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N-D Delaunay triangulation


T = delaunayn(X)
T = delaunayn(X,options)


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 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.


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.

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

  • You cannot plot delaunayn output for n > 3.


collapse all

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 = 

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


Introduced before R2006a

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