MATLAB Function Reference    

3-D Delaunay tessellation



TES = delaunay3(x,y,z) returns an array TES, each row of which contains the indices of the points in (x,y,z) that make up a tetrahedron in the tessellation of (x,y,z). TES is a numtes-by-4 array where numtes is the number of facets in the tessellation. x, y, and z are vectors of equal length. If the original data points are collinear or x, y, and z define an insufficient number of points, the triangles cannot be computed and delaunay3 returns an empty matrix.


Use tetramesh to plot delaunay3 output. tetramesh displays the tetrahedrons defined in TES as mesh. tetramesh uses the default tranparency parameter value 'FaceAlpha' = 0.9.


This example generates a 3-D Delaunay tessellation, then uses tetramesh to plot the tetrahedrons that form the corresponding simplex. camorbit rotates the camera position to provide a meaningful view of the figure.


delaunay3 is based on Qhull [2]. It uses the Qhull joggle option ('QJ'). For information about qhull, see For copyright information, see

See Also

delaunay, delaunayn


[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.

  delaunay delaunayn