Uncertain geometry with dependencies

Yonatan Myers*, Leo Joskowicz

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


Classical computational geometry algorithms handle geometric constructs whose shapes and locations are exact. However, many real-world applications require computing with geometric uncertainties, which are often coupled and mutually dependent. Existing uncertainty models cannot be used to handle dependencies among objects resulting in overestimation of the mutual errors. We have recently developed the Linear Parametric Geometric Uncertainty Model (LPGUM), a general and computationally efficient worst-case first-order linear approximation of geometric uncertainty that supports dependencies among uncertainties. In this paper, we present the properties of the uncertainty ones of a point and a line, and offer efficient algorithms to compute them. We also describe new efficient algorithms to handle relative position queries, e.g., the classification of an uncertain point with respect to an uncertain line. We show that, in all cases, the overhead of computing with dependent uncertainties is low.

Original languageAmerican English
Title of host publicationProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10
Number of pages6
StatePublished - 2010
Event14th ACM Symposium on Solid and Physical Modeling, SPM'10 - Haifa, Israel
Duration: 1 Sep 20103 Sep 2010

Publication series

NameProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10


Conference14th ACM Symposium on Solid and Physical Modeling, SPM'10


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