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delaunay_n

Delaunay triangulation of a set of points in some n-dimensional space

Calling Sequence

[tes,ptr]=delaunay_n(S);

Parameters

S
: is an (m,n) array representing m points in n-D space.
tes
: is a (nbsimplices,dcur+1) array where each row contains the indices into S of the vertices of the corresponding simplex, where dcur is the affine dimension of S and nbsimplices is the number of simplices.
ptr
: is a pointer representing the Delaunay triangulation, dtn. The associated functions of Delaunay triangulation that using "ptr" are: dtn_insert_points, dtn_get_connectivity and dtn_delete

Description

tes = delaunay_n(S) is a Delaunay triangulation of a set S of points in some n-dimensional space. We call S the underlying point set and n the dimension of the underlying space. A Delaunay triangulation is a simplicial complex. All simplices in the Delaunay triangulation have dimension dcur. In the nearest site Delaunay triangulation the circumsphere of any simplex in the triangulation contains no point of S in its interior. In the furthest site Delaunay triangulation the circumsphere of any simplex contains no point of S in its exterior. If the points in S are co-circular then any triangulation of S is a nearest as well as a furthest site Delaunay triangulation of S.

Examples

x = rand(1,10);
y = rand(1,10);
z = rand(1,10);
t = rand(1,10);
w = rand(1,10);
S = [x' y' z' t' w'];
tes = delaunay_n(S)

See Also

For more details see CGAL Manual.

Remark: you may experience robustness problems (errors, loops) because this cglab function does not yet make use of CGAL's exactness features.

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

Authors

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