Journal of Zhejiang University-SCIENCE A

, Volume 9, Issue 12, pp 1685–1693 | Cite as

Computing the topology of an arrangement of implicitly defined real algebraic plane curves

  • Jorge Caravantes
  • Laureano Gonzalez-Vega


We introduce a new algebraic approach dealing with the problem of computing the topology of an arrangement of a finite set of real algebraic plane curves presented implicitly. The main achievement of the presented method is a complete avoidance of irrational numbers that appear when using the sweeping method in the classical way for solving the problem at hand. Therefore, it is worth mentioning that the efficiency of the proposed method is only assured for low-degree curves.

Key words

Topology computation Real plane curves Sweeping method 

CLC number



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Copyright information

© Zhejiang University and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and ComputationUniversity of Cantabria, SantanderCantabriaSpain

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