bool testCellularGridSpaceND()
{
  typedef typename KSpace::Cell Cell;
  typedef typename KSpace::SCell SCell;
  typedef typename KSpace::Point Point;
  typedef typename KSpace::DirIterator DirIterator;
  typedef typename KSpace::Cells Cells;
  typedef typename KSpace::SCells SCells;
  unsigned int nbok = 0;
  unsigned int nb = 0;
  
  trace.beginBlock ( "Testing block KSpace instantiation and scan ..." );
  KSpace K;
  int xlow[ 4 ] = { -3, -2, -2, -1 };
  int xhigh[ 4 ] = { 5, 3, 2, 3 };
  Point low( xlow );
  Point high( xhigh ); 
  bool space_ok = K.init( low, high, true );
  nbok += space_ok ? 1 : 0; 
  nb++;
  trace.info() << "(" << nbok << "/" << nb << ") "
         << "K.init( low, high )" << std::endl;
  trace.info() << "K.dim()=" << K.dimension << endl;
  int spel[ 4 ] = { 1, 1, 1, 1 }; // pixel
  Point kp( spel );
  Cell center = K.uCell( kp );
  Cell c1 = K.uCell( kp );
  Cell clow = K.uCell( low, kp );
  Cell chigh = K.uCell( high, kp );
  trace.info() << c1 << clow << chigh 
         << " topo(c1)=" << K.uTopology( c1 ) << " dirs=";
  for ( DirIterator q = K.uDirs( clow ); q != 0; ++q )
    trace.info() << " " << *q;
  trace.info() << endl;
  Cell f = K.uFirst( c1 );
  Cell l = K.uLast( c1 );
  trace.info() << "Loop in " << clow << chigh << endl;
  c1 = f;
  unsigned int nbelems = 0;
  do {
    ++nbelems;
    // trace.info() << c1;
  } while ( K.uNext( c1, f, l ) );
  trace.info() << " -> " << nbelems << " elements." << endl;
  unsigned int exp_nbelems = 1;
  for ( Dimension i = 0; i < K.dimension; ++i )
    exp_nbelems *= K.size( i );
  nbok += nbelems == exp_nbelems ? 1 : 0; 
  nb++;
  trace.info() << "(" << nbok << "/" << nb << ") "
         << nbelems << " scanned elements == "
         << exp_nbelems << " space size."
         << std::endl;
  trace.endBlock();
  trace.beginBlock ( "Testing neighborhoods in KSpace..." );
  Cells N = K.uNeighborhood( center );
  nbok += N.size() == ( K.dimension*2 + 1 ) ? 1 : 0; 
  nb++;
  trace.info() << "(" << nbok << "/" << nb << ") "
         << N.size() << "(neighborhood size) == "
         << ( K.dimension*2 + 1 ) << "(2*dim()+1)" << endl;
  Cells Np = K.uProperNeighborhood( center );
  nbok += Np.size() == ( K.dimension*2 ) ? 1 : 0; 
  nb++;
  trace.info() << "(" << nbok << "/" << nb << ") "
         << Np.size() << "(proper neighborhood size) == "
         << ( K.dimension*2 ) << "(2*dim())" << endl;
  trace.endBlock();

  trace.beginBlock ( "Testing faces in KSpace..." );
  Cells Nf = K.uFaces( center );
  nbok += Nf.size() == ceil( std::pow( 3.0 ,(int) K.dimension ) - 1 ) ? 1 : 0; 
  nb++;
  trace.info() << "(" << nbok << "/" << nb << ") "
         << Nf.size() << "(faces size) == "
         << floor( std::pow( 3.0, (int)K.dimension ) - 1 ) << "(3^dim()-1)" << endl;
  trace.endBlock();
  
  trace.beginBlock ( "Testing block Incidence in KSpace..." );
  SCell sspel = K.sCell( kp, K.POS );
  for ( DirIterator q1 = K.sDirs( sspel ); q1 != 0; ++q1 )
    for ( DirIterator q2 = K.sDirs( sspel ); q2 != 0; ++q2 )
      {
  if ( *q1 != *q2 )
    {
      SCell s0 = K.sIncident( sspel, *q1, true );
      SCell s1 = K.sIncident( sspel, *q2, true );
      SCell l10 = K.sIncident( s0, *q2, true );
      SCell l01 = K.sIncident( s1, *q1, true );
      trace.info() << "D+_" << *q2 << "(D+_" << *q1 << "(V))=" << l10 
       << " D+_" << *q1 << "(D+_" << *q2 << "(V))=" << l01
       << endl;
      nbok += l10 == K.sOpp( l01 ) ? 1 : 0; 
      nb++;
    }
      }
  trace.info() << "(" << nbok << "/" << nb << ") "
         << "anti-commutativity of incidence operators." << std::endl;
  trace.endBlock();

  trace.beginBlock ( "Testing direct Incidence in KSpace..." );
  for ( DirIterator q1 = K.sDirs( sspel ); q1 != 0; ++q1 )
    for ( DirIterator q2 = K.sDirs( sspel ); q2 != 0; ++q2 )
      {
  if ( *q1 != *q2 )
    {
      SCell s0 = K.sDirectIncident( sspel, *q1 );
      SCell l10 = K.sDirectIncident( s0, *q2 );
      SCell s1 = K.sDirectIncident( sspel, *q2 );
      SCell l01 = K.sDirectIncident( s1, *q1 );
      trace.info() << "Dd_" << *q2 << "(Dd_" << *q1 << "(V))=" << l10 
       << " Dd_" << *q1 << "(Dd_" << *q2 << "(V))=" << l01
       << endl;
      nbok += l10 != l01 ? 1 : 0; 
      nbok += K.sSign( s0 ) == K.POS ? 1 : 0;
      nbok += K.sSign( s1 ) == K.POS ? 1 : 0;
      nbok += K.sSign( l10 ) == K.POS ? 1 : 0;
      nbok += K.sSign( l01 ) == K.POS ? 1 : 0;
      nbok += s0 == K.sIncident( sspel, *q1, K.sDirect( sspel, *q1 ) )
        ? 1 : 0;
      nbok += s1 == K.sIncident( sspel, *q2, K.sDirect( sspel, *q2 ) )
        ? 1 : 0;
      nbok += l10 == K.sIncident( s0, *q2, K.sDirect( s0, *q2 ) )
        ? 1 : 0;
      nbok += l01 == K.sIncident( s1, *q1, K.sDirect( s1, *q1 ) )
        ? 1 : 0;
      nb += 9;
    }
      }
  trace.info() << "(" << nbok << "/" << nb << ") "
         << "correctness of direct and indirect orientations." << std::endl;
  
  trace.endBlock();
  
  
  return nbok == nb;
}