DGtal 1.3.0
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geometry/tools/exampleLatticeBallDelaunay3D.cpp

Computation of the Delaunay complex of a set of lattice points in 3D by Quick Hull algorithm.

./examples/geometry/tools/exampleLatticeBallDelaunay3D


outputs

Compute convex hull in higher dimension
assign ridges/faces to cell and conversely
takes care of vertex positions
[ConvexCellComplex<3> #C=466 #F=976 #V=100 hasFaceGeometry ]

Delaunay cell decomposition of randomly chosen points in a 3D lattice ball with radius 10
QuickHull algorithm in arbitrary dimension for convex hull and Delaunay cell complex computation
#include "DGtal/base/Common.h"
#include "DGtal/kernel/PointVector.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/geometry/volumes/ConvexityHelper.h"
using namespace DGtal;
using namespace DGtal::Z3i;
int main( int argc, char* argv[] )
{
int nb = argc > 1 ? atoi( argv[ 1 ] ) : 100; // nb points
double dR = argc > 2 ? atof( argv[ 2 ] ) : 10.; // radius of balla
double eps = argc > 3 ? atof( argv[ 3 ] ) : 0.1; // retraction
// (1) create range of random points in ball
std::vector< Point > V;
const auto R2 = dR * dR;
const int R = ceil( dR );
for ( int i = 0; i < nb; ) {
Point p( rand() % (2*R+1) - R, rand() % (2*R+1) - R, rand() % (2*R+1) - R );
if ( p.squaredNorm() <= R2 ) { V.push_back( p ); i++; }
}
// (2) compute convex hull
bool ok =
if ( ! ok )
{
trace.error() << "Input set of points is not full dimensional." << std::endl;
return 1;
}
dcomplex.requireFaceGeometry();
std::cout << dcomplex << std::endl;
// (3) build the mesh that is made of the exploded 3d cells
std::vector< RealPoint > positions;
std::vector< std::vector< Index > > facets;
Index idxv = 0;
for ( auto c = 0; c < dcomplex.nbCells(); ++c )
{
RealPoint b = dcomplex.cellBarycenter( c );
auto c_vtcs = dcomplex.cellVertices( c );
std::map< Index, Index > v2v;
for ( auto v : c_vtcs ) {
RealPoint x = dcomplex.toReal( dcomplex.position( v ) );
v2v[ v ] = idxv++;
positions.push_back( b + ( x - b ) * ( 1.0 - eps ) );
}
for ( const auto& f : dcomplex.cellFaces( c ) ) {
auto f_vtcs = dcomplex.faceVertices( f );
for ( auto& vertex : f_vtcs )
vertex = v2v[ vertex ];
facets.push_back( f_vtcs );
}
}
SMesh mesh( positions.cbegin(), positions.cend(),
facets.cbegin(), facets.cend() );
// (4) output result as OBJ file
std::ofstream out( "delaunay3d.obj" );
::writeOBJ( out, mesh );
out.close();
return 0;
}
std::ostream & error()
SurfaceMesh< RealPoint, RealVector > SMesh
SMesh::Index Index
Z3i this namespace gathers the standard of types for 3D imagery.
DGtal is the top-level namespace which contains all DGtal functions and types.
Aim: represents a d-dimensional complex in a d-dimensional space with the following properties and re...
const VertexRange & cellVertices(const Cell c) const
Point position(const Vertex v) const
VertexRange faceVertices(const Face f) const
RealPoint toReal(const Point p) const
RealPoint cellBarycenter(const Cell c) const
void requireFaceGeometry()
Forces the computation of face geometry.
const FaceRange & cellFaces(const Cell c) const
Aim: Provides a set of functions to facilitate the computation of convex hulls and polytopes,...
Aim: An helper class for writing mesh file formats (Waverfront OBJ at this point) and creating a Surf...
Aim: Represents an embedded mesh as faces and a list of vertices. Vertices may be shared among faces ...
Definition: SurfaceMesh.h:92
Z2i::RealPoint RealPoint
int main()
Definition: testBits.cpp:56
MyPointD Point
Definition: testClone2.cpp:383