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IEEE Computer Graphics and Applications
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SSD '99 Proceedings of the 6th International Symposium on Advances in Spatial Databases
Probabilistic range queries in moving objects databases with uncertainty
Proceedings of the 3rd ACM international workshop on Data engineering for wireless and mobile access
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Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
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
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Computer-Aided Design
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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 modeling and computing with geometric uncertainties, which are often coupled and mutually dependent. In this paper we address distance problems and orthogonal range queries in the plane, subject to geometric uncertainty. Point coordinates and range uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), a general and computationally efficient worst-case, first-order linear approximation of geometric uncertainty that supports dependence among uncertainties. We present algorithms for closest pair, diameter and bounding box problems, and efficient algorithms for uncertain range queries: uncertain range/nominal points, nominal range/uncertain points, uncertain range/uncertain points, with independent/dependent uncertainties.