
Title  Simpifications of Closed Triangulated Surfaces Using Simulated Annealing
(In Book) 
in  Mathematical Methods in CAGD: Oslo 2000 
Author(s) 
Peer Timo Bremer, Bernd Hamann, Oliver Kreylos, F.E. Wolter 
Editor(s) 
T. Lyche, L. L. Schumaker 
Year 
2001

Publisher  Vanderbilt University Press 
Address  Nashville, Tennessee 
Pages  4554 
Download  
BibTeX  
Abstract 
We describe a method to approximate a closed surface tri
angulation 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 dierent for dierent 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.
