Optimal decomposition of polygonal models into triangle strips

Abstract

Motivated by applications in computer graphics, we study the problem of computing an optimal encoding in triangle strips of a triangulation of a polygonal surface model. The goal is to facilitate the transmission and rendering of a polygonal model by decomposing its triangulation into a minimum number of tristrips, each of which has its connectivity stored implicitly in the ordering of the data points. While this optimization problem has been conjectured to be hard, its complexity status has been open. We prove that the tristrip decomposition problem is, in fact, NP-complete. We also propose two methods for solving the problem to optimality, one based on an integer programming formulation, one based on a branch-and-bound scheme that relies on lower bounding techniques for its efficiency. We perform an extensive set of experiments to test the efficiencies of these methods and some of their variants. These methods have been integrated also with the practical system FTSG (Fast Triangle Strip Generator), in order to utilize optimization methods on small subproblems to improve the quality of the heuristic solutions obtained by FTSG. We use experimentation to judge the quality of the improvements.