DelaunayComplex

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ProGAL.geom3d.complex.delaunayComplex
Class DelaunayComplex

java.lang.Object
  ProGAL.geom3d.complex.delaunayComplex.DelaunayComplex

All Implemented Interfaces:: SimplicialComplex

Direct Known Subclasses:: RegularComplex

public class DelaunayComplex
extends java.lang.Object
implements SimplicialComplex
extends java.lang.Object
implements SimplicialComplex

A Delaunay complex for a set of d-dimensional points is a tesselation of the points such that no point is inside the circumscribing hypersphere of the d-simplices (for the 3D case: Tetrahedra).

This class builds a three-dimensional Delaunay complex in the constructor and accesses it using e.g. the getTetrahedra method. The following example displays the Delaunay complex of ten random points.

  //Generate the complex
  List<Point> pl = PointList.generatePointsInCube(10);
  DelaunayComplex dc = new DelaunayComplex(pl);
    
  //Display the complex
  J3DScene scene = J3DScene.createJ3DSceneInFrame();
  for(CTetrahedron t: dc.getTetrahedra()){
    scene.addShape(t, new Color(200,100,100,100));
  }

The original point-set is left unaltered and non-referenced by this class. A new set of vertices is allocated using the CVertex class. These are randomly perturbed to avoid degeneracies. If one wishes to associate the original points with a vertex in the complex it would be sufficient to test if the distance between the point and the vertex is less than 0.0001.

The complex is bounded by a big tetrahedron whose corner-points are located sufficiently far from any of the vertices of the complex. The simplices that have one of these 'big points' as corners can not be accessed directly via the getter-methods, but they will be neighbors of other normal simplices. For instance:

  DelaunayComplex dc = new DelaunayComplex( PointList.generatePointsInCube(4) );
  for(CTetrahedron t: dc.getTetrahedra()){
        System.out.println( t.containsBigPoint() );
        System.out.println( t.getNeighbor(0).containsBigPoint() );
        System.out.println( t.getNeighbor(1).containsBigPoint() );
        System.out.println( t.getNeighbor(2).containsBigPoint() );
        System.out.println( t.getNeighbor(3).containsBigPoint() );
  }

Will print false, true, true, true and true.

Author:: R.Fonseca

Constructor Summary
`DelaunayComplex(java.util.List<Point> points)` Builds the Delaunay complex of the specified point-set

Method Summary
`boolean`	`checkTetrahedra()` Checks that all tetrahedra comply with the Delaunay-criteria.
`java.util.List<CTetrahedron>`	`getAllTetrahedra()` returns all tetrahedra (including tetrahedra with bigPoint
`java.util.List<CTetrahedron>`	`getBigTetrahedra()` returns all big tetrahedra
`java.util.List<CEdge>`	`getEdges()` Get the edges in the complex.
`java.util.List<CTetrahedron>`	`getTetrahedra()` Get the tetrahedra in the complex.
`java.util.List<CTriangle>`	`getTriangles()` Get the triangles in the complex.
`CVertex`	`getVertex(int i)`
`java.util.Set<CTetrahedron>`	`getVertexHull(CVertex v)` The vertex-hull of v is the set of all tetrahedrons that has v as a corner-point
`java.util.List<CVertex>`	`getVertices()` Get the vertices in the complex.
`boolean`	`isDelaunay()` TODO: Finish

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail