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COMPGEOM
2004
ACM
13 years 8 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...
ESA
2003
Springer
141views Algorithms» more  ESA 2003»
13 years 10 months ago
Jacobi Curves: Computing the Exact Topology of Arrangements of Non-singular Algebraic Curves
We present an approach that extends the BentleyOttmann sweep-line algorithm [3] to the exact computation of the topology of arrangements induced by non-singular algebraic curves o...
Nicola Wolpert
SMA
2008
ACM
149views Solid Modeling» more  SMA 2008»
13 years 5 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
COMGEO
2006
ACM
13 years 5 months ago
An exact and efficient approach for computing a cell in an arrangement of quadrics
We present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and ...
Elmar Schömer, Nicola Wolpert
ESA
2004
Springer
124views Algorithms» more  ESA 2004»
13 years 8 months ago
Code Flexibility and Program Efficiency by Genericity: Improving Cgal's Arrangements
Arrangements of planar curves are fundamental structures in computational geometry. We describe the recent developments in the arrangement package of Cgal, the Computational Geomet...
Efi Fogel, Ron Wein, Dan Halperin