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Open AccessArticle
Dupin Cyclides as a Subspace of Darboux Cyclides
by
Jean Michel Menjanahary
Jean Michel Menjanahary 1,†
and
Raimundas Vidunas
Raimundas Vidunas 2,*,†
1
Institute of Computer Science, Vilnius University, 08303 Vilnius, Lithuania
2
Institute of Applied Mathematics, Vilnius University, 03225 Vilnius, Lithuania
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2024, 12(15), 2390; https://doi.org/10.3390/math12152390 (registering DOI)
Submission received: 21 June 2024
/
Revised: 29 July 2024
/
Accepted: 30 July 2024
/
Published: 31 July 2024
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 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.
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MDPI and ACS Style
Menjanahary, J.M.; Vidunas, R.
Dupin Cyclides as a Subspace of Darboux Cyclides. Mathematics 2024, 12, 2390.
https://doi.org/10.3390/math12152390
AMA Style
Menjanahary JM, Vidunas R.
Dupin Cyclides as a Subspace of Darboux Cyclides. Mathematics. 2024; 12(15):2390.
https://doi.org/10.3390/math12152390
Chicago/Turabian Style
Menjanahary, Jean Michel, and Raimundas Vidunas.
2024. "Dupin Cyclides as a Subspace of Darboux Cyclides" Mathematics 12, no. 15: 2390.
https://doi.org/10.3390/math12152390
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