delaunayn (MATLAB Function Reference)

n-D Delaunay tessellation

Syntax

T = delaunayn(X)

Description

T = delaunayn(X) computes a set of simplices such that no data points of X are contained in any circumspheres of the simplices. The set of simplices forms the Delaunay tessellation. X is an m-by-n array representing m points in n-D space. T is a numt-by-(n+1) array where each row contains the indices into X of the vertices of the corresponding simplex.

Note delaunayn is based on qhull [1]. For information about qhull, see http://www.geom.umn.edu/software/qhull/. For copyright information, see http://www.geom.umn.edu/software/download/COPYING.html.

Example

d = [-1 1];
[x,y,z] = meshgrid(d,d,d);  % A cube
x = [x(:);0];
y = [y(:);0];
z = [z(:);0];
% [x,y,z] are corners of a cube plus the center.
X = [x(:) y(:) z(:)];
Tes = delaunayn(X)

Tes =

    9 7 3 5
    1 9 3 5
    1 2 9 5
    4 9 7 3
    4 9 7 8
    4 1 9 3
    4 1 2 9
    6 2 9 5
    6 9 7 5
    6 9 7 8
    6 4 9 8
    6 4 2 9

Reference

[1] National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center), University of Minnesota. 1993.

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