ABSTRACT Quadrilateral and Tetrahedral Mesh Stripification Using 2-Factor Partitioning of the Dual Graph

Finding a 2-factor of a generic graph is a difficult problem and there are randomized algorithms proposed to solve this problem in O(n 3) complexity [12]. In this paper, we propose algorithms that find a 2-factor of a graph, if one exists, for a restricted class of graphs in which all vertices have degree four or less, in O(n 2) complexity where n is the number of vertices of the graph. Such graphs are actually dual graphs of quadrilateral and tetrahedral meshes that are widely used in graphics and visualization applications. We use the 2-factor of these graphs to find linear ordering of the primitives in the form of strips. Applications like compression, access and rendering of such data benefits a lot from such linear ordering. We use the similarity between the dual graphs of the quadrilateral and tetrahedral meshes to introduce a novel, unified graph based algorithm to produce quad and tetrahedral strip representations respectively. Further, by introducing a few additional vertices, we can represent the entire quad-surface using a single quad-strip loop. We can use a similar technique to reduce the number of tetrahedral strips, to represent the entire tetrahedral mesh

M.: Quadrilateral and tetrahedral mesh stripification using 2-factor partitioning of the dual graph

Abstract In order to find a 2-factor of a graph, there exist O(n 1.5) deterministic algorithm [7] and O(n 3) randomized algorithm [14]. In this paper, we propose novel O(n log 3 n log log n) algorithms to find a 2-factor, if one exists, of a graph in which all n vertices have degree four or less. Such graphs are actually dual graphs of quadrilateral and tetrahedral meshes. A 2-factor of such graphs implicitly defines a linear ordering of the mesh primitives in the form of strips. Further, by introducing a few additional primitives, we reduce the number of tetrahedral strips to represent the entire tetrahedral mesh, and represent the entire quad-surface using a single quad-strip