Geise, G.; Langbecker, U. Finite quadric segments with four conic boundary curves. (English) Zbl 0716.65012 Comput. Aided Geom. Des. 7, No. 1-4, 141-150 (1990). Authors’ abstract: Finite quadric segments bounded by four plane curves and smooth in the sense of differential geometry are considered. Such a quadric segment which can swept by one conic possesses a representation \(x=x(u,v)\) on [0,1]\(\times [0,1]\) as rational tensor product Bézier surface of degree (m,n) with \(m\leq 6\) and \(n\leq 2\). This is founded on known facts concerning rational Bézier representations of conics from the viewpoint of stereographic projection. Some special cases are investigated, especially patches on ruled quadrics bounded by four line segments. Reviewer: C.Simerská Cited in 5 Documents MSC: 65D17 Computer-aided design (modeling of curves and surfaces) Keywords:rational Bézier curves; Finite quadric segments; conic; rational tensor product Bézier surface; stereographic projection PDFBibTeX XMLCite \textit{G. Geise} and \textit{U. Langbecker}, Comput. Aided Geom. Des. 7, No. 1--4, 141--150 (1990; Zbl 0716.65012) Full Text: DOI References: [1] Farin, G., Rational curves and surfaces, (Lyche, T.; Schumaker, L. L., Mathematical Methods in Computer Aided Geometric Design (1989), Academic Press: Academic Press Boston) · Zbl 0835.65020 [2] Hoschek, J.; Lasser, D., Grundlagen der geometrischen Datenverarbeitung (1989), Teubner: Teubner Stuttgart · Zbl 0682.68002 [3] Langbecker, U., Quadrik-Flächenstücke, die durch Kegelschnitte berandet sind, (Diplomarbeit (1988), Technische Universität Dresden: Technische Universität Dresden GDR) [4] Pedoe, D., A Course of Geometry (1970), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0213.22001 [5] Schaal, H., Lineare Algebra und Analytische Geometrie, Bd. II (1980), Vieweg: Vieweg Braunschweig, Wiesbaden · Zbl 0508.15001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.