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2007
Springer

Fast and exact geometric analysis of real algebraic plane curves

10 years 4 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 plane, augmented with adjacency information. The adjacency information describes the curve’s topology by a topologically equivalent planar graph. The numerical data in the CAD gives an embedding of the graph. The algorithm is designed to provide the exact result for all inputs but to perform only few symbolic operations for the sake of efficiency. In particular, the roots of f(α, y) at a critical x-coordinate α are found with adaptive-precision arithmetic in all cases, using a variant of the Bitstream Descartes method (Eigenwillig et al., 2005). The algorithm may choose a generic coordinate system for parts of the analysis but provides its result in the original system. The algorithm is implemented as C++ library AlciX in the EXACUS project. Running time comparisons with top by Gonzalez-Vega and Necula (2002...
Arno Eigenwillig, Michael Kerber, Nicola Wolpert
Added 08 Jun 2010
Updated 08 Jun 2010
Type Conference
Year 2007
Where ISSAC
Authors Arno Eigenwillig, Michael Kerber, Nicola Wolpert
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