In this paper we introduce a fast and efficient linear time and space algorithm to detect and reconstruct uniform Loop subdivision structure, or triangle quadrisection, in irregular triangular meshes. Instead of a naive sequential traversal algorithm, and motivated by the concept of covering surface in Algebraic Topology, we introduce a new algorithm based on global connectivity properties of
the covering mesh. We consider two main applications for this algorithm. The first one is to enable interactive modeling systems that support Loop subdivision surfaces, to use popular interchange
file formats which do not preserve the subdivision structure, such as VRML, without loss of information. The second application is to improve the compression efficiency of existing lossless connectivity
compression schemes, by optimally compressing meshes with Loop subdivision connectivity. Extensions to other popular uniform primal subdivision schemes such as Catmul-Clark, and dual
schemes such as Doo-Sabin, are relatively strightforward but will be studied elsewhere.
By: Gabriel Taubin
Published in: RC21880 in 2000
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