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
Dynamic view-dependent simplification for polygonal models
Proceedings of the 7th conference on Visualization '96
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
Hierarchy of surface models and irreducible triangulations
Computational Geometry: Theory and Applications
Evaluating approximations generated by the GNG3D method for mesh simplification
AIKED'08 Proceedings of the 7th WSEAS International Conference on Artificial intelligence, knowledge engineering and data bases
On Contracting Graphs to Fixed Pattern Graphs
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
On graph contractions and induced minors
Discrete Applied Mathematics
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We consider the problem of simplifying a triangle mesh using edge contractions, under the restriction that the resulting vertices must be a subset of the input set. That is, contraction of an edge must be made onto one of its adjacent vertices. In order to maintain a high number of contractible edges under this restriction, a small modification of the mesh around the edge to be contracted is allowed. Such a contraction is denoted a 2-step contraction. Given m “important” points or edges it is shown that a simplification hierarchy of size O(n) and depth O(log(n/m)) may be constructed in O(n) time. Further, for many edges not even 2-step contractions may be enough, and thus, the concept is generalized to k-step contractions.