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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computation, University of Cantabria, Santander, 39005, Cantabria, Spain

    Jorge Caravantes & Laureano Gonzalez-Vega

Authors
  1. Jorge Caravantes
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  2. Laureano Gonzalez-Vega
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Correspondence to Jorge Caravantes.

Additional information

Presented as a Keynote at Geometric Modeling and Processing 2008 (GMP 2008), April 23-25, 2008, Hangzhou, China

Project (No. MTM2005-08690-C02-02) partially supported by the Spanish Ministry of Science and Innovation Grant

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Caravantes, J., Gonzalez-Vega, L. Computing the topology of an arrangement of implicitly defined real algebraic plane curves. J. Zhejiang Univ. Sci. A 9, 1685–1693 (2008). https://doi.org/10.1631/jzus.A08GMP01

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  • DOI: https://doi.org/10.1631/jzus.A08GMP01

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