Unduloid
Unduloid is a singly periodic constant-mean-curvature surface, of constant mean curvature, given by a parametrisation, genus 0, embedded, with a continuous symmetry group.
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cmc def-parametric embedded implemented singly-periodic tradition-classical tradition-physical
Properties
- Family
- cmc
- Given by
- a parametrisation
- Curvature
- constant mean curvature
- Periodicity
- singly periodic
- Genus
- 0
- Ends
- 0
- Embedding
- embedded
- Orientable
- yes
- Symmetry kind
- continuous symmetry group
- Fidelity
- exact
Definition
No chart is stored: the Delaunay meridian is the roulette of an ellipse focus, a quadrature (elliptic integral) done numerically by the builder. 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, J. Math. Pures Appl. 6 (1841) -- the roulette of an ellipse.