Still a work in progress but I_m happy_

Tim Hutton - 2016-05-12 09:56:55+0000 - Updated: 2016-05-12 09:56:55+0000

Still a work in progress but I'm happy to have captured the 3-way clam-shell folding that wraps the fundamental domain of the Klein Quartic onto its matching edges in the 3D embedding.

Rather than animate by hand, I'm letting the mesh relax with a spring model after making cuts, then playing the animation backwards to show the mesh folding itself up.

https://github.com/timhutton/klein-quartic

Shared with: Public, Gerard Westendorp

+1'd by: Nilay Engineer, Math Solver, Jeff Erickson, Gerard Westendorp, David Eppstein, Niles Johnson, Scott Vorthmann, Roice Nelson, Jeremy Wall, Doug Hackworth, Torolf Sauermann, Rubén Perblac

Gerard Westendorp - 2016-05-12 21:04:25+0000

Cool!
I am doing the same myself, but I got caught up in some other projects. I think I found a way to avoid the self-intersections of the surface as it warps. Hope to get back to it soon.
Did you sub-mesh the heptagons?

Tim Hutton - 2016-05-13 12:22:17+0000

+Gerard Westendorp Look forward to seeing your work. Yes, each heptagon is meshed into five triangles and then I'm recomputing the normals on every frame and Gouraud shading is enough to make it look smooth in the early stages.

It would also be fun to explore subdividing a lot more, and get a smooth 3D shape instead of a mesh with sharp corners. I'm thinking that linear subdivision followed by Laplacian smoothing might just work out of the box for that. VTK is quite good for playing around with these ideas.

This post was originally on Google+