int main ()
{
Delaunay t;
trace.beginBlock("Construction the shape");
typedef Ellipse2D<Z2i::Space> Ellipse;
int a = 5, b = 3;
Ellipse2D<Z2i::Space> ellipse(Z2i::Point(0,0), a, b, 0.3 );
// Ellipse2D<Z2i::Space> ellipse(Z2i::Point(0,0), 5.5, 5.5, 0 );
double h = 0.25;
GaussDigitizer<Z2i::Space,Ellipse> dig;
dig.attach( ellipse );
dig.init( ellipse.getLowerBound()+Z2i::Vector(-1,-1),
ellipse.getUpperBound()+Z2i::Vector(1,1), h );
// typedef Flower2D<Z2i::Space> Flower;
// Flower2D<Z2i::Space> flower(Z2i::Point(0,0), 15, 2, 5, 0);
// double h = 0.25;
// GaussDigitizer<Z2i::Space,Flower> dig;
// dig.attach( flower );
// dig.init( flower.getLowerBound()+Z2i::Vector(-1,-1),
// flower.getUpperBound()+Z2i::Vector(1,1), h );
Z2i::KSpace ks;
ks.init( dig.getLowerBound(), dig.getUpperBound(), true );
SurfelAdjacency<2> sAdj( true );
Z2i::SCell bel = Surfaces<Z2i::KSpace>::findABel( ks, dig, 1000 );
std::vector<Z2i::Point> boundaryPoints;
Surfaces<Z2i::KSpace>
::track2DBoundaryPoints( boundaryPoints, ks, sAdj, dig, bel );
Z2i::Curve c;
c.initFromVector( boundaryPoints );
typedef Z2i::Curve::PointsRange Range;
Range r = c.getPointsRange();
trace.endBlock();
trace.beginBlock("Delaunay");
for(Range::ConstIterator it=r.begin(), itend=r.end(); it != itend;
++it)
{
t.insert( Point( (*it)[0], (*it)[1]));
t.insert( Point( (*it)[0] + 3 + (int) ceil( ((double)b)/h ),
(*it)[1] - 3 - (int) ceil( ((double)a)/h ) ));
}
trace.endBlock();
std::cout << "number of vertices : " ;
std::cout << t.number_of_vertices() << std::endl;
std::cout << "number of faces : " ;
std::cout << t.number_of_faces() << std::endl;
trace.beginBlock("Area minimizing triangulation");
Edge_iterator itnext;
bool flip = true;
bool inverse = false;
unsigned int pass = 0;
while ( flip ) {
std::cout << "----------- pass " << pass << " -------------------" << std::endl;
inverse = false;
flip = false;
int nb_flip = 0;
int nb_random_flip = 0;
for( Edge_iterator it = t.edges_begin(), itend=t.edges_end();
it != itend; it = itnext )
{
// vertex(cw(i)) and vertex(ccw(i)) of f.
itnext = it; ++itnext;
Edge e1 = *it;
if ( isEdgeElementary( t,
e1.first->vertex( t.ccw( e1.second ) ),
e1.first->vertex( t.cw( e1.second ) ) ) )
continue;
Edge e2 = t.mirror_edge( e1 );
if ( ! isQuadrilateral( t,
e1.first->vertex( e1.second ),
e1.first->vertex( t.ccw( e1.second ) ),
e2.first->vertex( e2.second ),
e1.first->vertex( t.cw( e1.second ) ) ) )
continue;
int nb_f1 = twiceNbLatticePointsInTriangle( t, e1.first );
int nb_f2 = twiceNbLatticePointsInTriangle( t, e2.first );
int nb_flip_f1 = twiceNbLatticePointsInTriangle( t,
e1.first->vertex( e1.second ),
e1.first->vertex( t.ccw( e1.second ) ),
e2.first->vertex( e2.second ) );
int nb_flip_f2 = twiceNbLatticePointsInTriangle( t,
e1.first->vertex( e1.second ),
e1.first->vertex( t.cw( e1.second ) ),
e2.first->vertex( e2.second ) );
int nb_min = nb_f1 <= nb_f2 ? nb_f1 : nb_f2;
int nb_flip_min = nb_flip_f1 <= nb_flip_f2 ? nb_flip_f1 : nb_flip_f2;
if ( nb_flip_min < nb_min )
{
std::cout << "flipped " << e1.first->vertex( e1.second )->point()
<< "->" << e1.first->vertex( e1.second )->point()
<< std::endl;
t.flip( e1.first, e1.second );
nb_flip++;
flip = true;
}
if ( nb_flip_min == nb_min )
{
inverse = true;
if ( random() % 2 == 1 )
{
std::cout << "Random flipped " << e1.first->vertex( e1.second )->point()
<< "->" << e1.first->vertex( e1.second )->point()
<< std::endl;
t.flip( e1.first, e1.second );
nb_random_flip++;
}
}
// if ( ( empty_f1 == false )
// && ( empty_f2 == false ) )
// { // try if flip is better.
