testVoronoiMap.cpp File Reference

#include <iostream>
#include <array>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/helpers/StdDefs.h"
#include "DGtal/images/CConstImage.h"
#include "DGtal/geometry/volumes/distance/VoronoiMap.h"
#include "DGtal/geometry/volumes/distance/ExactPredicateLpSeparableMetric.h"
#include "DGtal/geometry/volumes/distance/InexactPredicateLpSeparableMetric.h"
#include "DGtal/geometry/volumes/distance/DistanceTransformation.h"
#include "DGtal/kernel/BasicPointPredicates.h"
#include "DGtal/io/boards/Board2D.h"
#include "DGtal/io/colormaps/HueShadeColorMap.h"

Include dependency graph for testVoronoiMap.cpp:

Go to the source code of this file.

Functions
template<typename Point >
double	mynorm (const Point &point, const double p)
template<typename VoroMap >
void	saveVoroMap (const std::string &filename, const VoroMap &output, const double p)
template<typename Point , typename Domain >
Point	calcPointModuloDomain (Point aPoint, Domain const &aDomain)
template<std::size_t N>
std::array< bool, N >	getPeriodicityFromInteger (std::size_t anInteger)
template<std::size_t N>
std::string	formatPeriodicity (std::array< bool, N > const &aPeriodicity)
template<typename Set , typename Voro >
bool	checkVoronoi (const Set &aSet, const Voro &voro)
bool	testCheckConcept ()
bool	testVoronoiMap (std::array< bool, 2 > const &periodicity={ {false, false} })
template<typename Set >
bool	testVoronoiMapFromSites2D (const Set &aSet, const std::string &name, std::array< bool, 2 > const &periodicity={ {false, false} })
template<typename Set >
bool	testVoronoiMapFromSites (const Set &aSet)
template<typename Set >
bool	testVoronoiMapFromSites (const Set &aSet, std::array< bool, Set::Space::dimension > const &periodicity)
bool	testSimple2D ()
bool	testSimpleRandom2D ()
bool	testSimple3D ()
bool	testSimpleRandom3D ()
bool	testSimple4D ()
int	main (int argc, char **argv)

Detailed Description

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Author

David Coeurjolly (david.nosp@m..coe.nosp@m.urjol.nosp@m.ly@l.nosp@m.iris..nosp@m.cnrs.nosp@m..fr ) Laboratoire d'InfoRmatique en Image et Systèmes d'information - LIRIS (CNRS, UMR 5205), CNRS, France

Date

2012/08/14

Functions for testing class VoronoiMap.

This file is part of the DGtal library.

Definition in file testVoronoiMap.cpp.

Function Documentation

calcPointModuloDomain()

template<typename Point , typename Domain >

Point calcPointModuloDomain	(	Point	aPoint,
		Domain const &	aDomain )

Modify a point coordinates as if the given domain is periodic and so that the coordinates are between the lower and upper bounds of the domain.

Parameters

aPoint	the point.
aDomain	the periodic domain.

Returns

the same point with coordinates between domain's lower and upper bounds.

Definition at line 95 of file testVoronoiMap.cpp.

{
  auto const & lowerBound = aDomain.lowerBound();
  auto const & upperBound = aDomain.upperBound();
 
  for ( typename Domain::Dimension i = 0; i < Domain::dimension; ++i )
    aPoint[i] = ( aPoint[i] - 2*lowerBound[i] + upperBound[i] + 1 ) % ( upperBound[i] - lowerBound[i] + 1 ) + lowerBound[i];
 
  return aPoint;
}

References aPoint(), DGtal::HyperRectDomain< TSpace >::lowerBound(), and DGtal::HyperRectDomain< TSpace >::upperBound().

checkVoronoi()

template<typename Set , typename Voro >

bool checkVoronoi	(	const Set &	aSet,
		const Voro &	voro )

Validates the VoronoiMap

Definition at line 145 of file testVoronoiMap.cpp.

