Exact and efficient evaluation of the InCircle predicate for parametric ellipses and smooth convex objects

We study the Voronoi diagram, under the Euclidean metric, of a set of ellipses, given in parametric representation. The article concentrates on the InCircle predicate, which is the hardest to compute, and describes an exact and complete solution. It consists of a customized subdivision-based method...

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Bibliographic Details
Published in:Computer aided design Vol. 40; no. 6; pp. 691 - 700
Main Authors: Emiris, Ioannis Z., Tzoumas, George M.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.06.2008
Subjects:
Algebra
Computer aided design
Concentrates
Convergence
Ellipses
Mathematical models
Parametric ellipse
Real time
Representations
Robust predicate
Symbolic–numeric computation
Voronoi diagram
Robust predicate
Voronoi diagram
Parametric ellipse
Symbolic–numeric computation
ISSN:0010-4485, 1879-2685
Online Access:Get full text
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Summary:We study the Voronoi diagram, under the Euclidean metric, of a set of ellipses, given in parametric representation. The article concentrates on the InCircle predicate, which is the hardest to compute, and describes an exact and complete solution. It consists of a customized subdivision-based method that achieves quadratic convergence, leading to a real-time implementation for non-degenerate inputs. Degenerate cases are handled using exact algebraic computation. We conclude with experiments showing that most instances run in less than 0.1 s, on a 2.6 GHz Pentium-4, whereas degenerate cases may take up to 13 s. Our approach readily generalizes to smooth convex objects.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2008.05.001