Determining the separation of preprocessed polyhedra: a unified approach
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Note on irreducible triangulations of surfaces
Journal of Graph Theory
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
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Dynamic view-dependent simplification for polygonal models
Proceedings of the 7th conference on Visualization '96
View-dependent refinement of progressive meshes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th 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
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models
IEEE Transactions on Visualization and Computer Graphics
Generating Triangulations of 2-Manifolds
CG '91 Proceedings of the International Workshop on Computational Geometry - Methods, Algorithms and Applications
On Contracting Graphs to Fixed Pattern Graphs
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Irreducible triangulations are small
Journal of Combinatorial Theory Series B
On the maximum number of cliques in a graph embedded in a surface
European Journal of Combinatorics
Restricted mesh simplification using edge contractions
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
On graph contractions and induced minors
Discrete Applied Mathematics
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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 ċ 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. Although several implementations exist for constructing hierarchies, our work is the first to show that a greedy algorithm can efficiently compute a hierarchy of provably small size and low 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}.