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Rational parameterization of quadrics and their offsets

Rationale Parametrisierung von Quadriken und ihren Parallelflächen

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Abstract

In this paper, we study two problems related to quadrics. One is the representation of triangular and quadrangular patches on quadrics: a necessary and sufficient condition is given for triangular patches on quadrics to be representable as rational quadratic triangular Bézier surfaces. The other is the rationality of the offsets to quadrics: the offsets of regular quadrics are shown to be rational and the algorithms are given for computing their rational parameterizations.

Zusammenfassung

Die Arbeit studiert zwei mit Quadriken in Zusammenhang stehenden Probleme. Einerseits werden quadratische Bézier Dreiecke auf Quadriken gekennzeichnet. Andererseits wird gezeigt, daß die Parallelflächen regulärer Flächen zweiter Ordnung stets rational sind, und es werden Algorithmen zur Berechnung der rationalen Parametrisierung angegeben.

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  1. W. Lü

    Present address: Department of Applied Mathematics, Zhejiang University, 310027, Hangzhou, P.R. China

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  1. Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    W. Lü

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Lü, W. Rational parameterization of quadrics and their offsets. Computing 57, 135–147 (1996). https://doi.org/10.1007/BF02276876

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  • DOI: https://doi.org/10.1007/BF02276876

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