Fast and effective stripification of polygonal surface models

Abstract

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 tristips. 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 algorithms through a battery of experiments. In comparison with the recently released STRIPE system for stripification, we find that our stripifier, FTSG, produces comparable or better quality encodings, while requiring significantly less computing time on a large variety of datasets. Further, FTSG is carefully engineered and implemented to be robust, even in the face of highly degenerate and corrupted real-world data.

Single-strips for fast interactive rendering

“…As mentioned above, we note that the basic problem of finding an optimal set of triangle strips for a given triangulation is NP-complete [13,15], and a large body of work has addressed the problem of heuristics to minimize the number of triangle strips for static triangle meshes [1,16,2,37,22,34,35]. Provably good and high-quality triangle strips have been reported in [37] and the Tunneling approach [34].…”

“…Provably good and high-quality triangle strips have been reported in [37] and the Tunneling approach [34]. For real-time, continuously adaptive multiresolution meshes [27], it is much more important to compute a reasonably good set of triangle strips fast than to compute the optimal solution.…”

Efficiently computing and updating triangle strips for real-time rendering

“…Speckmann and Snoeyink [35] have computed the triangle strips for triangulated irregular networks by creating a spanning tree of the dual graph of the TIN and then traversing the tree in a modified depth-first fashion. More recently, Xiang et al [40] have presented a triangle stripping algorithm that computes a spanning tree of the dual graph of a triangulation, partitions this tree into triangle strips, and then concatenates these triangle strips into larger strips. Within computational geometry, interest has focused on constructing and recognizing Hamiltonian and sequential triangulations.…”

Single Triangle Strip and Loop on Manifolds with Boundaries

“…Most stripification algorithms use a greedy technique to incrementally grow the strips [3,11], possibly followed by local optimizations to increase the strip length [15,13]. An exception is [14], which takes quadrilateral meshes as its input, and then appropriately splits them into triangles before constructing a hamiltonian triangle strip.…”