# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# DelaunayMesh

DelaunayMesh[{p1,p2,}]
gives a MeshRegion representing the Delaunay mesh from the points , , .

## Details and OptionsDetails and Options

• DelaunayMesh is also known as Delaunay triangulation and Delaunay tetrahedralization.
• A Delaunay mesh consists of intervals (in 1D), triangles (in 2D), tetrahedra (in 3D), and -dimensional simplices (in D).
• A Delaunay mesh has simplex cells defined by points, such that the circumsphere for the same points contains no other points from the original points .
• The Delaunay mesh gives a triangulation where the minimum interior angle is maximized.
• DelaunayMesh takes the same options as MeshRegion.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

A 1D Delaunay mesh:

 Out[6]=

A 2D Delaunay mesh from a list of points:

 Out[3]=

A 3D Delaunay mesh from a list of points:

 Out[3]=