Construction of Pseudo-triangulation by Incremental Insertion

A pseudo-triangulation is a planar subdivision into pseudo triangles - polygons with three convex vertices, used mainly in motion planning problems in robotics. As it is a rather new concept, not too many algorithms to construct it exist. In this paper, we propose an online version of incremental insertion, with generalized flips to improve the shape of pseudo-triangles. This algorithmic paradigm is often used for Delaunay triangulations, but for pseudo-triangulations it has been used only in an off-line version (for sorted input points). We also experimented with several optimization criteria for the flips and show their influence on the shape of pseudo-triangles.