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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Computer aided design Ročník 40; číslo 6; s. 691 - 700
Hlavní autoři: Emiris, Ioannis Z., Tzoumas, George M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.06.2008
Témata:
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
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2008.05.001