/**
* 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
}
}
