Geometric and topological guarantees for the WRAP reconstruction algorithm

Authors:
Edgar A. Ramos;Bardia Sadri
Affiliations:
University of Illinois, Urbana, IL;University of Illinois, Urbana, IL
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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Abstract

We describe a variant of Edelsbrunner's WRAP algorithm for surface reconstruction, for which we can prove geometric and topological guarantees within the ε-sampling model. The WRAP algorithm is based on ideas from Morse theory applied to the flow map induced by certain distance function. The variant is made possible by a previous result on the "separation" of critical points for a related distance function that directly applies in this case. Though the variant is easily proposed, in order to prove the quality guarantees for the output, we need to closely investigate the geometric properties of the flow map.