testBoundedLatticePolytope.cpp

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#include <iostream>
#include <vector>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/kernel/SpaceND.h"
#include "DGtal/geometry/volumes/BoundedLatticePolytope.h"
#include "DGtalCatch.h"
 
using namespace std;
using namespace DGtal;
 
 
// Functions for testing class BoundedLatticePolytope.
 
SCENARIO( "BoundedLatticePolytope< Z2 > unit tests", "[lattice_polytope][2d]" )
{
  typedef SpaceND<2,int>                   Space;
  typedef Space::Point                     Point;
  typedef Space::Vector                    Vector;
  typedef BoundedLatticePolytope< Space >  Polytope;
 
  GIVEN( "A triangle P at (0,0), (5,0), (0,7)" ) {
    Point a( 0, 0 );
    Point b( 5, 0 );
    Point c( 0, 7 );
    Polytope P { a, b, c };
    THEN( "Its domain contains its vertices" ) {
      REQUIRE( P.isDomainPointInside( a ) );
      REQUIRE( P.isDomainPointInside( b ) );
      REQUIRE( P.isDomainPointInside( c ) );
    }
    THEN( "Its vertices lie on its boundary" ) {
      REQUIRE( P.isBoundary( a ) );
      REQUIRE( P.isBoundary( b ) );
      REQUIRE( P.isBoundary( c ) );
      REQUIRE( ! P.isInterior( a ) );
      REQUIRE( ! P.isInterior( b ) );
      REQUIRE( ! P.isInterior( c ) );
    }
    THEN( "It contains more than 3 integer points" ) {
      REQUIRE( P.count() > 3 );
    }
    THEN( "It contains more points than its area" ) {
      REQUIRE( P.count() > (5*7/2) );
    }
    THEN( "It satisfies Pick's formula, ie 2*Area(P) = 2*#Int(P) + #Bd(P) - 2" ) {
      Polytope IntP = P.interiorPolytope();
      auto   nb_int = IntP.count();
      auto    nb_bd = P.count() - IntP.count();
      auto    area2 = 5*7;
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      CAPTURE( area2 );
      REQUIRE( area2 == 2*nb_int + nb_bd - 2 );
    }
    THEN( "It satisfies #In(P) <= #Int(P) + #Bd(P)" ) {
      auto     nb = P.count();
      auto nb_int = P.countInterior();
      auto  nb_bd = P.countBoundary();
      CAPTURE( nb );
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      REQUIRE( nb <= nb_int + nb_bd );
    }
    WHEN( "Cut by some half-space" ) {
      Polytope Q = P;
      Q.cut( Vector( -1, 1 ), 3 );
      THEN( "It contains less points" ) {
        REQUIRE( Q.count() < P.count() );
      }
    }
    THEN( "Its boundary points and interior points are its inside points (closed polytope)" ) {
      std::vector<Point> inside;
      std::vector<Point> interior;
      std::vector<Point> boundary;
      std::vector<Point> all;
      P.getPoints( inside );
      P.getInteriorPoints( interior );
      P.getBoundaryPoints( boundary );
      std::sort( inside.begin(), inside.end() );
      std::sort( interior.begin(), interior.end() );
      std::sort( boundary.begin(), boundary.end() );
      std::set_union( interior.cbegin(), interior.cend(), boundary.cbegin(), boundary.cend(),
                      std::back_inserter( all ) );
      REQUIRE( std::equal( inside.cbegin(), inside.cend(), all.cbegin() ) );
    }
  }
  GIVEN( "A closed segment S at (4,0), (-8,-4)" ) {
    Point a( 4, 0 );
    Point b( -8, -4 );
    Polytope P { a, b };
    THEN( "Its interior is empty #Int(P) == 0" ) {
      auto nb_int = P.countInterior();
      REQUIRE( nb_int == 0 );
    }
    THEN( "It satisfies #In(P) == #Int(P) + #Bd(P) == #Bd(P) == 5" ) {
      auto     nb = P.count();
      auto nb_int = P.countInterior();
      auto  nb_bd = P.countBoundary();
      CAPTURE( nb );
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      std::vector<Point> Ppts;
      P.getPoints( Ppts );
      CAPTURE( Ppts );
      REQUIRE( nb_bd == 5 );
      REQUIRE( nb == nb_int + nb_bd );
    }
  }
}
 
SCENARIO( "BoundedLatticePolytope< Z3 > unit tests", "[lattice_polytope][3d]" )
{
  typedef SpaceND<3,int>                   Space;
  typedef Space::Point                     Point;
  typedef BoundedLatticePolytope< Space >  Polytope;
 
  GIVEN( "A twisted simplex P at (0,0,0), (1,0,0), (0,1,0), (1,1,z)" ) {
    Point a( 0, 0, 0 );
    Point b( 1, 0, 0 );
    Point c( 0, 1, 0 );
    Point d( 1, 1, 8 );
    Polytope P { a, b, c, d };
    THEN( "Its domain contains its vertices" ) {
      REQUIRE( P.isDomainPointInside( a ) );
      REQUIRE( P.isDomainPointInside( b ) );
      REQUIRE( P.isDomainPointInside( c ) );
      REQUIRE( P.isDomainPointInside( d ) );
    }
    THEN( "Its vertices lie on its boundary" ) {
      REQUIRE( P.isBoundary( a ) );
      REQUIRE( P.isBoundary( b ) );
      REQUIRE( P.isBoundary( c ) );
      REQUIRE( P.isBoundary( d ) );
      REQUIRE( ! P.isInterior( a ) );
      REQUIRE( ! P.isInterior( b ) );
      REQUIRE( ! P.isInterior( c ) );
      REQUIRE( ! P.isInterior( d ) );
    }
    THEN( "It satisfies #In(P) <= #Int(P) + #Bd(P)" ) {
      auto     nb = P.count();
      auto nb_int = P.countInterior();
      auto  nb_bd = P.countBoundary();
      CAPTURE( nb );
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      REQUIRE( nb <= nb_int + nb_bd );
    }
    THEN( "It contains only 4 integer points" ) {
      REQUIRE( P.count() == 4 );
    }
 
