An Algorithm for Parametric Quadric Patch Construction

Gudrun Albrecht ()
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Gudrun Albrecht: Université de Valenciennes, ENSIAME — Laboratoire MACS

A chapter in Geometric Modelling, 2004, pp 1-12 from Springer

Abstract: Abstract An algorithm for constructing arbitrary parametric quadratic quadric triangles in rational Bézier form is presented. The algorithm does not require the knowledge of the underlying quadric, an important property in view of applying this method for the interpolation of triangulated 3D data points. The algorithm consists of four steps starting with the arbitrary choice of the three corner points and corner weights of the patch, by then constructing a certain triangle and a tetrahedron by means of which the remaining inner control points and weights are obtained guaranteeing the resulting patch to lie on a quadric surface.

Keywords: Quadric; rational parametric Bézier triangle; 3D point interpolation; 65D17; 68U07; 51N15; 51N10; 13P10 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-7091-0587-0_1

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