Update to CMC6 node, creates Nodoids and Unduloids, in particular their profile curves.

Rebuild, Mirror, Array, and Revolve left to the user.

Place CMC6.js and the helper functions ellipsefn.js file in the nodeeditor>nodes>extension directory.
CMC6_test.nod produces symmetric half of the nodary curve.

The CMC6 node script creates profile curves in the xy plane, including of most interest, the nodary curve and the undulary curve, depending upon the values of mu and lambda.

The Delaunay Constant Mean Curvature (CMC) surfaces consist of the cylinder, sphere, catenoid, unduloid, and nodoid. The surfaces may be produced by revolving their respective profile curves about a revolve axis equal to the rolling (roulette) line, which was used to generate the profiles. The profile curves are the roulettes of line, circle, parabola, ellipse, or hyperbola, along said roulette line.

The roulette axis for the nodary curve passes through the upper vertex of the hyperbola, which the script has not yet found.

There are additional notes in the comments in the script js file.

This node script uses ellipticfn.js for F(phi,k) and E(phi,k) the incompletic elliptic integrals of the first and second kind. It is assumed that "k" in the paper is the same as"k" in the elliptic functions, rather that using "k*k" in the functions.

- Brian

(Strangely, the y values must be divided by 2 to get the proper sphere and cylinder profiles.)

[See post 1777 for updated CMC files.]