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» Exact Geometric and Algebraic Computations in CGAL
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ISVC
2009
Springer
14 years 1 months ago
Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast
Given a Cylindrical Algebraic Decomposition of an implicit algebraic curve, visualizing distinct curve arcs is not as easy as it stands because, despite the absence of singularitie...
Pavel Emeliyanenko, Eric Berberich, Michael Sagral...
COMPGEOM
2004
ACM
13 years 10 months ago
Complete, exact, and efficient computations with cubic curves
The Bentley-Ottmann sweep-line method can be used to compute the arrangement of planar curves provided a number of geometric primitives operating on the curves are available. We d...
Arno Eigenwillig, Lutz Kettner, Elmar Schömer...
SODA
2008
ACM
106views Algorithms» more  SODA 2008»
13 years 8 months ago
Exact and efficient 2D-arrangements of arbitrary algebraic curves
We show how to compute the planar arrangement induced by segments of arbitrary algebraic curves with the Bentley-Ottmann sweep-line algorithm. The necessary geometric primitives r...
Arno Eigenwillig, Michael Kerber
SMA
2008
ACM
149views Solid Modeling» more  SMA 2008»
13 years 6 months ago
Exact arrangements on tori and Dupin cyclides
An algorithm and implementation is presented to compute the exact arrangement induced by arbitrary algebraic surfaces on a parametrized ring Dupin cyclide. The family of Dupin cyc...
Eric Berberich, Michael Kerber
SODA
2003
ACM
131views Algorithms» more  SODA 2003»
13 years 8 months ago
Root comparison techniques applied to computing the additively weighted Voronoi diagram
This work examines algebraic techniques for comparing quadratic algebraic numbers, thus yielding methods for deciding key predicates in various geometric constructions. Our motiva...
Menelaos I. Karavelas, Ioannis Z. Emiris