{
  typedef typename Voro::Point Point;
 
  // Domain extent
  Point const extent = voro.domain().upperBound() - voro.domain().lowerBound() + Point::diagonal();
 
  // Site shifting depending on the periodicity.
  std::vector< typename Voro::PeriodicitySpec > periodicShift;
  for ( std::size_t i = 0; i < ( 1u << Voro::Space::dimension ); ++i )
    {
      const auto periodicity = getPeriodicityFromInteger< Voro::Space::dimension >( i );
 
      // Checking if this periodicity possibility is valid.
      bool isValid = true;
      for ( typename Voro::Space::Dimension j = 0; j < periodicity.size(); ++j )
        if ( periodicity[j] && ! voro.isPeriodic(j) )
          {
            isValid = false;
            break;
          }
 
      if ( isValid )
        periodicShift.push_back( periodicity );
    }
 
  // Checking site for all domain points.
  for ( auto const& pt : voro.domain() )
    {
      // Calculating reference (raw-)distance.
      const Point psite  = voro(pt);
      const auto dist = voro.metric()->rawDistance( pt, psite );
 
      // Checking that the reference site is actually a given site.
      // Also testing projectPoint method.
      if ( std::find( aSet.begin(), aSet.end(), voro.projectPoint( psite ) ) == aSet.end() )
        {
          trace.error() << "The Voro point " << psite
                        << " projected to " << voro.projectPoint( psite )
                        << " is not a valid site." << std::endl;
          return false;
        }
 
      // Checking if we can found a better site.
      for ( auto site : aSet )
        {
          // Trying all shifting possibilities of the site depending on the domain periodicity.
          for ( auto const & periodicity : periodicShift )
            {
              auto currSite = site;
 
              // Shifting site.
              for ( typename Voro::Space::Dimension dim = 0; dim < Voro::Space::dimension ; ++dim )
                if ( periodicity[dim] )
                  currSite[dim] += ( pt[dim] < currSite[dim] ? -1 : 1 ) * extent[dim];
 
              // Checking raw-distance.
              const auto dbis = voro.metric()->rawDistance( pt, currSite );
              if ( dbis < dist )
                {
                  trace.error() << "DT Error at " << pt
                                << "  Voro:" << psite << " (" << dist << ")"
                                << "  from set:" << site << "(" << dbis << ")"
                                << " projected from " << currSite << "." << std::endl;
                  return false;
                }
            }
        }
    }
 
  return true;
}

References dim, DGtal::Trace::error(), getPeriodicityFromInteger(), and DGtal::trace.

Referenced by testVoronoiMapFromSites().

formatPeriodicity()

template<std::size_t N>

std::string formatPeriodicity

(

std::array< bool, N > const &

aPeriodicity

)

Format a periodicity specification array as a string.

Parameters

aPeriodicity

the periodicity specification array.

Returns

a string which ith character is '0' if the ith dimension is non-periodic, '1' otherwise.

Definition at line 133 of file testVoronoiMap.cpp.

{
  std::string str;
  for ( std::size_t i = 0; i < N; ++i )
    str += aPeriodicity[i] ? '1' : '0';
 
  return str;
}

Referenced by testSimple2D(), testSimple3D(), testSimple4D(), testSimpleRandom2D(), and testSimpleRandom3D().

getPeriodicityFromInteger()

template<std::size_t N>

std::array< bool, N > getPeriodicityFromInteger

(

std::size_t

anInteger

)

Returns periodicity specification from an integer between 0 and 2^n - 1.

From an integer between 0 and 2^n-1, it returns a boolean array of size n whith value true at position i if the ith bit of the integer is set, false otherwise.

Template Parameters

N	size of the periodicity specification array.

Parameters

anInteger

an integer between 0 and 2^N-1.

Returns

a periodicity specification array.

Definition at line 117 of file testVoronoiMap.cpp.

{
  std::array<bool, N> periodicity;
  for ( std::size_t i = 0, mask = 1 ; i < N ; ++i, mask *= 2 )
    periodicity[i] = anInteger & mask;
 
  return periodicity;
}

Referenced by checkVoronoi(), testSimple2D(), testSimple3D(), testSimple4D(), testSimpleRandom2D(), and testSimpleRandom3D().

main()

int main	(	int	argc,
		char **	argv )

Definition at line 680 of file testVoronoiMap.cpp.