// bool empty_flip_f1
// = twiceNbLatticePointsInTriangle( t,
// e1.first->vertex( e1.second ),
// e1.first->vertex( t.ccw( e1.second ) ),
// e2.first->vertex( e2.second ) ) == 0;
// bool empty_flip_f2
// = twiceNbLatticePointsInTriangle( t,
// e2.first->vertex( e2.second ),
// e2.first->vertex( t.ccw( e2.second ) ),
// e1.first->vertex( e1.second ) ) == 0;
// if ( empty_flip_f1 || empty_flip_f2 )
// {
// if ( isEdgeElementary( t,
// e1.first->vertex( t.ccw( e1.second ) ),
// e1.first->vertex( t.cw( e1.second ) ) ) )
// {
// std::cout << "Flip forbidden: " << e1.first->vertex( e1.second )->point()
// << "->" << e1.first->vertex( e1.second )->point()
// << std::endl;
// }
// else
// {
// std::cout << "flipped " << e1.first->vertex( e1.second )->point()
// << "->" << e1.first->vertex( e1.second )->point()
// << std::endl;
// t.flip( e1.first, e1.second );
// flip = true;
// }
// }
// }
}
std::cout << "----------- nb_flip " << nb_flip
<< ", nb_random " << nb_random_flip << " -------------" << std::endl;
++pass;
if ( inverse && ( (nb_random_flip+4) > log(pass) ) )
flip = true;
}
trace.endBlock();
// GridCurve
Z2i::Curve gc;
gc.initFromPointsRange( r.begin(), r.end() );
typedef Z2i::Curve::PointsRange::ConstIterator ConstIterator;
typedef ArithmeticalDSS<ConstIterator,int,4> DSS4;
typedef SaturatedSegmentation<DSS4> Segmentation;
//Segmentation
Z2i::Curve::PointsRange range = gc.getPointsRange();
DSS4 dss4RecognitionAlgorithm;
Segmentation theSegmentation( range.begin(), range.end(), dss4RecognitionAlgorithm );
DGtal::Board2D board;
Z2i::Point dP;
board << CustomStyle( dP.className(),
new CustomPen( Color(0,0,0), Color(230,230,230), 1,
Board2D::Shape::SolidStyle,
Board2D::Shape::RoundCap,
Board2D::Shape::RoundJoin ));
for(Range::ConstIterator it=r.begin(), itend=r.end(); it != itend;
++it)
board << *it;
for(Faces_iterator it = t.finite_faces_begin(), itend=t.finite_faces_end();
it != itend; ++it)
{
Z2i::Point a( toDGtal(it->vertex(0)->point())),
b(toDGtal(it->vertex(1)->point())),
c(toDGtal(it->vertex(2)->point()));
// Z2i::Vector ab( b - a ), ac( c - a );
// int d = ab[ 0 ] * ac[ 1 ] - ab[ 1 ] * ac[ 0 ];
if ( emptyLatticeTriangle( t, it ) ) //( ( d == 1 ) || (d == -1 ) )
{
board.setPenColor(DGtal::Color::Blue);
board.setFillColor( DGtal::Color::None );
board.setLineWidth( 3.0 );
board.drawTriangle(a[0],a[1],b[0],b[1],c[0],c[1]);
}
else
{
board.setPenColor(DGtal::Color::Red);
board.setFillColor( DGtal::Color::None );
// board.setFillColorRGBi(200,200,200,128);
board.setLineWidth( 2.0 );
board.drawTriangle(a[0],a[1],b[0],b[1],c[0],c[1]);
}
}
Segmentation::SegmentComputerIterator i = theSegmentation.begin();
Segmentation::SegmentComputerIterator end = theSegmentation.end();
board.setPenColor(DGtal::Color::Green);
board.setFillColor( DGtal::Color::None );
