Given a triangulated closed surface, the problem of constructing a hierarchy of surface models of decreasing level of detail has attracted much attention in computer graphics. A hierarchy provides view-dependent refinement and facilitates the computation of parameterization. For a triangulated closed surface of n vertices and genus g, we prove that there is a constant c > 0 such that if n > c · g, a greedy strategy can identify Θ(n) topology-preserving edge contractions that do not interfere with each other. Further, each of them affects only a constant number of triangles. Repeatedly identifying and contracting such edges produces a topology-preserving hierarchy of O(n + g2) size and O(logn + g) depth. When no contractible edge exists, the triangulation is irreducible. Nakamoto and Ota showed that any irreducible triangulation of an orientable 2-manifold has at most max{342g - 72,4} vertices. Using our proof techniques we obtain a new bound of max{240g, 4}. © Springer-Verlag Berlin Heidelberg 2002.
CITATION STYLE
Cheng, S. W., Dey, T. K., & Poon, S. H. (2002). Hierarchy of surface models and irreducible triangulation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2518 LNCS, pp. 286–295). https://doi.org/10.1007/3-540-36136-7_26
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