On levels of detail in terrains
Proceedings of the eleventh annual symposium on Computational geometry
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Building and traversing a surface at variable resolution
VIS '97 Proceedings of the 8th conference on Visualization '97
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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 驴 g, a greedy strategy can identify 驴(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(log n + 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}.