| Title |
Dupin cyclides as a subspace of Darboux cyclides / |
| Authors |
Menjanahary, Jean Michel ; Vidunas, Raimundas |
| DOI |
10.3390/math12152390 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2024, vol. 12, iss. 15, art. no. 2390, p. [1-22].. eISSN 2227-7390 |
| Keywords [eng] |
architecture ; canal surface ; Darboux cyclide ; Dupin cyclide ; geometric design |
| Abstract [eng] |
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 (Formula presented.) 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. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
