Hi there, this is my first post. I proposed my work on the CG Society but they didn't like it enough. So I'll try it here to see whether your community is more interested: I am a mathematician and as such produce images (like knotwork) and I can deform images in some special ways (conformal maps).

The method I setup in order to draw knots has already been noticed in this forum since I am the author of the website entrelacs.net. This methode can be used to produce tilings for example, but as well 3D objects as a knotwork drawn on a surface embedded in 3D.

The second method I am describing deals with deforming images. Mathematical functions from the plane to the plane can be used to deform images. Here, I am talking about functions of a certain kind which are called conformal, or holomorphic, or analytic (mathematicians love to give several names to the same thing depending on which side they are looking at it). What they are good for is to deform pictures in such a way that there is no shear: the angles are locally preserved, a small circle is going to be mapped to a small circle. I put up here a small applet where you can try it out: you have to acknowledge that a java application is on the web page, then look for the "Charger une image à déformer" button, meaning "Load a picture to deform", click on it, locate a (not too large) JPEG picture, give a function of z (try exp(z), z^2, 1/z, log(z) ...) and see what happen in the "final" frame, which is the result of the computation.

You can mix the two and get spirals or inversion of knots for example.

I would like to know whether some people are interested, and whether it is difficult to make a plugin out of this sort of applet in order to deform a texture mapping on a surface in 3D.

Thanks, Christian Mercat