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Conference Papers Year : 2008

A CGAL-based Univariate Algebraic Kernel and Application to Arrangements


Solving univariate polynomials and operations with real algebraic numbers are critical in geometric computing with curved objects. Moreover, the real roots need to be computed in a certified way in order to avoid possible inconsistency in geometric algorithms. We present a CGAL-based univariate algebraic kernel, which follows the CGAL~specifications for univariate kernels. It provides certified real-root isolation of univariate polynomials with integer coefficients (based on the library \rs) and standard functionalities such as basic arithmetic operations, gcd and square-free factorization, as well as comparison and sign evaluations of real algebraic numbers. We compare our implementation with the univariate algebraic kernel developed at MPII, that also follows CGAL~specifications, on various data sets, using polynomials of degree up to 2 000 and maximum coefficient bit-size up to 25 000. Finally we apply our kernel to the computation of arrangements of univariate polynomial functions, and we present a bit complexity analysis of the algorithm for computing the arrangement of planar curves defined by univariate polynomials.
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inria-00336563 , version 1 (04-11-2008)


  • HAL Id : inria-00336563 , version 1


Sylvain Lazard, Luis Mariano Peñaranda, Elias P. P. Tsigaridas. A CGAL-based Univariate Algebraic Kernel and Application to Arrangements. 24th European Workshop on Computational Geometry - EuroCG 2008, Mar 2008, Nancy, France. pp.91--94. ⟨inria-00336563⟩
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