Delaunay Triangulation - From 2-D Delaunay to 3-D Delaunay
Author: Jing Wang
Institute: School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Delaunay triangulation are
widely used in scientific computing in many diverse applications. While
there are numerous algorithms for computing triangulations, it is the
favorable geometric properties of the Delaunay triangulation that make
it so useful.
fundamental property is the Delaunay criterion. In the case of 2-D
triangulations, this is often called the empty circumcircle criterion.
For a set of points in 2-D, a Delaunay triangulation of these points
ensures the circumcircle associated with each triangle contains no other
point in its interior. This property is important. In the illustration
below, the circumcircle associated with T1 is empty. It does not contain
a point in its interior. The circumcircle associated with T2 is empty.
It does not contain a point in its interior. This triangulation is a
Delaunay triangulation. This presentation discusses how to extend 2-D
Delaunay to 3-D Delaynay.