A 1D Delaunay mesh:

A 2D Delaunay mesh from a list of points:

A 3D Delaunay mesh from a list of points:

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

Create a 1D Delaunay mesh from a set of points:

Basic properties:

Delaunay meshes are full dimensional:

Delaunay meshes are bounded:

Find its measure and centroid:

Find nearest distance and nearest point:

Create a 2D Delaunay mesh from a set of points:

Basic properties:

Delaunay meshes are full dimensional:

Delaunay meshes are bounded:

Find its area and centroid:

Test for point membership or distance to the closest point in the region:

Create a 3D Delaunay mesh from a set of points:

Basic properties:

Delaunay meshes are full dimensional:

Delaunay meshes are bounded:

Find its area and centroid:

Test for point membership or distance to the closest point in the region:

Generate lattice points of a 3D lattice basis:

Construct and visualize the mesh region:

Construct a 3D region from a point set:

Compare original region to Delaunay mesh:

Visualize the piecewise constant interpolation of city elevations in Colorado:

Voronoi mesh from city coordinates:

Create a function to map a given coordinate pair to the nearest known elevation:

Function to rescale elevation values to , suitable for color functions:

Piecewise constant contour plot of city elevations:

A similar plot can also be achieved with ListContourPlot:

Solve a PDE over a region defined by point set:

Create a mesh from selected points on a raster:

Initial locator points:

Function to convert a raster and a mesh region to polygons:

Function to create an overlay mesh:

Click the image to add and remove draggable vertices:

The output of DelaunayMesh is always a full-dimensional MeshRegion:

DelaunayMesh consists of intervals in 1D:

Triangles in 2D:

Tetrahedra in 3D:

The circumcircle for each triangle in a DelaunayMesh contains no other point:

Find circumcircles for all triangles:

Plot the circumcircles as disks:

The circumsphere for each tetrahedron in a DelaunayMesh contains no other point:

Find circumspheres for all tetrahedra:

Plot the circumspheres:

ConvexHullMesh is effectively the BoundaryMesh of a DelaunayMesh:

Use TriangulateMesh to retriangulate a region:

VoronoiMesh is the dual of the DelaunayMesh:

Each Voronoi cell has a single point from the original point set: