Quartic Supercyclides I: Basic Theory

Published

January 1, 1997

Author(s)

Mike Pratt

Abstract

Various classes of algebraic surfaces have been examined as to their suitability for Computer Aided Geometric Design purposes. This paper co~tributes further to the study of a class of quartic surfaces recently investigated by Degeni having strong potential for use in blending, and possibly also in free-form surface design. These surfaces are here put in the context of a classification of quartic surfaces originally given more than~one hundred years ago. An algebra) representation is provided for them, and a simple geometric interpretation given for their rational biquadratic parametric formulation. Their theory is established from an analytic geometry viewpoint which is more straightforward than Degen''s original approach and gives fur the useful geometric insight into their- properties. A major subclass of Doggone''s surfaces consists of projective transforms of the Dupin cyclides; for this reason (and others, explained in the text) the name supercyclides is proposed for them.

Citation

Computer Aided Geometric Design

Volume

Volume 14, No. 7

Pub Type

Journals

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Keywords

Algebraic surfaces, blending, cyclides, quartics, supercyclides

Citation

Pratt, M. (1997), Quartic Supercyclides I: Basic Theory, Computer Aided Geometric Design, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=821429 (Accessed October 12, 2025)