On sorting triangles in a delaunay tessellation

In a two-dimensional Delaunay-triangulated domain, there exists a partial ordering of the triangles (with respect to a vertex) that is consistent with the two-dimensional visibility of the triangles from that vertex. An equivalent statement is that a polygon that is star-shaped with respect to a given vertex can be extended, one triangle at a time, until it includes the entire domain. Arbitrary planar triangulations do not possess this useful property which allows incremental processing of the triangles.This work was partially supported by the National Science Foundation's US-Italy Collaborative Research Program under Grant INT-8714578 and Information, Robotics, and Intelligent Research Grant IRI-8704781.