DelaunayMesh

DelaunayMesh[{p1,p2,}]

gives a MeshRegion representing the Delaunay mesh from the points p1, p2, .

Details 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 pi.
  • The Delaunay mesh gives a triangulation where the minimum interior angle is maximized.
  • DelaunayMesh takes the same options as MeshRegion.

Examples

open allclose all

Basic Examples  (4)

A 1D Delaunay mesh:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=

A 2D Delaunay mesh from a list of points:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=

A 3D Delaunay mesh from a list of points:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=

Delaunay mesh from points corresponding to minimal vectors of the hexagonal close packing lattice:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Scope  (3)

Options  (11)

Applications  (5)

Properties & Relations  (7)

See Also

VoronoiMesh  ConvexHullMesh  TriangulateMesh  MeshRegion  Simplex  Circumsphere

Introduced in 2014
(10.0)
| Updated in 2015
(10.2)