Sphere: catenoid + Enneper end

Sphere: catenoid + Enneper end is a minimal surface, given by a Weierstrass representation, genus 0, 2 ends, immersed.

Open Sphere: catenoid + Enneper end in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g

\rho \left(z - \frac{1}{z}\right)

Height differential dh

z - \frac{1}{z}

Properties

Family: minimal
Given by: a Weierstrass representation
Curvature: zero mean curvature
Periodicity: not periodic
Genus: 0
Ends: 2
Embedding: immersed
Fidelity: exact
Exactness: numerical-integral

Definition

Extracted from the shipped row's source by AST (complete multi-line lambdas, g/dh lambdas) 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 M3_CATENN) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 0); 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).