Scilab Function
Last update : November 2005

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

Calling Sequence

[tes,ptr]=cgal_delaunay_n(S);

Parameters

Description

tes = cgal_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 = cgal_delaunay_n(S)
 tes  =
!   1.    2.    3.    4.    5.    6.  !
!   1.    3.    4.    5.    6.    8.  !
!   1.    2.    3.    4.    6.    8.  !
!   1.    8.    4.    5.    6.    9.  !
!   1.    7.    4.    5.    8.    9.  !
!   1.    3.    8.    5.    6.    9.  !
!   1.    3.    7.    5.    8.    9.  !
!   1.    2.    3.    8.    6.    9.  !
!   1.    2.    3.    7.    8.    9.  !
!   1.    2.    8.    4.    6.    9.  !
!   1.    2.    7.    4.    8.    9.  !
!   1.    2.    4.    5.    6.    9.  !
!   1.    2.    3.    5.    6.    9.  !
!   1.    9.    4.    5.    7.    10. !
!   1.    2.    4.    9.    7.    10. !
!   1.    2.    4.    5.    9.    10. !
!   1.    9.    3.    5.    7.    10. !
!   1.    2.    3.    9.    7.    10. !
!   1.    2.    3.    5.    9.    10. !
!   1.    2.    3.    4.    5.    10. !
!   1.    8.    4.    5.    7.    10. !
!   1.    3.    8.    5.    7.    10. !
!   1.    3.    4.    5.    8.    10. !
!   1.    2.    8.    4.    7.    10. !
!   1.    2.    3.    8.    7.    10. !
!   1.    2.    3.    4.    8.    10. !
 
  

See Also

cgal_delaunay_2 ,   cgal_delaunay_3 ,   cgal_constrained_delaunay_2 ,  

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

Naceur MESKINI.