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C++ API

: T = delaunayn (pts)
: T = delaunayn (pts, options)

Compute the Delaunay triangulation for an N-dimensional set of points.

The Delaunay triangulation is a tessellation of the convex hull of a set of points such that no N-sphere defined by the N-triangles contains any other points from the set.

The input matrix pts of size [n, dim] contains n points in a space of dimension dim. The return matrix T has size [m, dim+1]. Each row of T contains a set of indices back into the original set of points pts which describes a simplex of dimension dim. For example, a 2-D simplex is a triangle and 3-D simplex is a tetrahedron.

An optional second argument, which must be a string or cell array of strings, contains options passed to the underlying qhull command. See the documentation for the Qhull library for details http://www.qhull.org/html/qh-quick.htm#options. The default options depend on the dimension of the input:

  • 2-D and 3-D: options = {"Qt", "Qbb", "Qc", "Qz"}
  • 4-D and higher: options = {"Qt", "Qbb", "Qc", "Qx"}

If options is not present or [] then the default arguments are used. Otherwise, options replaces the default argument list. To append user options to the defaults it is necessary to repeat the default arguments in options. Use a null string to pass no arguments.

See also: delaunay, convhulln, voronoin, trimesh, tetramesh.

Package: octave