How to Make Geometric Algorithms Robust

Kokichi SUGIHARA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E83-D   No.3   pp.447-454
Publication Date: 2000/03/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8532
Type of Manuscript: INVITED SURVEY PAPER
Category: Algorithms for Geometric Problems
Keyword: 
computational geometry,  robust computation,  exact arithmetic,  topology-oriented method,  symbolic perturbation,  lazy evaluation,  

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Summary: 
This paper surveys two methods for designing numerically robust geometric algorithms. The first method is the exact-arithmetic method, in which numerical computations are done in sufficiently high precision so that all the topological judgements can be done correctly. This method is usually accompanied with lazy evaluation and symbolic perturbation in order to reduce the computational cost and the implementation cost. The second method is the topology-oriented method, in which the consistency of the topological structure is considered as higher-priority information than numerical computation, and thus inconsistency is avoided. Both of the methods are described with the implementation examples.