Dupin Cyclides as a Subspace of Darboux Cyclides

Jean Michel Menjanahary and Raimundas Vidunas ()
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Jean Michel Menjanahary: Institute of Computer Science, Vilnius University, 08303 Vilnius, Lithuania
Raimundas Vidunas: Institute of Applied Mathematics, Vilnius University, 03225 Vilnius, Lithuania

Mathematics, 2024, vol. 12, issue 15, 1-22

Abstract: Dupin cyclides are interesting algebraic surfaces used in geometric design and architecture to join canal surfaces smoothly and to construct model surfaces. Dupin cyclides are special cases of Darboux cyclides, which in turn are rather general surfaces in R 3 of degree 3 or 4. This article derives the algebraic conditions for the recognition of Dupin cyclides among the general implicit form of Darboux cyclides. We aim at practicable sets of algebraic equations on the coefficients of the implicit equation, each such set defining a complete intersection (of codimension 4) locally. Additionally, the article classifies all real surfaces and lower-dimensional degenerations defined by the implicit equation for Dupin cyclides.

Keywords: Dupin cyclide; Darboux cyclide; canal surface; geometric design; architecture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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