Delaunay triangulation

He invented what is now called Delaunay triangulation in 1934.

A note on point location in Delaunay triangulations of random points.

However in these cases a Delaunay triangulation is not guaranteed to exist or be unique.

However, the Delaunay triangulation does not necessarily minimize the maximum angle.

In the plane, the Delaunay triangulation maximizes the minimum angle.

Such techniques are generally more efficient than Delaunay triangulation and may provide similar accuracy in reconstruction.

In the past, accurate reconstruction methods employed Delaunay triangulations.

A quasi-triangulation may have some of the characteristics of a Delaunay triangulation.

The relative neighborhood graph can be computed in linear time from the Delaunay triangulation of the point set.

It is a subgraph of the Delaunay triangulation.

The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line.

The algorithm begins with a constrained Delaunay triangulation of the input vertices.

Consider an edge e between two input points p and q which is not an edge of a Delaunay triangulation.

Fast randomized point location without preprocessing in two and three-dimensional Delaunay triangulations.

Therefore, unlike the closely related Delaunay triangulation, β-skeletons are not geometric spanners.

The proof is based on two properties of minimum spanning trees and Delaunay triangulations:

For some graphs, such as Delaunay triangulations, both metric and topological properties are of importance.

By considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions.

In particular, the Delaunay triangulation avoids narrow triangles (as they have large circumcircles compared to their area).

A very efficient algorithm for parallel Delaunay triangulations appears in Blelloch et al.

For example, a scattered set of data points could be connected with a Delaunay triangulation to allow the data field to be contoured.

However point sets with no Pitteway triangulation will still have a Delaunay triangulation.

Circumcircles of triangles have an intimate relationship with the Delaunay triangulation of a set of points.

It works by adding points, one at a time, to a valid Delaunay triangulation of a subset of the desired points.

There are special triangulations like the Delaunay triangulation which is the geometric dual of the Voronoi diagram.