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Publication summary
Author(s): Mike Pratt
Publication date: March 1997
Citation: Mike Pratt: Quartic Supercyclides I: Basic Theory, Published in Computer Aided Geometric Design, North-Holland Publishing Co., Volume 14, No. 7, 1997, 671 - 692.
Key words: Algebraic surfaces, quartics, cyclides, supercyclides, blending
Availability:
Abstract:
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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.
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