
Title  Simplification of Closed Triangulated Surfaces
(In Proceedings) 
in  Proceedings of 2000 UC Davis Student Workshop on Computing, TR CSE20009 
Author(s) 
Peer Timo Bremer, Oliver Kreylos, Bernd Hamann, F.E. Wolter 
Editor(s) 
M.L. Haungs 
Year 
2000

Publisher  University of California, Davis 
Address  Davis, California 
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BibTeX  
Abstract 
. We describe a method to approximate a closed surface triangulation using simulated annealing. Our approach guarantees that all vertices and triangles in an approximating surface triangulation are within a userdefined distance of the original surface triangulation. We introduce the idea of atomic envelopes to guarantee error bounds that are independent of the surface geometry. Atomic envelopes also allow approximation
distance to be different for different parts of the surface. We start with the original triangulation and perturb it randomly and improve an approximating triangulation by locally changing the triangulation, using a simulated annealing algorithm. Our algorithm is not restricted to using only original vertices; the algorithm considers every point inside the envelope triangulation as a possible position. The algorithm attempts to minimize the total number of vertices needed to approximate the original surface triangulation within the prescribed error bound.
