"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:

> > Have you thought about geometrically inverting the patches to become a cylinder
> > or a cone?  :D
>
> I'm not sure what you mean by "inverting the patches".
>
> I have not yet made cones with Bezier patches. But I have made
> cylinders. This document shows an example:
>
>
https://github.com/t-o-k/Maxima-bezier/blob/main/cylinder_made_with_4_rational_bezier_surfaces_3d.pdf

https://en.wikipedia.org/wiki/Dupin_cyclide#Dupin_cyclides_and_geometric_inversions

So you could start with a cylinder, invert it into a torus, and then re-invert
it into a cone.  :D  Invert it again into a Dupin cyclide, and then you could
invert a final time back to the original cylinder and have QUITE the cyclic
animation!

> The attached image shows the 3x3x3 = 3x9 = 27 control points for
> two of the patches in the animation. Note that the patches do
> not get very close to the 9 cyan "intermediate" control points.

Ah yes - that makes it much clearer.

Though if you're interpolating between control grids composed of u,w
coordinates, via splines controlled by u, then technically u and w are
parametric equations in u even not explicitly written that way.   Right? (?)

Beautiful work as always.
I always enjoy the ballet of the math and graphics, and admire and appreciate
the skill and discipline to make it all happen.

I'm glad you had the free time to put this one together.  :)

- BW

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