from an arbitrary mesh. All faces have also the property that their points lies in the naive/standard plane defined by its vertices. It uses DigitalConvexity::relativeEnvelope for computations.

 
#include <iostream>
#include <queue>
#include "DGtal/base/Common.h"
#include "DGtal/helpers/StdDefs.h"
#include "DGtal/geometry/volumes/DigitalConvexity.h"
 
 
using namespace std;
using namespace DGtal;
 
template <typename Point>
void makeRandom( Point& p, int width )
{
  for ( Dimension i = 0; i < Point::dimension; i++ )
    p[ i ] = rand() % width;
}
 
template <typename Point>
void makeRandomRange( std::vector< Point >& X, int nb, int width )
{
  X.resize( nb );
  for ( int i = 0; i < nb; i++ )
    makeRandom( X[ i ], width );
}
 
template <typename ProjectedPoint, typename Point >
void project( ProjectedPoint& pp, const Point& p, Dimension a )
{
  Dimension j = 0;
  for ( Dimension i = 0; i < Point::dimension; i++ )
    if ( i != a ) pp[ j++ ] = p[ i ];
}
 
template <typename ProjectedPoint, typename Point >
void projectRange( std::vector< ProjectedPoint >& pp,
                   const std::vector< Point > & p, Dimension a )
{
  pp.resize( p.size() );
  for ( auto i = 0; i < p.size(); i++ )
    project( pp[ i ], p[ i ], a );
  std::sort( pp.begin(), pp.end() );
  auto last = std::unique( pp.begin(), pp.end() );
  pp.erase( last, pp.end() );
}
 
 
// @param width the width of the domain
template <typename Space>
bool
checkSkelStarCvxHFullConvexity( int width )
{
  typedef typename Space::Integer Integer;
  typedef DGtal::KhalimskySpaceND< Space::dimension, Integer > KSpace;
  typedef DGtal::DigitalConvexity< KSpace > DConvexity;
  typedef typename KSpace::Point  Point;
  typedef std::vector<Point>      PointRange;
 
  // Generate a random polytope in the specified domain
  Point lo = Point::zero;
  Point hi = Point::diagonal( width );
  DConvexity dconv( lo, hi );
  std::vector< Point > X;
  int   nb = Space::dimension + rand() % 7;
  makeRandomRange( X, nb, width );
  auto  C  = dconv.StarCvxH( X );
  auto  E  = dconv.envelope( X );
  auto  Y  = C.extremaOfCells();
  bool  ok1 = dconv.isFullyConvex( E );
  if ( ! ok1 )
    trace.warning() << "FC*(X) is not fully convex !" << std::endl;
  bool  ok2 = dconv.isFullyConvex( Y );
  if ( ! ok2 )
    {
      trace.warning() << "Extr(Star(CvxH(X))) is not fully convex !" << std::endl;
      for ( auto p : Y ) std::cout << " " << p;
      trace.warning() << std::endl;
    }
  bool ok3 = std::includes( Y.cbegin(), Y.cend(), E.cbegin(), E.cend() );
  trace.info() << "#X=" << X.size()
               << " #FC*(X)=" << E.size() << ( ok1 ? "/FC" : "/ERROR" )
               << " #Extr(Star(CvxH(X)))=" << Y.size()
               << ( ok2 ? "/FC" : "/ERROR" )
               << ( ok3 ? " FC*(X) subset Extr(Star(CvxH(X)))" : " Inclusion ERROR" )
               << std::endl;
  return ok1 && ok2 && ok3;
}
 
// @param width the width of the domain
template <typename Space>
bool
checkCvxHPlusHypercubeFullConvexity( int width )
{
  typedef typename Space::Integer Integer;
  typedef DGtal::KhalimskySpaceND< Space::dimension, Integer > KSpace;
  typedef DGtal::DigitalConvexity< KSpace > DConvexity;
  typedef typename KSpace::Point  Point;
  typedef std::vector<Point>      PointRange;
 