board << SetMode( "ArithmeticalDSS", "BoundingBox" );
std::string aStyleName = "ArithmeticalDSS/BoundingBox";
for ( ; i != end; ++i) {
DSS4 current(*i);
board << CustomStyle( aStyleName,
new CustomPenColor( DGtal::Color::Green ) )
<< current;
}
// Display Voronoi.
// for(Edge_iterator it = t.edges_begin(), itend=t.edges_end();
// it != itend; ++it)
// {
// // vertex(cw(i)) and vertex(ccw(i)) of f.
// Face_handle itf = it->first;
// int i = it->second;
// Z2i::Point a( toDGtal(itf->vertex( t.cw( i ) )->point()));
// Z2i::Point b( toDGtal(itf->vertex( t.ccw( i ) )->point()));
// CGAL::Object o = t.dual( it );
// if (CGAL::object_cast<K::Segment_2>(&o))
// {
// const K::Segment_2* ptrSegment = CGAL::object_cast<K::Segment_2>(&o);
// board.setPenColor(DGtal::Color::Black);
// board.setFillColor( DGtal::Color::None );
// board.setLineWidth( 2.0 );
// board.drawLine( ptrSegment->source().x(),
// ptrSegment->source().y(),
// ptrSegment->target().x(),
// ptrSegment->target().y() );
// }
// else if (CGAL::object_cast<K::Ray_2>(&o))
// {
// const K::Ray_2* ptrRay = CGAL::object_cast<K::Ray_2>(&o);
// board.setPenColor(DGtal::Color::Black);
// board.setFillColor( DGtal::Color::None );
// board.setLineWidth( 2.0 );
// double dx = ptrRay->to_vector().x();
// double dy = ptrRay->to_vector().y();
// double norm = sqrt( dx*dx+dy*dy );
// dx = 5.0 * dx / norm;
// dy = 5.0 * dy / norm;
// board.drawArrow( ptrRay->source().x(),
// ptrRay->source().y(),
// ptrRay->source().x() + dx, //1*ptrRay->to_vector().x(),
// ptrRay->source().y() + dy ); //1*ptrRay->to_vector().y() );
// }
// }
board.saveSVG("delaunay.svg");
board.saveEPS("delaunay.eps");
return 0;
}
/**
* Algorithms that computes the alpha-shape
* of a point set
*/
void alphaShape()
{
//Digitization of a disk of radius 8
Ball2D<Z2i::Space> ball(Z2i::Point(0,0), 8);
Z2i::Domain domain(ball.getLowerBound(), ball.getUpperBound());
Z2i::DigitalSet digitalSet(domain);
Shapes<Z2i::Domain>::euclideanShaper(digitalSet, ball);
//Contour of the digital set
Z2i::KSpace kspace;
kspace.init(domain.lowerBound()-Z2i::Point(1,1), domain.upperBound()+Z2i::Point(1,1), true);
typedef DigitalSetBoundary<Z2i::KSpace, Z2i::DigitalSet> DigitalSurfaceContainer;
typedef DigitalSurface<DigitalSurfaceContainer> CustomDigitalSurface;
DigitalSurfaceContainer digitalSurfaceContainer( kspace, digitalSet );
CustomDigitalSurface digitalSurface( digitalSurfaceContainer );
//Grid curve
Z2i::Curve gridCurve;
typedef DepthFirstVisitor<DigitalSurface<DigitalSurfaceContainer> > CustomVisitor;
CustomVisitor visitor( digitalSurface, *digitalSurface.begin() );
while ( ! visitor.finished() )
{
gridCurve.pushBack( visitor.current().first );
visitor.expand();
}
//Point set defined as the set of (not duplicated) inner points
