Enumerating pseudo-triangulations in the plane

Enumerating pseudo-triangulations in the plane

A pseudo-triangle is a simple polygon with exactly three convex vertices. A pseudo-triangulation of a finite point set S in the plane is a partition of the convex hull of S into interior disjoint pseudo-triangles whose vertices are points of S. A pointed pseudo-triangulation is one which has the least number of pseudo-triangles. We study the graph G whose vertices represent the pointed pseudo-t...

Enumerating pseudo-triangulations in the plane

Improved Algorithm for Enumerating Plane Triangulations

In this paper we give an algorithm to generate all biconnected plane triangulations having exactly n vertices including exactly r vertices on the outer face. The algorithm uses O(n) space in total and generates such triangulations without duplications in O(rn) time per triangulation, while the previous best algorithm generates such triangulations in O(rn) time per triangulation.

Counting and enumerating pseudo-triangulations with the greedy flip algorithm∗

This paper studies pseudo-triangulations for a given point set in the plane. Pseudo-triangulations have many properties of triangulations, and have more freedom since polygons with more than three vertices are allowed as long as they have exactly inner angles less than π. In particular, there is a natural flip operation on every internal edge. We establish fundamental properties of pseudo-trian...

Enumerating Triangulations of Convex Polytopes

A triangulation of a finite point set A in IRd is a geometric simplicial complex which covers the convex hull of A and whose vertices are points of A. We study the graph of triangulations whose vertices represent the triangulations and whose edges represent geometric bistellar flips. The main result of this paper is that the graph of triangulations in three dimensions is connected when the poin...