DGtal 1.3.0
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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
{
typedef typename Space::Integer Integer;
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
{
typedef typename Space::Integer Integer;
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
{
typedef typename Space::Integer Integer;
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
{
typedef typename Space::Integer Integer;
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;
}
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" );
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.beginBlock( "Check SkelStarCvxH(X) full convexity 3D" );
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.beginBlock( "Check SkelStarCvxH(X) full convexity 4D" );
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.beginBlock( "Check Projection full convexity 3D" );
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.beginBlock( "Check Projection full convexity 4D" );
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.beginBlock( "Check CvxH plus Hypercube full convexity 2D" );
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.beginBlock( "Check CvxH plus Hypercube full convexity 3D" );
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.beginBlock( "Check CvxH plus Hypercube full convexity 4D" );
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.beginBlock( "Check full convexity characterization 3D" );
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.beginBlock( "Check full convexity characterization 4D" );
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;
}
return 0;
}
void makeRandomRange(std::vector< Point > &X, int nb, int width)
void projectRange(std::vector< ProjectedPoint > &pp, const std::vector< Point > &p, Dimension a)
bool checkSkelStarCvxHFullConvexity(int width)
void makeRandom(Point &p, int width)
bool checkProjectionFullConvexity(int width)
bool checkFullConvexityCharacterization(int width)
void project(ProjectedPoint &pp, const Point &p, Dimension a)
bool checkCvxHPlusHypercubeFullConvexity(int width)
void displayPointRange2D(const std::vector< Point > &X)
void getPoints(std::vector< Point > &pts) const
PointRange U(Dimension i, const PointRange &X) const
bool isFullyConvex(const PointRange &X, bool convex0=false) const
bool is0Convex(const PointRange &X) const
PointRange envelope(const PointRange &Z, EnvelopeAlgorithm algo=EnvelopeAlgorithm::DIRECT) const
LatticeSet StarCvxH(const PointRange &X, Dimension axis=dimension) const
LatticePolytope makePolytope(const PointRange &X, bool make_minkowski_summable=false) const
Aim: This class is a model of CCellularGridSpaceND. It represents the cubical grid as a cell complex,...
void beginBlock(const std::string &keyword="")
std::ostream & warning()
std::ostream & info()
double endBlock()
std::vector< Point > PointRange
Point::Coordinate Integer
DGtal is the top-level namespace which contains all DGtal functions and types.
DGtal::uint32_t Dimension
Definition: Common.h:137
Trace trace
Definition: Common.h:154
STL namespace.
int main()
Definition: testBits.cpp:56
MyPointD Point
Definition: testClone2.cpp:383