{
  trace.beginBlock ( "Testing class VoronoiMap" );
  trace.info() << "Args:";
  for ( int i = 0; i < argc; ++i )
    trace.info() << " " << argv[ i ];
  trace.info() << endl;
 
  bool res = testCheckConcept()
    && testVoronoiMap()
    && testVoronoiMap( { {true, false} } )
    && testVoronoiMap( { {false, true} } )
    && testVoronoiMap( { {true, true} } )
    && testSimple2D()
    && testSimpleRandom2D()
    && testSimple3D()
    && testSimpleRandom3D()
    && testSimple4D()
    ; // && ... other tests
 
  trace.emphase() << ( res ? "Passed." : "Error." ) << endl;
  trace.endBlock();
  return res ? 0 : 1;
}

References DGtal::Trace::beginBlock(), DGtal::Trace::emphase(), DGtal::Trace::endBlock(), DGtal::Trace::info(), testCheckConcept(), testSimple2D(), testSimple3D(), testSimple4D(), testSimpleRandom2D(), testSimpleRandom3D(), testVoronoiMap(), and DGtal::trace.

mynorm()

template<typename Point >

double mynorm	(	const Point &	point,
		const double	p )

Definition at line 54 of file testVoronoiMap.cpp.

{
  double res=0.0;
  for(unsigned int i=0; i< Point::dimension; i++)
    res +=  std::pow ( (double)abs(point[i]) , p);
 
  return std::pow(res, 1.0/p);
}

Referenced by saveVoroMap().

saveVoroMap()

template<typename VoroMap >

void saveVoroMap	(	const std::string &	filename,
		const VoroMap &	output,
		const double	p )

Definition at line 64 of file testVoronoiMap.cpp.

{
  typedef HueShadeColorMap<double,2> Hue;
 
  const double maxdt = mynorm( output.domain().upperBound() - output.domain().lowerBound(), p );
 
  Board2D board;
  Hue hue(0, maxdt);
 
  for(typename VoroMap::Domain::ConstIterator it = output.domain().begin(),
        itend = output.domain().end();
      it != itend; ++it)
    {
      typename VoroMap::Value point = output(*it);
      board << CustomStyle( (*it).className(), new CustomColors( hue(mynorm(point- (*it),p)),
                                                                 hue(mynorm(point- (*it),p))))
            << (*it);
    }
 
  board.saveSVG(filename.c_str());
}

References mynorm(), and LibBoard::Board::saveSVG().

testCheckConcept()

bool testCheckConcept

(

)

Definition at line 219 of file testVoronoiMap.cpp.

{
  typedef ExactPredicateLpSeparableMetric<Z3i::Space,2> L2Metric;
  BOOST_CONCEPT_ASSERT(( concepts::CConstImage< VoronoiMap<Z3i::Space, Z3i::DigitalSet, L2Metric> >));
 
  return true;
}

Referenced by main().

testSimple2D()

bool testSimple2D

(

)

Definition at line 525 of file testVoronoiMap.cpp.

{
 
  Z2i::Point a(-10,-10);
  Z2i::Point b(10,10);
  Z2i::Domain domain(a,b);
 
  Z2i::DigitalSet sites(domain);
  bool ok = true;
 
  sites.insertNew( Z2i::Point(3,-6));
  sites.insertNew( Z2i::Point(9,0));
  sites.insertNew( Z2i::Point(-3,0));
 
  for ( std::size_t i = 0; i < 4; ++i )
    {
      auto const periodicity = getPeriodicityFromInteger<2>(i);
      trace.beginBlock( "Simple2D with periodicity " + formatPeriodicity(periodicity) );
      ok = ok && testVoronoiMapFromSites2D( sites, "simple", periodicity );
      trace.endBlock();
    }
 
  return ok;
 
}

References DGtal::Trace::beginBlock(), domain, DGtal::Trace::endBlock(), formatPeriodicity(), getPeriodicityFromInteger(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::insertNew(), testVoronoiMapFromSites2D(), and DGtal::trace.

Referenced by main().

testSimple3D()

bool testSimple3D

(

)

Definition at line 593 of file testVoronoiMap.cpp.

