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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2008, Vol. 9 Issue (12): 1685-1693    DOI: 10.1631/jzus.A08GMP01
Electrical & Electronic Engineering     
Computing the topology of an arrangement of implicitly defined real algebraic plane curves
Jorge CARAVANTES, Laureano GONZALEZ-VEGA
Department of Mathematics, Statistics and Computation, University of Cantabria, Santander, 39005, Cantabria, Spain
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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.

Key words： Topology computation      Real plane curves      Sweeping method     
Received: 16 July 2008     
CLC:  TP391.72  
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Jorge CARAVANTES
Laureano GONZALEZ-VEGA
Cite this article:

Jorge CARAVANTES, Laureano GONZALEZ-VEGA. Computing the topology of an arrangement of implicitly defined real algebraic plane curves. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(12): 1685-1693.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A08GMP01     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2008/V9/I12/1685

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