MATLAB Function Reference    

n-D Delaunay tessellation



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.


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


This example generates an n-D Delaunay tessellation, where n = 3.

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.


delaunayn is based on Qhull [2],. It uses the Qhull joggle option ('QJ'). For information about qhull, see For copyright information, see

See Also

convhulln, delaunayn, delaunay3, tetramesh, voronoin


[1]  Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Transactions on Mathematical Software, Vol. 22, No. 4, Dec. 1996, p. 469-483. Available in HTML format at pubs/citations/journals/toms/1996-22-4/p469-barber/ and in PostScript format at

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

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