General Classification of (1,2) Parametric Surfaces in 葳3

Thi-Ha Lê () and André Galligo ()
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Thi-Ha Lê: Université de Nice Sophia-Antipolis, Laboratoire J-A. Dieudonné

Chapter 6 in Geometric Modeling and Algebraic Geometry, 2008, pp 93-113 from Springer

Abstract: Patches of parametric real surfaces of low degrees are commonly used in Computer Aided Geometric Design and Geometric Modeling. However the precise description of the geometry of the whole real surface is generally difficult to master, and few complete classifications exist. Here we study surfaces of bidegree (1,2). We present a classification and a geometric study of parametric surfaces of bidegree (1,2) over the complex field and over the real field by considering a dual scroll.We detect and describe (if it is not void) the trace of self-intersection and singular locus in the system of coordinates attached to the control polygon of a patch (1,2) in the box [0; 1] ˟ [0; 1].

Keywords: Parametric Equation; Double Point; Conjugate Point; Singular Locus; Implicit Equation (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-72185-7_6

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DOI: 10.1007/978-3-540-72185-7_6

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