Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Handbook of discrete and computational geometry
Probabilistic range queries in moving objects databases with uncertainty
Proceedings of the 3rd ACM international workshop on Data engineering for wireless and mobile access
Efficient indexing methods for probabilistic threshold queries over uncertain data
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Tolerance envelopes of planar mechanical parts with parametric tolerances
Computer-Aided Design
Technical note: Uncertain lines and circles with dependencies
Computer-Aided Design
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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 zones 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.