typedef Z2i::Curve::InnerPointsRange PointRange;
PointRange pointsRange = gridCurve.getInnerPointsRange();
vector<Z2i::Point> border;
unique_copy( pointsRange.begin(), pointsRange.end(), back_inserter( border ) );
//namespace for hull functions
using namespace functions::Hull2D;
{ //alpha = 0
trace.info() << " alpha == 0 " << endl;
vector<Z2i::Point> res;
//! [Hull2D-RadiusPredicateInf]
typedef AvnaimEtAl2x2DetSignComputer<DGtal::int64_t> DetComputer;
typedef InGeneralizedDiskOfGivenRadius<Z2i::Point, DetComputer> Functor;
Functor functor(true, 1, 0); //alpha = 0; 1/alpha -> +inf
typedef PredicateFromOrientationFunctor2<Functor> Predicate;
Predicate predicate( functor );
//! [Hull2D-RadiusPredicateInf]
//! [Hull2D-ClosedGrahamScan]
closedGrahamScanFromAnyPoint( border.begin(), border.end(), back_inserter( res ), predicate );
//! [Hull2D-ClosedGrahamScan]
//display
Board2D board;
drawPolygon( res.begin(), res.end(), board );
board.saveSVG( "AlphaShape0.svg" );
#ifdef WITH_CAIRO
board.saveCairo("AlphaShape0.png", Board2D::CairoPNG);
#endif
}
{ //alpha = 0
trace.info() << " alpha == 0 " << endl;
vector<Z2i::Point> res;
//comparator and functor
typedef InHalfPlaneBySimple3x3Matrix<Z2i::Point, DGtal::int64_t> Functor;
Functor functor;
typedef PredicateFromOrientationFunctor2<Functor> Predicate;
Predicate predicate( functor );
closedGrahamScanFromAnyPoint( border.begin(), border.end(), back_inserter( res ), predicate );
//display
Board2D board;
drawPolygon( res.begin(), res.end(), board );
board.saveSVG( "AlphaShape0bis.svg" );
#ifdef WITH_CAIRO
board.saveCairo("AlphaShape0bis.png", Board2D::CairoPNG);
#endif
}
//negative alpha shape
{ //alpha = -1
trace.info() << " alpha == -1 " << endl;
vector<Z2i::Point> res;
typedef AvnaimEtAl2x2DetSignComputer<DGtal::int64_t> DetComputer;
typedef InGeneralizedDiskOfGivenRadius<Z2i::Point, DetComputer> Functor;
//! [Hull2D-RadiusPredicateM1]
Functor functor(false, 1, 1); //1/alpha = -sqrt(1/1) = -1
//! [Hull2D-RadiusPredicateM1]
typedef PredicateFromOrientationFunctor2<Functor> Predicate;
Predicate predicate( functor );
closedGrahamScanFromAnyPoint( border.begin(), border.end(), back_inserter( res ), predicate );
//display
Board2D board;
drawPolygon( res.begin(), res.end(), board );
board.saveSVG( "AlphaShapeM1.svg" );
#ifdef WITH_CAIRO
board.saveCairo("AlphaShapeM1.png", Board2D::CairoPNG);
#endif
}
{ //alpha = -sqrt(5)
trace.info() << " alpha == -sqrt(5) " << endl;
vector<Z2i::Point> res;
typedef AvnaimEtAl2x2DetSignComputer<DGtal::int64_t> DetComputer;
typedef InGeneralizedDiskOfGivenRadius<Z2i::Point, DetComputer> Functor;
//! [Hull2D-RadiusPredicateMsqrt5]
Functor functor(false, 5, 1); //1/alpha = -sqrt(5)
//! [Hull2D-RadiusPredicateMsqrt5]
typedef PredicateFromOrientationFunctor2<Functor> Predicate;
Predicate predicate( functor );
