Seifert Surface
Seifert Surface is a topological surface, given by a parametrisation, immersed.
Open Seifert Surface in the interactive viewer →
aperiodic def-parametric immersed implemented topological
Properties
- Family
- topological
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: assembled by Seifert's algorithm from a braid word: disks stacked per Seifert circle joined by half-twisted bands along rotation-minimising frames; combinatorial geometry, no 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.
- Seifert's algorithm and the genus of a knot: Herbert Seifert, "Ueber das Geschlecht von Knoten", Math. Ann. 110, 1934.
- Stacked disk/band layout: J. J. van Wijk & A. M. Cohen, "Visualization of Seifert Surfaces", IEEE TVCG 12(4), 2006, 485-496.
- Braid generators s_i after Emil Artin (braid groups B_n).
- Non-orientable state surfaces: E. Kalfagianni, "State surfaces of links", arXiv:1804.05281, Lemma 2.2 (bipartite orientability criterion).
- Implicit mean-curvature fairing: M. Desbrun, M. Meyer, P. Schroeder,
- A. H. Barr, "Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow", SIGGRAPH 1999. Cotangent weights: U. Pinkall & K. Polthier, "Computing Discrete Minimal Surfaces and Their Conjugates", Experiment. Math. 2(1), 1993.