Le_Forgeron <jgr### [at] freefr> wrote:
> Le 16/05/2017 à 13:41, Bald Eagle a écrit :
> > I didn't have as much time as I would have liked to explore this,
> > but after fiddling with the Dupin cyclide in both isosurface (implicit) and
> > parametric form, I found the parameters to be highly unintuitive, the desired
> > shape very difficult to achieve and control, and the constraints on the
> > parameters too complex to be easily implemented.
> >
> > I hadn't gotten around to unraveling the implicit equation to fit the syntax for
> > a polynomial.

> I asked the other Internets about that, they had a round tuit left so I
> got a nice answer.

>
> > It is, however, SLLLLllllllllllooooooooooowwwwwwww.
> It is not slow with a polynomial.

I had wondered / suspected / hoped that were the case.

> True Duplin Cyclide !

That, sir, is a very beautiful thing  :)
You did indeed get a very nice answer.

I'm wondering how a, b, c, and d relate to the radii of the shape, and how to
know what values to plug in.  The large end always seems to be VERY large
compared to the smaller side, though IIRC, with certain values one can get a
normal torus, so I suppose that might not be inherent in the object.

I found a very interesting paper by Langevin: "Geometry with two screens and
computational graphics" (2014) where he points out some very interesting and
useful properties of the true Dupin cyclide.

Thank you as always, Jerome - and please thank your friends for me as well.
I'm sure I will have some fun playing with this new algebraic surface and
finding ways to harness it in some future scenes.

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