{
 
  Z3i::Point a(-10,-10,-10);
  Z3i::Point b(10,10,10);
  Z3i::Domain domain(a,b);
 
  Z3i::DigitalSet sites(domain);
  bool ok = true;
 
  sites.insertNew( Z3i::Point(0,0,-6));
  sites.insertNew( Z3i::Point(6,0,0));
  sites.insertNew( Z3i::Point(-6,0,3));
 
  for ( auto i = 0; i < 8; ++i )
    {
      auto const periodicity = getPeriodicityFromInteger<3>(i);
      trace.beginBlock( "Simple3D with periodicity " + formatPeriodicity(periodicity) );
      ok = ok && testVoronoiMapFromSites( sites, periodicity );
      trace.endBlock();
    }
 
  return ok;
}

References DGtal::Trace::beginBlock(), domain, DGtal::Trace::endBlock(), formatPeriodicity(), getPeriodicityFromInteger(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::insertNew(), testVoronoiMapFromSites(), and DGtal::trace.

Referenced by main().

testSimple4D()

bool testSimple4D

(

)

Definition at line 650 of file testVoronoiMap.cpp.

{
 
  typedef SpaceND<4> Space4;
  Space4::Point a(0,0,0,0);
  Space4::Point b(5,5,5,5);
  HyperRectDomain<Space4> domain(a,b);
 
  DigitalSetBySTLSet< HyperRectDomain<Space4> > sites(domain);
  bool ok = true;
 
  sites.insertNew( Space4::Point(1,4,1,1));
  sites.insertNew( Space4::Point(3,1,3,1));
  sites.insertNew( Space4::Point(0,0,0,0));
 
  for ( std::size_t i = 0; i < 16; ++i )
    {
      auto const periodicity = getPeriodicityFromInteger<4>(i);
      trace.beginBlock( "Simple4D with periodicity " + formatPeriodicity(periodicity) );
      ok = ok && testVoronoiMapFromSites( sites, periodicity );
      trace.endBlock();
    }
 
  return ok;
}

References DGtal::Trace::beginBlock(), domain, DGtal::Trace::endBlock(), formatPeriodicity(), getPeriodicityFromInteger(), DGtal::DigitalSetBySTLSet< TDomain, TCompare >::insertNew(), testVoronoiMapFromSites(), and DGtal::trace.

Referenced by main().

testSimpleRandom2D()

bool testSimpleRandom2D

(

)

Definition at line 551 of file testVoronoiMap.cpp.

{
  unsigned size=16;
  Z2i::Point a(0,0);
  Z2i::Point b(size,size);
  Z2i::Domain domain(a,b);
 
  Z2i::DigitalSet sites(domain);
  bool ok = true;
 
  for(unsigned int i = 0 ; i < size; ++i)
    {
      Z2i::Point p(  rand() % (b[0]) -  a[0],  rand() % (b[1]) +  a[1]  );
      sites.insert( p );
    }
 
  for ( std::size_t i = 0; i < 4; ++i )
    {
      auto const periodicity = getPeriodicityFromInteger<2>(i);
      trace.beginBlock( "Random 2D with periodicity " + formatPeriodicity(periodicity) );
      ok = ok && testVoronoiMapFromSites2D( sites, "random", periodicity );
      trace.endBlock();
    }
 
  for(unsigned int i = 0 ; i < size*size-size; ++i)
    {
      Z2i::Point p(  rand() % (b[0]) -  a[0],  rand() % (b[1]) +  a[1]  );
      sites.insert( p );
    }
 
  for ( std::size_t i = 0; i < 4; ++i )
    {
      auto const periodicity = getPeriodicityFromInteger<2>(i);
      trace.beginBlock( "Random 2D (dense) with periodicity " + formatPeriodicity(periodicity) );
      ok = ok && testVoronoiMapFromSites2D( sites, "random-dense", periodicity );
      trace.endBlock();
    }
 
  return ok;
}

References DGtal::Trace::beginBlock(), domain, DGtal::Trace::endBlock(), formatPeriodicity(), getPeriodicityFromInteger(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::insert(), testVoronoiMapFromSites2D(), and DGtal::trace.

Referenced by main().

testSimpleRandom3D()

bool testSimpleRandom3D

(

)

Definition at line 618 of file testVoronoiMap.cpp.

