Vesicle script by Brian McMillin, October, 2014.
The vesicle script generates various 2d curves, which are unduloid-like.
They are GENERALIZED Delaunay unduloids, not actual Delaunay unduloids.
Revolve about the z axis is intended, which gives them the appearance of vesicles or chalices.

A general link is: http://www.imbm.bas.bg/uploads/pdfs/papers/VMV/DHMV_09.pdf

Front view is used. Rebuild and mirror are suggested.
Reset of the view may be needed, due to change in size.
There is more mathematical information in the .htm file. Elliptic integrals and Jacobi functions are used.

- Brian

The "slim" version of the curve is due to some error when the z value crosses the x axis to another quadrant.
This may explain the problems with programming the endpoints. (?)

The regular default version of the curve is correct. :-) (?)

The elliptic integral functions are not working correctly with this sign reversal. (?)

- Brian

The first "stable" release of the programming language Julia was released last week.
It has code to compute E(phi,m) for phi > pi/2, which adds pi/2 to phi, divides by pi, then applies the floor function. Modulus is used also.

- Brian