Tilted Scherk (doubly periodic)
Tilted Scherk (doubly periodic) is a doubly periodic minimal surface, given by a Weierstrass representation, immersed, with a layer group.
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def-weierstrass doubly-periodic immersed implemented minimal minimal-periodic tradition-classical
Formula
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- doubly periodic
- Ends
- 0
- Embedding
- immersed
- Symmetry kind
- layer group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
Extracted from the shipped row's source by AST (complete multi-line lambdas, phi triple (dh = phi3, g = phi3/(phi1 - i*phi2), a Weierstrass-representation identity)) and reproduced numerically against the shipped callables over the complex plane, exactly -- no scalar slack.
Sources
Weierstrass data reproduced numerically against the shipped implementation (math_art/minsurf/zoo.py, row TILT_SCHERK) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 5.24e-16); dh: matches over 144 complex samples (worst 0).
- R. Schoen / Lopez & Ros (1991) on the Lopez-Ros deformation; H. F. Scherk (1835) for the base Scherk surface; the decorated-Enneper symmetrization follows M. Weber's repository, https://minimalsurfaces.blog/ (Enneper with n Catenoids).