closedGrahamScanFromAnyPoint( border.begin(), border.end(), back_inserter( res ), predicate );
//display
Board2D board;
drawPolygon( res.begin(), res.end(), board );
board.saveSVG( "AlphaShapeMSqrt5.svg" );
#ifdef WITH_CAIRO
board.saveCairo("AlphaShapeMSqrt5.png", Board2D::CairoPNG);
#endif
}
{ //alpha = -5
trace.info() << " alpha == -5 " << endl;
vector<Z2i::Point> res;
typedef AvnaimEtAl2x2DetSignComputer<DGtal::int64_t> DetComputer;
typedef InGeneralizedDiskOfGivenRadius<Z2i::Point, DetComputer> Functor;
//! [Hull2D-RadiusPredicateM5]
Functor functor(false, 25, 1); //1/alpha = -sqrt(25/1) = -5
//! [Hull2D-RadiusPredicateM5]
typedef PredicateFromOrientationFunctor2<Functor> Predicate;
Predicate predicate( functor );
closedGrahamScanFromAnyPoint( border.begin(), border.end(), back_inserter( res ), predicate );
//display
Board2D board;
drawPolygon( res.begin(), res.end(), board );
board.saveSVG( "AlphaShapeM5.svg" );
#ifdef WITH_CAIRO
board.saveCairo("AlphaShapeM5.png", Board2D::CairoPNG);
#endif
}
//positive alpha shape
{
trace.info() << " alpha == 8 " << endl;
vector<Z2i::Point> res;
//! [Hull2D-RadiusPredicateP8]
typedef AvnaimEtAl2x2DetSignComputer<DGtal::int64_t> DetComputer;
typedef InGeneralizedDiskOfGivenRadius<Z2i::Point, DetComputer> Functor;
Functor functor(true, 64, 1); //1/alpha = sqrt(64/1) = 8
typedef PredicateFromOrientationFunctor2<Functor, false, true> Predicate;
Predicate predicate( functor );
//! [Hull2D-RadiusPredicateP8]
closedGrahamScanFromAnyPoint( border.begin(), border.end(), back_inserter( res ), predicate );
//display
Board2D board;
drawPolygon( res.begin(), res.end(), board );
board.saveSVG( "AlphaShapeP8.svg" );
#ifdef WITH_CAIRO
board.saveCairo("AlphaShapeP8.png", Board2D::CairoPNG);
#endif
}
//positive alpha shape
{
trace.info() << " alpha == 9 " << endl;
vector<Z2i::Point> res;
typedef AvnaimEtAl2x2DetSignComputer<DGtal::int64_t> DetComputer;
typedef InGeneralizedDiskOfGivenRadius<Z2i::Point, DetComputer> Functor;
//! [Hull2D-RadiusPredicateP9]
Functor functor(true, 81, 1); //1/alpha = sqrt(81/1) = 9
//! [Hull2D-RadiusPredicateP9]
typedef PredicateFromOrientationFunctor2<Functor> Predicate;
Predicate predicate( functor );
closedGrahamScanFromAnyPoint( border.begin(), border.end(), back_inserter( res ), predicate );
//display
Board2D board;
drawPolygon( res.begin(), res.end(), board );
board.saveSVG( "AlphaShapeP9.svg" );
#ifdef WITH_CAIRO
board.saveCairo("AlphaShapeP9.png", Board2D::CairoPNG);
#endif
}
}
int main()
{
//shape
typedef Flower2D<Z2i::Space> Flower;
Flower2D<Z2i::Space> flower(Z2i::Point(0,0), 20, 5, 5, 0);
//! [shapeGridCurveEstimator-dig]
//implicit digitization of a shape of type Flower
//into a digital space of type Space
double h = 1;
GaussDigitizer<Z2i::Space,Flower> dig;