{
  std::size_t const N = 16;
 
  Z3i::Point a(0, 0, 0);
  Z3i::Point b(N, N, N);
  Z3i::Domain domain(a,b);
 
  Z3i::DigitalSet sites(domain);
  bool ok = true;
 
  for(unsigned int i = 0 ; i < N; ++i)
    {
      Z3i::Point p(  rand() % (b[0]) -  a[0],
                     rand() % (b[1]) +  a[1],
                     rand() % (b[2]) +  a[2]  );
      sites.insert( p );
    }
 
  for ( std::size_t i = 0; i < 8; ++i )
    {
      auto const periodicity = getPeriodicityFromInteger<3>(i);
      trace.beginBlock( "Random 3D with periodicity " + formatPeriodicity(periodicity) );
      ok = ok && testVoronoiMapFromSites( sites, periodicity );
      trace.endBlock();
    }
 
  return ok;
}

References DGtal::Trace::beginBlock(), domain, DGtal::Trace::endBlock(), formatPeriodicity(), getPeriodicityFromInteger(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::insert(), testVoronoiMapFromSites(), and DGtal::trace.

Referenced by main().

testVoronoiMap()

bool testVoronoiMap

(

std::array< bool, 2 > const &

periodicity = { {false, false} }

)

Example of a test. To be completed.

Definition at line 231 of file testVoronoiMap.cpp.

                                                            { {false, false} } )
{
  unsigned int nbok = 0;
  unsigned int nb = 0;
 
  trace.beginBlock ( "Testing VoronoiMap2D with periodicity " + formatPeriodicity(periodicity) );
 
  Z2i::Point a(-10,-10);
  Z2i::Point b(10,10);
  Z2i::Domain domain(a,b);
 
  Z2i::DigitalSet mySet(domain);
 
  for(Z2i::Domain::ConstIterator it = domain.begin(), itend = domain.end();
      it != itend;
      ++it)
    mySet.insertNew( *it );
 
 
  Z2i::DigitalSet sites(domain);
 
  sites.insertNew( Z2i::Point(3,-6));
  sites.insertNew( Z2i::Point(9,0));
  sites.insertNew( Z2i::Point(-2,0));
 
  for(Z2i::DigitalSet::ConstIterator it = sites.begin(), itend = sites.end();
      it != itend; ++it)
    mySet.erase (*it);
 
 
 
  typedef ExactPredicateLpSeparableMetric<Z2i::Space, 2> L2Metric;
  typedef VoronoiMap<Z2i::Space, Z2i::DigitalSet, L2Metric> Voro2;
  L2Metric l2;
  Voro2 voro(&domain, &mySet, &l2, periodicity);
 
  for(int j=-10; j <= 10; j++)
    {
      for(int i=-10; i<=10; i++)
        trace.info() << "("<<voro( Z2i::Point(i,j))[0]<<","<< voro( Z2i::Point(i,j))[1]<<") ";
      trace.info()<<std::endl;
    }
 
  trace.info()<<"Exporting to SVG"<<std::endl;
 
  Board2D board;
  for(Voro2::OutputImage::Domain::ConstIterator it = voro.domain().begin(),
        itend = voro.domain().end();
      it != itend; ++it)
    {
      const auto p = calcPointModuloDomain( voro(*it), voro.domain() );
      const unsigned char c = ( p[1]*13 + p[0] * 7) % 256;
      board << CustomStyle( (*it).className(), new CustomColors(Color(c,c,c),Color(c,c,c)))
            << (*it);
    }
 
  board.saveSVG( ( "Voromap." + formatPeriodicity(periodicity) + ".svg" ).c_str() );
 
  trace.beginBlock("Validating the Voronoi Map");
  nbok += checkVoronoi(sites,voro) ? 1 : 0;
  nb++;
  trace.endBlock();
 
  trace.endBlock();
 
  return nbok == nb;
}

Referenced by main().

testVoronoiMapFromSites() [1/2]

template<typename Set >

bool testVoronoiMapFromSites

(

const Set &

aSet

)

Example of a test. To be completed.

Definition at line 464 of file testVoronoiMap.cpp.

{
  std::array<bool, Set::dimension> periodicity;
  periodicity.fill( false );
  return testVoronoiMapFromSites( aSet, periodicity );
}

References testVoronoiMapFromSites().

Referenced by testSimple3D(), testSimple4D(), testSimpleRandom3D(), and testVoronoiMapFromSites().

testVoronoiMapFromSites() [2/2]

template<typename Set >

bool testVoronoiMapFromSites	(	const Set &	aSet,
		std::array< bool, Set::Space::dimension > const &	periodicity )

Definition at line 472 of file testVoronoiMap.cpp.

