What is the Equation for the Batista-Costa Minimal Surface?

43 Views Asked by At

The Batista-Costa surface is a triply periodic minimal surface. Three photos of part of the same surface are below:

This is the Batista-Costa surface with many units This is the unit surface of the Batista-Costa surface. This highlights the unit patches of the Batista-Costa surface.

where the first two were taken form the research paper: The New Boundaries of 3D-Printed Clay Bricks Design: Printability of Complex Internal Geometries

and the third one was taken from minimalsurfaces.blog

There are many triply periodic minimal surfaces that can be found using equations that any person who has passed a trigonometry class can read and understandard (not necessarily solve). But when I Googled it and read papers that used it, as far as I can understand, they references back to the paper: A Family of Triply Perioidic Costa Surfaces . This paper is not something a non-expert would be able to understand, including me. And I wouldn't know how to apply it to graph it or find the equation that it is a solution of.

Many of them have nice equations like in the LaTeX table below:

$$ \begin{array} \hline \textbf{Minimal Surface} & \textbf{Equation} \\ \hline \text{Schwarz G (Gyroid)} & \cos(x)\sin(y) + \cos(y)\sin(z) + \cos(z)\sin(x) = 0 \\ \text{Schwarz P} & \cos(x) + \cos(y) + \cos(z) = 0 \\ \text{Schwarz D (Diamond)} & \sin(x)\sin(y)\sin(z) + \sin(x)\cos(y)\cos(z) + \cos(x)\sin(y)\cos(z) + \cos(x)\cos(y)\sin(z) = 0 \\ \text{Scherk's Tower} & \sinh(x)\sin(y) - \sin(z) = 0 \\ \text{Neovius} & 3(\cos(x) + \cos(y) + \cos(z)) + 4\cos(x)\cos(y)\cos(z) = 0 \\ \text{Schoen I-WP (Batwing)} & (\cos(x)\cos(y)) + (\cos(y)\cos(z)) + (\cos(z)\cos(x)) - \cos(x) - \cos(y) - \cos(z) = 0 \\ \text{PW Hybrid} & 10(\cos(x)\cos(y)) + (\cos(y)\cos(z)) + (\cos(z)\cos(x)) - 0.01(\cos(x)\cos(y)\cos(z)) = 0 \\ \text{Batista-Costa Surface} & ? \\ \hline \end{array} $$