# Francesco De Comité

Manipulation of digital images, and use of ray-tracing software can
help you to concretize mathematical concepts. Either for giving you an
idea of how a real object will look or to represent imaginary
landscapes only computers can handle.

Things become yet more interesting, when you can transform your
two-dimensional dream objects in real three dimensional sculptures.
You can then handle your creations, and look at them from an infinity
of view angles.

The three dimensional version of a virtual image is much more
fascinating than the original picture; it is like having in your
hands an infinity of different versions of the object, at no
cost.

Now, new technics let you use colours in your 3D prints. This
makes it yet more interesting: you can try to reproduce the
virtual object in real world: a kind of inverted "Trompe
l'oeil"...

Adding more Villarceau-like circles makes the shape of the cyclide
itself more visible, but we then loose the color contrast between
the two set of circles. As usual, one has to find a compromise
between those two ways of considering the mathematical concept.

Anyway, itis still funny to find titles...

Dupin cyclides are the images of tori by sphere inversion. Since
sphere inversion preserves circles, the set of Villarceau circles
one can draw on a torus is transformed in a set of circles on the
cyclide.

The game is then to find nice images illustrating this fact,
together with some story 'à la Raymond Roussel' to reinforce the
magic.