Here is a script to create most of Scherk's second minimal surface.
Note that the Wikipedia equations, as well as the Wolfram equations, are faulty. The y parametric equation should have ln in front of it,
similar to the x equation. The correct equations are shown here: http://www.math.mcgill.ca/gantumur/math580f12/minimal_surfaces.pdf
The literature states that the parametric equations are difficult to plot. An angle of 0, as well as a radius of 1 would cause division by zero, which
javascript, and MoI do not like. So an initial 2PI angle was substituted for 0.
The last "concentric" curve was discarded, due to its irregularity, and semicircles substituted to enable network. Afterwards, they were trimmed
off with red planes. So the surface should be the minimal surface, within a very small tolerance.
The curves in red were added manually.
The basic surface can be stacked, by rotation about the upper or lower red rotation line.
With such a stack, Flow and Twist could be done.
So this script is probably one that would only be used once. The surface is now created, so the script is not needed :-)
- Brian
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