{
  unsigned int nbok = 0;
  unsigned int nb = 0;
 
  Set mySet(aSet.domain());
 
  for(typename Set::Domain::ConstIterator it = aSet.domain().begin(),
      itend = aSet.domain().end();
      it != itend;
      ++it)
    mySet.insertNew( *it );
 
 
  for(typename Set::ConstIterator it = aSet.begin(), itend = aSet.end();
      it != itend; ++it)
    mySet.erase (*it);
 
 
 
  trace.beginBlock(" Voronoi computation l_2");
  typedef ExactPredicateLpSeparableMetric<typename Set::Space,2> L2Metric;
  typedef VoronoiMap<typename Set::Space, Set, L2Metric> Voro2;
  L2Metric l2;
  Voro2 voro(aSet.domain(), mySet, l2, periodicity);
  trace.endBlock();
 
  trace.beginBlock("Validating the Voronoi Map");
  nbok += checkVoronoi(aSet, voro) ? 1 : 0;
  nb++;
  trace.endBlock();
 
  trace.beginBlock(" Voronoi computation l_3");
  typedef ExactPredicateLpSeparableMetric<typename Set::Space,3> L3Metric;
  typedef VoronoiMap<typename Set::Space, Set, L3Metric> Voro3;
  L3Metric l3;
  Voro3 voro3(aSet.domain(), mySet, l3, periodicity);
  trace.endBlock();
 
  trace.beginBlock("Validating the Voronoi Map l_3");
  nbok += checkVoronoi(aSet, voro3) ? 1 : 0;
  nb++;
  trace.endBlock();
 
  trace.beginBlock(" DT computation");
  typedef DistanceTransformation<typename Set::Space, Set, L2Metric> DT;
  DT dt(aSet.domain(), mySet, l2, periodicity);
  trace.endBlock();
 
  return nbok == nb;
}

References DGtal::Trace::beginBlock(), checkVoronoi(), dt, DGtal::Trace::endBlock(), and DGtal::trace.

testVoronoiMapFromSites2D()

template<typename Set >

bool testVoronoiMapFromSites2D	(	const Set &	aSet,
		const std::string &	name,
		std::array< bool, 2 > const &	periodicity = { {false, false} } )

Example of a test. To be completed.

Definition at line 306 of file testVoronoiMap.cpp.

                                                                       { {false, false} } )
{
  unsigned int nbok = 0;
  unsigned int nb = 0;
 
  Set mySet(aSet.domain());
 
  for(typename Set::Domain::ConstIterator it = aSet.domain().begin(), itend = aSet.domain().end();
      it != itend;
      ++it)
    mySet.insertNew( *it );
 
 
  for(typename Set::ConstIterator it = aSet.begin(), itend = aSet.end();
      it != itend; ++it)
    mySet.erase (*it);
 
 
  trace.beginBlock(" Voro computation");
  typedef ExactPredicateLpSeparableMetric<typename Set::Space,2> L2Metric;
  typedef VoronoiMap<typename Set::Space, Set, L2Metric> Voro2;
  L2Metric l2;
  Voro2 voro(aSet.domain(), mySet, l2, periodicity );
 
  trace.endBlock();
 
  trace.beginBlock(" Voronoi computation l_6");
  typedef ExactPredicateLpSeparableMetric<typename Set::Space,6> L6Metric;
  L6Metric l6;
  typedef VoronoiMap<typename Set::Space, Set, L6Metric> Voro6;
  Voro6 voro6( aSet.domain(), mySet, l6, periodicity );
  trace.endBlock();
 
 
 
  trace.beginBlock(" DT computation");
  typedef DistanceTransformation<typename Set::Space, Set, L2Metric> DT;
  DT dt( aSet.domain(), mySet, l2, periodicity );
  trace.endBlock();
 
 
  if ( (aSet.domain().upperBound()[1] - aSet.domain().lowerBound()[1]) <20)
    {
      for(int j= aSet.domain().lowerBound()[1]; j <= aSet.domain().upperBound()[1]; j++)
        {
          for(int i=aSet.domain().lowerBound()[0]; i<=aSet.domain().upperBound()[0]; i++)
            if ( aSet.find( Z2i::Point(i,j) ) != aSet.end() )
              std::cout <<"X ";
            else
              std::cout<<"0 ";
          trace.info()<<std::endl;
        }
 
      trace.info() << std::endl;
 
      for(int j= aSet.domain().lowerBound()[1]; j <= aSet.domain().upperBound()[1]; j++)
        {
          for(int i=aSet.domain().lowerBound()[0]; i<=aSet.domain().upperBound()[0]; i++)
            trace.info() << "("<<voro( Z2i::Point(i,j))[0]<<","<< voro( Z2i::Point(i,j))[1]<<") ";
          trace.info()<<std::endl;
        }
    }
 
