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delaunay_3

Delaunay triangulation of a set of points in 3d space.

Calling Sequence

[tri [,ptr] ] = delaunay_3(x,y,z);

Parameters

x , y ,z
: are vectors of points coordinates.
tri
: is (nbtriangles,4) array, Each row of tri defines one tetraedral and contains indices into (x,y,z).
ptr
: is a pointer representing the Delaunay triangulation, dt3. The associated functions of Delaunay triangulation that using "ptr" are: - dt3_insert_points - dt3_remove_points - dt3_get_connectivity - dt3_delete

Description

A Delaunay triangulation of a set of points is a triangulation of the sets of points that fulfills the following empty circle property (also called Delaunay property): the circumscribing circle of any facet of the triangulation contains no point of the set in its interior. For a point set with no case of cocircularity of more than three points, the Delaunay triangulation is unique, it is the dual of the Voronoi diagram of the points.

Examples

x =rand(1,10);
y =rand(1,10);
z =rand(1,10);
tri = delaunay_3(x,y,z)
// use the pointer if you want to interact with dt3.
[tri,ptr] = delaunay_3(x,y,z);
dt3_insert_points(ptr,rand(1,100),rand(1,100),rand(1,100));
new_tri = dt3_get_connectivity(ptr);
dt3_delete(ptr,"ptr");
size(new_tri)

See Also

For more details seeCGAL Manual.

This function uses the Triangulation_3 package of CGAL, which is under QPL license. See License Terms

Authors

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