Delaunay Surface
Delaunay Surface is a singly periodic constant-mean-curvature surface, of constant mean curvature, given by a parametrisation, embedded or immersed depending on parameters, with a continuous symmetry group.
Open Delaunay Surface in the interactive viewer →
cmc def-parametric implemented singly-periodic tradition-classical
Properties
- Family
- cmc
- Given by
- a parametrisation
- Curvature
- constant mean curvature
- Periodicity
- singly periodic
- Ends
- 0
- Embedding
- embedded or immersed depending on parameters
- Orientable
- yes
- Symmetry kind
- continuous symmetry group
- Fidelity
- exact
Definition
No chart is stored: the meridian of a Delaunay surface is a QUADRATURE -- the generator's own header says so, and integrates it in a substituted variable to keep the endpoints finite -- so the profile exists only as the numerical integral, not as an expression in u. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- C. Delaunay, 'Sur la surface de revolution dont la courbure moyenne est constante', J. Math. Pures Appl. 6 (1841).