DGtal 1.3.0
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Example of curvature estimation based on Digital Circular Arc (DCA) estimator.

Curvature estimated using DCA estimator on a flower shape.
#include <iostream>
#include "DGtal/base/Common.h"
#include "DGtal/kernel/SpaceND.h"
#include "DGtal/kernel/domains/HyperRectDomain.h"
#include "DGtal/topology/KhalimskySpaceND.h"
#include "DGtal/topology/SurfelAdjacency.h"
#include "DGtal/topology/SurfelNeighborhood.h"
#include "DGtal/shapes/Shapes.h"
#include "DGtal/shapes/ShapeFactory.h"
#include "DGtal/shapes/GaussDigitizer.h"
#include "DGtal/geometry/curves/GridCurve.h"
#include "DGtal/geometry/curves/estimation/MostCenteredMaximalSegmentEstimator.h"
#include "DGtal/geometry/curves/StabbingCircleComputer.h"
using namespace std;
using namespace DGtal;
template <typename Shape, typename RealPoint>
estimatorOnShapeDigitization( const string& name,
Shape & aShape,
const RealPoint& low, const RealPoint& up,
double h )
using namespace Z2i;
trace.beginBlock ( ( "Curvature estimation on digitization of "
+ name ). c_str() );
// Creates a digitizer on the window (low, up).
dig.attach( aShape ); // attaches the shape.
dig.init( low, up, h );
// The domain size is given by the digitizer
// according to the window and the step.
// Create cellular space
bool ok = K.init( dig.getLowerBound(), dig.getUpperBound(), true );
if ( ! ok )
std::cerr << "[estimatorOnShapeDigitization]"
<< " error in creating KSpace." << std::endl;
try {
// Extracts shape boundary
SCell bel = Surfaces<KSpace>::findABel( K, dig, 10000 );
// Getting the consecutive surfels of the 2D boundary
std::vector<Point> points;
Surfaces<KSpace>::track2DBoundaryPoints( points, K, SAdj, dig, bel );
// Create GridCurve
GridCurve<KSpace> gridcurve( K );
gridcurve.initFromVector( points );
// Create range of incident points
typedef Range::ConstIterator ClassicIterator;
typedef Range::ConstCirculator CircularIterator;
Range r = gridcurve.getIncidentPointsRange();//building range
// Estimation
std::vector<double> estimations;
if (gridcurve.isOpen())
SCEstimator sce;
CurvatureEstimator estimator(sc, sce);
std::cout << "# open grid curve" << endl;
estimator.init( r.begin(), r.end() );
estimator.eval( r.begin(), r.end(), std::back_inserter(estimations), h );
SCEstimator sce;
CurvatureEstimator estimator(sc, sce);
std::cout << "# closed grid curve" << endl;
estimator.init( r.c(), r.c() );
estimator.eval( r.c(), r.c(), std::back_inserter(estimations), h );
// Print (standard output)
std::cout << "# idx kappa" << endl;
unsigned int i = 0;
for ( ClassicIterator it = r.begin(), ite = r.end();
it != ite; ++it, ++i )
std::cout << i << " " << estimations.at(i) << std::endl;
catch ( InputException& e )
std::cerr << "[estimatorOnShapeDigitization]"
<< " error in finding a bel." << std::endl;
ok = false;
trace.emphase() << ( ok ? "Passed." : "Error." ) << endl;
return ok;
int main( )
trace.beginBlock ( "Example exampleCurvature" );
trace.info() << " Curvature estimation using shape to digitize: flower" << std::endl
<< " with Grid step: 0.01" << std::endl;
// grid step
double h = 0.01;
// shape
string shapeName = "flower";
// parse shape
bool res = true;
typedef Z2i::Space Space;
typedef Space::RealPoint RealPoint;
if (shapeName == "flower")
Flower2D<Space> flower( 0.5, 0.5, 5.0, 3.0, 5, 0.3 );
res = estimatorOnShapeDigitization("flower", flower,
else if (shapeName == "ellipse")
Ellipse2D<Space> ellipse( 0.5, 0.5, 5.0, 3.0, 0.3 );
res = estimatorOnShapeDigitization("ellipse", ellipse,
else if (shapeName == "ball")
Ball2D<Space> ball( 0.5, 0.5, 5.0 );
res = estimatorOnShapeDigitization("ball", ball,
return res;
// //
Aim: Model of the concept StarShaped represents any circle in the plane.
Definition: Ball2D.h:61
Aim: model of CConstBidirectionalRange that adapts any range of elements bounded by two iterators [it...
Aim: Model of the concept StarShaped represents any ellipse in the plane.
Definition: Ellipse2D.h:65
Aim: Model of the concept StarShaped represents any flower with k-petals in the plane.
Definition: Flower2D.h:65
Aim: A class for computing the Gauss digitization of some Euclidean shape, i.e. its intersection with...
const Point & getUpperBound() const
void attach(ConstAlias< EuclideanShape > shape)
const Point & getLowerBound() const
void init(const RealPoint &xLow, const RealPoint &xUp, typename RealVector::Component gridStep)
Domain getDomain() const
Aim: describes, in a cellular space of dimension n, a closed or open sequence of signed d-cells (or d...
Definition: GridCurve.h:173
IncidentPointsRange getIncidentPointsRange() const
Definition: GridCurve.h:486
bool isOpen() const
bool initFromVector(const std::vector< Point > &aVectorOfPoints)
Aim: A model of CLocalCurveGeometricEstimator that assigns to each element of a (sub)range a quantity...
Aim: On-line recognition of a digital circular arcs (DCA) defined as a sequence of connected grid edg...
Aim: A utility class for constructing surfaces (i.e. set of (n-1)-cells).
Definition: Surfaces.h:79
Aim: Represent adjacencies between surfel elements, telling if it follows an interior to exterior ord...
void beginBlock(const std::string &keyword="")
std::ostream & emphase()
std::ostream & info()
double endBlock()
Z3i::SCell SCell
bool estimatorOnShapeDigitization(const string &name, Shape &aShape, const RealPoint &low, const RealPoint &up, double h)
DGtal is the top-level namespace which contains all DGtal functions and types.
Trace trace
Definition: Common.h:154
STL namespace.
ArithmeticalDSSComputer< std::vector< Z2i::Point >::const_iterator, int, 4 > SegmentComputer
Astroid2D< Space > Shape
Z2i::RealPoint RealPoint
int main()
Definition: testBits.cpp:56
KSpace K
Domain domain
HyperRectDomain< Space > Domain