The stochastic walk algorithms for point location in pseudo-triangulations

A pseudo-triangulation is a planar subdivision into polygons with three convex vertices, useful for ray shooting, visibility problems and kinetic collision detection. As pseudo-triangulations are quite young, there is a lack of specialized algorithms for them. In this paper, we address the question of location in pseudo-triangulations. We propose two location algorithms based on the so-called stochastic walk and present their experimental results. The class of walk location algorithms is very popular for triangulations, namely in engineering applications, due to simplicity and low memory requirements, in spite of their non-optimality. As far as we know, no walk algorithm specialized on pseudo-triangulations has been developed before.