  }
 
  GIVEN( "A closed arbitrary simplex P at (0,0,0), (6,3,0), (0,5,10), (6,4,8)" ) {
    Point a( 0, 0, 0 );
    Point b( 6, 3, 0 );
    Point c( 0, 5, 10 );
    Point d( 6, 4, 8 );
    Polytope P { a, b, c, d };
    
    THEN( "It satisfies #In(P) == #Int(P) + #Bd(P)" ) {
      auto     nb = P.count();
      auto nb_int = P.countInterior();
      auto  nb_bd = P.countBoundary();
      CAPTURE( nb );
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      REQUIRE( nb == nb_int + nb_bd );
    }
    THEN( "Its boundary points and interior points are its inside points (closed polytope)" ) {
      std::vector<Point> inside;
      std::vector<Point> interior;
      std::vector<Point> boundary;
      std::vector<Point> all;
      P.getPoints( inside );
      P.getInteriorPoints( interior );
      P.getBoundaryPoints( boundary );
      std::sort( inside.begin(), inside.end() );
      std::sort( interior.begin(), interior.end() );
      std::sort( boundary.begin(), boundary.end() );
      std::set_union( interior.cbegin(), interior.cend(), boundary.cbegin(), boundary.cend(),
                      std::back_inserter( all ) );
      REQUIRE( std::equal( inside.cbegin(), inside.cend(), all.cbegin() ) );
    }
    WHEN( "Cut by some axis aligned half-space (1,0,0).x <= 3" ) {
      Polytope Q = P;
      Q.cut( 0, true, 3 );
      THEN( "It contains less points" ) {
        CAPTURE( P );
        CAPTURE( P.getDomain() );
        CAPTURE( Q );
        CAPTURE( Q.getDomain() );
        auto     Pnb = P.count();
        auto Pnb_int = P.countInterior();
        auto  Pnb_bd = P.countBoundary();
        CAPTURE( Pnb );
        CAPTURE( Pnb_int );
        CAPTURE( Pnb_bd );
        auto     Qnb = Q.count();
        auto Qnb_int = Q.countInterior();
        auto  Qnb_bd = Q.countBoundary();
        CAPTURE( Qnb );
        CAPTURE( Qnb_int );
        CAPTURE( Qnb_bd );
        std::vector<Point> Qpts;
        Q.getPoints( Qpts );
        CAPTURE( Qpts );
        REQUIRE( Q.count() < P.count() );
      }
    }
  }
  GIVEN( "A closed triangle P at (0,0,0), (6,3,0), (2,5,10)" ) {
    Point a( 0, 0, 0 );
    Point b( 6, 3, 0 );
    Point c( 2, 5, 10 );
    Polytope P { a, b, c };
    THEN( "Its interior is empty #Int(P) == 0" ) {
      auto nb_int = P.countInterior();
      REQUIRE( nb_int == 0 );
    }
    THEN( "It satisfies #In(P) == #Int(P) + #Bd(P)" ) {
      auto     nb = P.count();
      auto nb_int = P.countInterior();
      auto  nb_bd = P.countBoundary();
      CAPTURE( nb );
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      std::vector<Point> Ppts;
      P.getPoints( Ppts );
      CAPTURE( Ppts );
      REQUIRE( nb == nb_int + nb_bd );
    }
  }
  GIVEN( "A closed triangle P with relatively prime coordinates (3,0,0), (0,4,0), (0,0,5)" ) {
    Point a( 3, 0, 0 );
    Point b( 0, 4, 0 );
    Point c( 0, 0, 5 );
    Polytope P { a, b, c };
    THEN( "Its interior is empty #Int(P) == 0" ) {
      auto nb_int = P.countInterior();
      REQUIRE( nb_int == 0 );
    }
    THEN( "It satisfies #In(P) == #Int(P) + #Bd(P) == #Bd(P) == 3" ) {
      auto     nb = P.count();
      auto nb_int = P.countInterior();
      auto  nb_bd = P.countBoundary();
      CAPTURE( nb );
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      std::vector<Point> Ppts;
      P.getPoints( Ppts );
      CAPTURE( Ppts );
      REQUIRE( nb_bd == 3 );
      REQUIRE( nb == nb_int + nb_bd );
    }
  }
  GIVEN( "A closed segment S at (0,0,0), (8,-4,2)" ) {
    Point a( 0, 0, 0 );
    Point b( 8, -4, 2 );
    Polytope P { a, b };
    THEN( "Its interior is empty #Int(P) == 0" ) {
      auto nb_int = P.countInterior();
      REQUIRE( nb_int == 0 );
    }
    THEN( "It satisfies #In(P) == #Int(P) + #Bd(P) == #Bd(P) == 3" ) {
      auto     nb = P.count();
      auto nb_int = P.countInterior();
      auto  nb_bd = P.countBoundary();
      CAPTURE( nb );
      CAPTURE( nb_int );
      CAPTURE( nb_bd );
      std::vector<Point> Ppts;
      P.getPoints( Ppts );
      CAPTURE( Ppts );
      REQUIRE( nb_bd == 3 );
      REQUIRE( nb == nb_int + nb_bd );
    }
  }
}
 
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