2013/02/28 by A. Blasco, Ángel Blasco, Sonia Pérez-Dı́az +1 · 18 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic curve #Algebraic number #Algebraic surface #Geometry #Infinity #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Plane (geometry) #Plane curve #Polynomial and algebraic computation #Pure mathematics #math.AG #msc:14H50
paper · pdf · doi:10.1016/j.cagd.2014.04.002
published in Computer Aided Geometric Design 31(7-8), 345-357 (Elsevier BV)
arxiv created 2013/07/24 · openalex publication_date 2014/05/21 · arxiv updated 2014/10/21 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
In this paper, we introduce the notion of infinity branches as well as approaching curves. We present some properties which allow us to obtain an algorithm that compares the behavior of two implicitly defined algebraic plane curves at the infinity. As an important result, we prove that if two plane algebraic curves have the same asymptotic behavior, the Hausdorff distance between them is finite.