  // Generate a random polytope in the specified domain
  Point lo = Point::zero;
  Point hi = Point::diagonal( width );
  DConvexity dconv( lo, hi );
  std::vector< Point > X, XpH, Y;
  int   nb = Space::dimension + rand() % 7;
  makeRandomRange( X, nb, width );
  std::sort( X.begin(), X.end() );
  XpH = X;
  for ( Dimension k = 0;  k < Space::dimension; k++ )
    XpH = dconv.U( k, XpH );
  auto  P  = dconv.makePolytope( XpH );
  P.getPoints( Y );
  auto  E  = dconv.envelope( X );
  bool  ok1 = dconv.isFullyConvex( E );
  if ( ! ok1 )
    trace.warning() << "FC*(X) is not fully convex !" << std::endl;
  bool  ok2 = dconv.isFullyConvex( Y );
  if ( ! ok2 )
    {
      trace.warning() << "CvxH(X+H) cap Z^d is not fully convex !" << std::endl;
      for ( auto p : Y ) std::cout << " " << p;
      trace.warning() << std::endl;
    }
  bool ok3 = std::includes( Y.cbegin(), Y.cend(), E.cbegin(), E.cend() );
  trace.info() << "#X=" << X.size()
               << " #CvxH(X+H) cap Z^d=" << Y.size()
               << ( ok2 ? "/FC" : "/ERROR" )
               << " #FC*(X)=" << E.size() << ( ok1 ? "/FC" : "/ERROR" )
               << ( ok3 ? " FC*(X) subset CvxH(X+H) cap Z^d"
                    : " FC*(X) not subset CvxH(X+H) cap Z^d" )
               << std::endl;
  return ok1 && ok2;
}
 
// @param width the width of the domain
template <typename Space>
bool
checkProjectionFullConvexity( int width )
{
  typedef typename Space::Integer    Integer;
  typedef DGtal::KhalimskySpaceND< Space::dimension, Integer > KSpace;
  typedef DGtal::DigitalConvexity< KSpace > DConvexity;
  typedef typename KSpace::Point     Point;
  typedef std::vector<Point>         PointRange;
  typedef DGtal::KhalimskySpaceND< Space::dimension-1, Integer > ProjKSpace;
  typedef DGtal::DigitalConvexity< ProjKSpace > ProjDConvexity;
  typedef typename ProjKSpace::Point ProjPoint;
  typedef std::vector<ProjPoint>     ProjPointRange;
 
  // Generate a random polytope in the specified domain
  Point lo = Point::zero;
  Point hi = Point::diagonal( width );
  DConvexity dconv( lo, hi );
  std::vector< Point > X;
  int   n = Space::dimension + rand() % 7;
  makeRandomRange( X, n, width );
  auto  E  = dconv.envelope( X );
  unsigned int nb    = 0;
  unsigned int nb_ok = 0;
  for ( Dimension a = 0; a < Space::dimension; a++ )
    {
      ProjPoint plo, phi;
      project( plo, lo, a ); 
      project( phi, hi, a ); 
      ProjDConvexity pdconv( plo, phi );
      std::vector< ProjPoint > PE;
      projectRange( PE, E, a );
      bool ok = pdconv.isFullyConvex( PE );
      if ( !ok )
        trace.warning() << "Projection is not fully convex !" << std::endl;
      nb_ok  += ok ? 1 : 0;
      nb     += 1;
      std::cout << "#E=" << E.size() << " #Proj(E)=" << PE.size()
                << (ok ? "/FC" : "/ERROR" ) << std::endl;
    }
  return nb_ok == nb;
}
 
template <typename Point>
void displayPointRange2D( const std::vector< Point >& X )
{
  if ( X.empty() ) return;
  Point lo  = X[ 0 ];
  Point hi  = X[ 0 ];
  for ( auto&& p : X ) { lo = lo.inf( p ); hi = hi.sup( p ); }
  auto w = hi[ 0 ] - lo[ 0 ] + 1;
  auto h = hi[ 1 ] - lo[ 1 ] + 1;
  for ( int y = 0; y < h; y++ )
    {
      for ( int x = 0; x < w; x++ )
        {
          Point q( lo[ 0 ] + x, lo[ 1 ] + y );
          std::cout << ( std::binary_search( X.cbegin(), X.cend(), q ) ? "*" : "." );
        }
      std::cout << std::endl;
    }
}
// @param width the width of the domain
template <typename Space>
bool
checkFullConvexityCharacterization( int width )
{
  typedef typename Space::Integer    Integer;
  typedef DGtal::KhalimskySpaceND< Space::dimension, Integer > KSpace;
  typedef DGtal::DigitalConvexity< KSpace > DConvexity;
  typedef typename KSpace::Point     Point;
  typedef std::vector<Point>         PointRange;
  typedef DGtal::KhalimskySpaceND< Space::dimension-1, Integer > ProjKSpace;
  typedef DGtal::DigitalConvexity< ProjKSpace > ProjDConvexity;
  typedef typename ProjKSpace::Point ProjPoint;
  typedef std::vector<ProjPoint>     ProjPointRange;
 
