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» Jacobi Curves: Computing the Exact Topology of Arrangements ...
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COMPGEOM
2001
ACM
13 years 10 months ago
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
We present two approaches to the problem of calculating a cell in a 3-dimensional arrangement of quadrics. The first approach solves the problem using rational arithmetic. It work...
Nicola Geismann, Michael Hemmer, Elmar Schöme...
MICS
2010
123views more  MICS 2010»
13 years 5 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...
PG
2007
IEEE
14 years 1 months ago
A Subdivision Arrangement Algorithm for Semi-Algebraic Curves: An Overview
We overview a new method for computing the arrangement of semi-algebraic curves. A subdivision approach is used to compute the topology of the algebraic objects and to segment the...
Julien Wintz, Bernard Mourrain
COMPGEOM
2009
ACM
14 years 1 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...
ISSAC
2007
Springer
146views Mathematics» more  ISSAC 2007»
14 years 1 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