Curve arrangement studying is a subject of great interest in Computational Geometry and CAGD. In our paper, a new method for computing the topology of an arrangement of algebraic plane curves, defined by implicit and parametric equations, is presented. The polynomials appearing in the equations are given in the Lagrange basis, with respect to a suitable set of nodes. Our method is of sweep-line class, and its novelty consists in applying algebra by values for solving systems of two bivariate polynomial equations. Moreover, at our best knowledge, previous works on arrangements of curves consider only implicitly defined curves.
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