A fundamental algorithmic problem in computer graphics is that of computing a succinct encoding of a triangulation of a polygonal surface model in order to be able to transmit and render it efficiently. The goal is to take a given polygonal surface model, whose facets are given by (possibly multiply-connected) polygons, triangulate its facets, and then decompose the triangulation into a small number of "tristrips," each of which has its connectivity stored implicitly in the ordering of the data points. We develop methods that are effective in solving the stripification problem, both in theory (provably good encodings) and in practice. Our methods are based on carefully constructed search trees in the dual graph, followed by algorithms to decompose dual trees into tristrips. One decomposition algorithm is provably optimal (based on dynamic programming), allowing us a sound basis of comparison among our other (heuristic) algorithms. We demonstrate the speed and effectiveness of our algor...

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 e#ciency. We perform an extensive set of experiments to test the e#ciencies 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.

A preliminary version of this paper has appeared as an extended abstract at CGI'98; see [26]. y

Triangle strips are a widely used hardware-supported data-structure to compactly represent and efficiently render polygonal meshes. In this paper we survey the efficient generation of triangle strips as well as their variants. We present efficient algorithms for partitioning polygonal meshes into triangle strips. Triangle strips have traditionally used a buffer size of two vertices. In this paper we also study the impact of larger buffer sizes and various queuing disciplines on the effectiveness of triangle strips. View-dependent simplification has emerged as a powerful tool for graphics acceleration in visualization of complex environments. However, in a view-dependent framework the triangle mesh connectivity changes at every frame making it difficult to use triangle strips. In this paper we present a novel data-structure, Skip Strip, that efficiently maintains triangle strips during such view-dependent changes. A Skip Strip stores the vertex hierarchy nodes in a skip-list-like manner with path compression.

We consider the problem of nding the largest area axis-aligned rectangle contained in an n vertex polygon. We present an algorithm that solves this problem in O(n log n) time. This is an improvement by a factor of O(log n) over the best known algorithm. Our method of achieving this improvement is noteworthy. The previous algorithm constructs a cover of the polygon by a collection of subpolygons, of the type we call SAM polygons, such that any rectangle in the polygon is contained in one of the SAM subpolygons. This cover requires O(n log n) time and space to construct. Our algorithm also constructs a cover of the polygon by SAM subpolygons such that any rectangle in the polygon is contained in one of the subpolygons but does so using only linear time and space. 1

We study an engineering approach to computing Voronoi diagrams of points and line segments in the two-dimensional Euclidean space. Our Voronoi code, named vroni, uses standard oating-point arithmetic. It is based on Sugihara and Iri's topology-oriented approach, a very careful implementation of the numerical computations required, an automatic relaxation of epsilon thresholds, and on a multi-level recovery process combined with \desperate mode". Vroni was tested extensively on real-world data and turned out to be reliable. CPU-time statistics document that it is always faster than other popular Voronoi codes. 1 Introduction In a recent editorial, Fortune [2] wrote that \it is notoriously dicult to obtain a practical implementation of an abstractly described geometric algorithm". According to the author's personal experience this remark is particularly true for the implementation of Voronoi diagrams of line segments. This paper discusses the design and implementation of a reliable an...