Abstract: A triangular mesh is the piecewise linear approximation of a sampled or analytical surface, when each patch is a triangle. The connectivity of the mesh can be easily represented using its dual graph. Each node of such a graph has at most three incident edges; if the surface is homeomorphic to a sphere, each node has exactly three incident edges. Several triangular meshes, representing the same surface, with an increasing number of triangles are a representation of the surface at different levels of detail (LOD). When the number of triangles from one LOD to another varies continuously we call such a structure a continuous level of detail (CLOD) approximation of the surface. Given a CLOD data structure we can extract, at each level, the mesh representing the surface and derive its dual graph. If we group the triangles forming each mesh in strips, to accelerate their rendering, we should use two colors for the dual graph’s edges to distinguish between the edges linking nodes belonging to the same strip or not. The main goal of this paper is to present a set of rules to recolor the dual graph of the mesh when passing from one LOD to the next and back. The operations used to change the mesh are a Vertex Split (VS) when the resolution increases, and an Edge Collapse (EC) when the resolution decreases. We can, then, use a local topological analysis to derive the rules allowing to recolor the graph, and to show that, under certain conditions, the recoloring is optimal. This allows to keep effectively an optimal triangle strip structure over the mesh, while changing its resolution.
Authors: M. Porcu, R. Scateni.
Rewriting Rules for the Dual Graph of a Stripified CLOD Mesh.
EuroGraphics Italian Chapter 2007, 23-30.
Trento, Italia, Febbraio 2007.
Abstract: Triangle meshes are the most used representations for three-dimensional objects, and triangle strips are the organization of triangles mostly used for efficient rendering. Since the problem of optimal strip decomposition of a given mesh is NP-complete, many different heuristics have been proposed; the quality of the stripification is usually evaluated using standard indicators as the total number of strips, the number of isolated triangles, the cache coherence, the number of swap vertices. In this paper we present the Enhanced Tunnelling Algorithm (ETA), a stripification method working on the dual graph of a mesh. The method uses a sophisticated mechanism of dynamical update of identifiers, guided by a localization procedure. The algorithm adopts a modified search approach in the dual graph that accelerated the convergence speed of the algorithm. The ETA results efficient and robust, able to deal with datasets of any dimension. The quality of the stripification is remarkable: very few strips (not seldom just one), no isolated triangles, good cache coherence (ACMR value), good number of vertex per triangle.
Abstract: In this paper we describe the data structure and some implementation details of the tunneling algorithm for generating a set of triangle strips from a mesh of triangles. The algorithm uses a simple topological operation on the dual graph of the mesh, to generate an initial stripification and iteratively rearrange and decrease the number of strips. Our method is a major improvement of a proposed one originally devised for both static and continuous level-of-detail (CLOD) meshes and retains this feature. The usage of a dynamical identification strategy for the strips allows us to drastically reduce the length of the searching paths in the graph needed for the rearrangement and produce loop-free triangle strips without any further controls and post-processing, while requiring a more sophisticated implementation to manage the search and undo operations.
Abstract: This paper describes the preliminary results obtained using an iterative method for generating a set of triangle strips from a mesh of triangles. The algorithm uses a simple topological operation on the dual graph of the mesh, to generate an initial stripification and iteratively rearrange and decrease the number of strips. Our method is a major improvement of a proposed one originally devised for both static and continuous level-of-detail (CLOD) meshes and retains this feature. The usage of a dynamical identification strategy for the strips allows us to drastically reduce the length of the searching paths in the graph needed for the rearrangement and produce loop-free triangle strips without any further controls and post-processing.