  // Generate a random polytope in the specified domain
  Point lo = Point::zero;
  Point hi = Point::diagonal( width );
  DConvexity dconv( lo, hi );
  std::vector< Point > X, Y;
  int   n = Space::dimension + rand() % 17;
  makeRandomRange( X, n, width );
  auto  P  = dconv.makePolytope( X );
  P.getPoints( Y );  
  const bool cvx = dconv.is0Convex( Y );
  const bool fc = dconv.isFullyConvex( Y );
  bool  proj_fc = true;
  std::cout << "#X=" << Y.size()
            << " " << ( cvx ? "X C" : "X NC" )
            << "/" << ( fc ? "X FC" : "X NFC" );
  for ( Dimension a = 0; a < Space::dimension; a++ )
    {
      ProjPoint plo, phi;
      project( plo, lo, a ); 
      project( phi, hi, a ); 
      ProjDConvexity pdconv( plo, phi );
      std::vector< ProjPoint > PE;
      projectRange( PE, Y, a );
      if ( Space::dimension == 3 )
        {
          std::cout << std::endl;
          displayPointRange2D( PE );
        }
      bool ok  = pdconv.isFullyConvex( PE );
      bool ok0 = pdconv.is0Convex( PE );
      std::cout << "/" << a << ( ok0 ? ( ok ? "FC" : "NFC" ) : "NC" );
      proj_fc = proj_fc && ok;
      if ( fc && !ok )
        trace.warning() << "Projection is not fully convex !" << std::endl;
    }
  if ( fc != proj_fc )
    trace.warning() << "X is " << ( fc ? "FCvx" : "not FCvx" )
                    << "proj(X) " << ( proj_fc ? "FCvx" : "not FCvx" )
                    << std::endl;
  else std::cout << ( fc ? " => FC ok" : " => Not FC ok" ) << std::endl;
  return fc == proj_fc;
}
 
int main( int argc, char* argv[] )
{
  int NB_TEST1 = 5;
  int NB_TEST2 = 5;
  int NB_TEST3 = 5;
  int NB_TEST4 = 25;
  {
    trace.beginBlock( "Check SkelStarCvxH(X) full convexity 2D" );
    typedef DGtal::SpaceND< 2, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST1; i++ )
      {
        nb_ok += checkSkelStarCvxHFullConvexity< Space >( 100 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check SkelStarCvxH(X) full convexity 3D" );
    typedef DGtal::SpaceND< 3, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST1; i++ )
      {
        nb_ok += checkSkelStarCvxHFullConvexity< Space >( 30 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check SkelStarCvxH(X) full convexity 4D" );
    typedef DGtal::SpaceND< 4, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST1; i++ )
      {
        nb_ok += checkSkelStarCvxHFullConvexity< Space >( 10 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check Projection full convexity 3D" );
    typedef DGtal::SpaceND< 3, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST2; i++ )
      {
        nb_ok += checkProjectionFullConvexity< Space >( 30 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check Projection full convexity 4D" );
    typedef DGtal::SpaceND< 4, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST2; i++ )
      {
        nb_ok += checkProjectionFullConvexity< Space >( 10 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check CvxH plus Hypercube full convexity 2D" );
    typedef DGtal::SpaceND< 2, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST3; i++ )
      {
        nb_ok += checkCvxHPlusHypercubeFullConvexity< Space >( 100 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check CvxH plus Hypercube full convexity 3D" );
    typedef DGtal::SpaceND< 3, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST3; i++ )
      {
        nb_ok += checkCvxHPlusHypercubeFullConvexity< Space >( 30 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check CvxH plus Hypercube full convexity 4D" );
    typedef DGtal::SpaceND< 4, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST3; i++ )
      {
        nb_ok += checkCvxHPlusHypercubeFullConvexity< Space >( 10 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check full convexity characterization 3D" );
    typedef DGtal::SpaceND< 3, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST4; i++ )
      {
        nb_ok += checkFullConvexityCharacterization< Space >( 10 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  {
    trace.beginBlock( "Check full convexity characterization 4D" );
    typedef DGtal::SpaceND< 4, int > Space;
    unsigned int nb    = 0;
    unsigned int nb_ok = 0;
    for ( int i = 0; i < NB_TEST4; i++ )
      {
        nb_ok += checkFullConvexityCharacterization< Space >( 10 ) ? 1 : 0;
        nb    += 1;
      }
    trace.info() << nb_ok << "/" << nb << " OK tests" << std::endl;
    trace.endBlock();
  }
  return 0;
}