Genus-g Surface
Genus-g Surface is a topological surface, given by a parametrisation, genus varies, embedded.
Open Genus-g Surface in the interactive viewer →
aperiodic closed closed-orientable def-parametric embedded implemented topological tradition-classical
Properties
- Family
- topological
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Genus
- varies
- Ends
- 0
- Embedding
- embedded
- Orientable
- yes
- Fidelity
- exact
Definition
No chart is stored: meshed by marching tetrahedra on an implicit field (a product of normalised circle factors plus k z^2); it is an implicit surface with no parametric chart. 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.
- The classification theorem of closed orientable surfaces.