  Board2D board;
  board << voro.domain();
  for(typename Voro2::OutputImage::Domain::ConstIterator it = voro.domain().begin(), itend = voro.domain().end();
      it != itend; ++it)
    {
      if (!mySet(*it))
        board  << (*it);
    }
  std::string filename = "Voromap-" + name + "-orig." + formatPeriodicity(periodicity) + ".svg";
  board.saveSVG(filename.c_str());
 
  board.clear();
  board << voro.domain();
  board.setPenColor(Color(0,0,0));
  for(typename Voro2::OutputImage::Domain::ConstIterator it = voro.domain().begin(), itend = voro.domain().end();
      it != itend; ++it)
    {
      Z2i::Point p = voro(*it);
      if ((p != (*it)) && (p != voro.domain().upperBound() + Z2i::Point::diagonal(1))
          &&  (p != voro.domain().lowerBound()))
        Display2DFactory::draw( board,   p - (*it), (*it));
    }
 
  filename = "Voromap-" + name + "-diag." + formatPeriodicity(periodicity) + ".svg";
  board.saveSVG(filename.c_str());
 
 
  board.clear();
  board << voro.domain();
  for(typename Voro2::OutputImage::Domain::ConstIterator it = voro.domain().begin(), itend = voro.domain().end();
      it != itend; ++it)
    {
      const auto p = calcPointModuloDomain( voro(*it), voro.domain() );
      unsigned char c = (p[1]*13 + p[0] * 7) % 256;
      board << CustomStyle( (*it).className(), new CustomColors(Color(c,c,c),Color(c,c,c)))
            << (*it);
    }
 
  filename = "Voromap-" + name + "." + formatPeriodicity(periodicity) + ".svg";
  board.saveSVG(filename.c_str());
 
  filename = "Voromap-" + name + "-hue." + formatPeriodicity(periodicity) + ".svg";
  saveVoroMap(filename.c_str(),voro,2);
 
 
  board.clear();
  for(typename Voro6::OutputImage::Domain::ConstIterator it = voro6.domain().begin(),
      itend = voro6.domain().end();
      it != itend; ++it)
    {
      Z2i::Point p = voro6(*it);
      if (p != (*it))
        Display2DFactory::draw( board,   p - (*it), (*it));
    }
 
  filename = "Voromap-diag-l6-" + name + "." + formatPeriodicity(periodicity) + ".svg";
  board.saveSVG(filename.c_str());
 
  board.clear();
  for(typename Voro6::OutputImage::Domain::ConstIterator it = voro6.domain().begin(), itend = voro6.domain().end();
      it != itend; ++it)
    {
      const auto p = calcPointModuloDomain( voro6(*it), voro6.domain() );
      unsigned char c = (p[1]*13 + p[0] * 7) % 256;
      board << CustomStyle( (*it).className(), new CustomColors(Color(c,c,c),Color(c,c,c)))
            << (*it);;
    }
 
  filename = "Voromap-l6" + name + "." + formatPeriodicity(periodicity) + ".svg";
  board.saveSVG(filename.c_str());
 
  filename = "Voromap-hue-l6-" + name + "." + formatPeriodicity(periodicity) + ".svg";
  saveVoroMap(filename.c_str(),voro6,3);
 
 
  trace.beginBlock("Validating the Voronoi Map");
  nbok += checkVoronoi(aSet, voro) ? 1 : 0;
  nb++;
  trace.endBlock();
 
  trace.beginBlock("Validating the Voronoi Map l_6");
  nbok += checkVoronoi(aSet, voro6) ? 1 : 0;
  nb++;
  trace.endBlock();
 
  return nbok == nb;
}

Referenced by testSimple2D(), and testSimpleRandom2D().