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ISSAC
2007
Springer
146views Mathematics» more  ISSAC 2007»
13 years 10 months ago
Fast and exact geometric analysis of real algebraic plane curves
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...
Arno Eigenwillig, Michael Kerber, Nicola Wolpert
COMPGEOM
2005
ACM
13 years 6 months ago
On the exact computation of the topology of real algebraic curves
We consider the problem of computing a representation of the plane graph induced by one (or more) algebraic curves in the real plane. We make no assumptions about the curves, in p...
Raimund Seidel, Nicola Wolpert
MICS
2010
123views more  MICS 2010»
13 years 3 months ago
On the Topology of Real Algebraic Plane Curves
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of...
Jinsan Cheng, Sylvain Lazard, Luis Mariano Pe&ntil...
SMA
2008
ACM
149views Solid Modeling» more  SMA 2008»
13 years 4 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
COMPGEOM
2009
ACM
13 years 11 months ago
On the topology of planar algebraic curves
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of...
Jinsan Cheng, Sylvain Lazard, Luis Mariano Pe&ntil...