delaunayn - N-D Delaunay triangulation

Syntax

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 triangulation. X is an m-by-n array representing m points in n-dimensional space. T is a numt-by-(n+1) array where each row contains the indices into X of the vertices of the corresponding simplex.

T = delaunayn(X, options) specifies a cell array of strings options. The default options are:

• {'Qt','Qbb','Qc'} for 2- and 3-dimensional input

• {'Qt','Qbb','Qc','Qx'} for 4 and higher-dimensional input

If options is [], the default options used. If options is {''}, no options are used, not even the default.

Visualization

Plotting the output of delaunayn depends of the value of n:

• For n = 2, use triplot, trisurf, or trimesh as you would for delaunay.

• For n = 3, use tetramesh as you would for delaunay3.

  For more control over the color of the facets, use patch to plot the output.

• You cannot plot delaunayn output for n > 3.

Examples

Example 1

This example generates an n-dimensional Delaunay triangulation, where n = 3.

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

You can use tetramesh to visualize the tetrahedrons that form the corresponding simplex. camorbit rotates the camera position to provide a meaningful view of the figure.

tetramesh(Tes,X);camorbit(20,0)

See Also

convhulln | delaunay3 | DelaunayTri | tetramesh | voronoin

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