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Dupin Cyclides as a Subspace of Darboux Cyclides

Author

Listed:
  • Jean Michel Menjanahary

    (Institute of Computer Science, Vilnius University, 08303 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Raimundas Vidunas

    (Institute of Applied Mathematics, Vilnius University, 03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Jean Michel Menjanahary & Raimundas Vidunas, 2024. "Dupin Cyclides as a Subspace of Darboux Cyclides," Mathematics, MDPI, vol. 12(15), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2390-:d:1447305
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