dig.attach( flower );
dig.init( flower.getLowerBound()+Z2i::Vector(-1,-1),
flower.getUpperBound()+Z2i::Vector(1,1), h );
//! [shapeGridCurveEstimator-dig]
//! [shapeGridCurveEstimator-prepareTracking]
//Khalimsky space
Z2i::KSpace ks;
ks.init( dig.getLowerBound(), dig.getUpperBound(), true );
//adjacency (4-connectivity)
SurfelAdjacency<2> sAdj( true );
//! [shapeGridCurveEstimator-prepareTracking]
//! [shapeGridCurveEstimator-tracking]
//searching for one boundary element
Z2i::SCell bel = Surfaces<Z2i::KSpace>::findABel( ks, dig, 1000 );
//tracking
vector<Z2i::Point> boundaryPoints;
Surfaces<Z2i::KSpace>
::track2DBoundaryPoints( boundaryPoints, ks, sAdj, dig, bel );
//! [shapeGridCurveEstimator-tracking]
//! [shapeGridCurveEstimator-instantiation]
Z2i::Curve c;
c.initFromVector( boundaryPoints );
//! [shapeGridCurveEstimator-instantiation]
DGtal::Board2D aBoard;
aBoard << c;
aBoard.saveEPS("DisplayGridCurve1.eps");
//! [shapeGridCurveEstimator-getRange]
//range of points
typedef Z2i::Curve::PointsRange Range;
Range r = c.getPointsRange();
//! [shapeGridCurveEstimator-getRange]
//! [shapeGridCurveEstimator-lengthEstimation]
//length estimation
DSSLengthEstimator< Range::ConstIterator > DSSlength;
DSSlength.init( h, r.begin(), r.end(), c.isClosed() );
double length1 = DSSlength.eval();
trace.info() << "Length (h=" << h << "): " << length1 << endl;
//! [shapeGridCurveEstimator-lengthEstimation]
//@TODO correct init method of trueLengthEstimator (remove &flower)
//! [shapeGridCurveEstimator-trueLengthEstimation]
typedef ParametricShapeArcLengthFunctor< Flower > Length;
TrueGlobalEstimatorOnPoints<
Range::ConstIterator,
Flower,
Length > trueLengthEstimator;
trueLengthEstimator.init( h, r.begin(), r.end(), &flower, c.isClosed());
double trueLength = trueLengthEstimator.eval();
trace.info() << "ground truth: " << trueLength << endl;
//! [shapeGridCurveEstimator-trueLengthEstimation]
//! [shapeGridCurveEstimator-higher]
//implicit digitization at higher resolution
h = 0.1;
dig.init( flower.getLowerBound()+Z2i::Vector(-1,-1),
flower.getUpperBound()+Z2i::Vector(1,1), h );
//a greater domain is needed in the Khalimsky space
ks.init( dig.getLowerBound(), dig.getUpperBound(), true );
//searching for one boundary element
bel = Surfaces<Z2i::KSpace>::findABel( ks, dig, 10000 );
//tracking
Surfaces<Z2i::KSpace>
::track2DBoundaryPoints( boundaryPoints, ks, sAdj, dig, bel );
//reset grid curve and its points range
c.initFromVector( boundaryPoints );
Range r2 = c.getPointsRange();
//estimate length
DSSlength.init( h, r2.begin(), r2.end(), c.isClosed() );
double length2 = DSSlength.eval();
trace.info() << "Length (h=" << h << "): " << length2 << endl;
//! [shapeGridCurveEstimator-higher]
aBoard.clear();
aBoard << c;
aBoard.saveEPS("DisplayGridCurve01.eps");
return 0;
}
