Friday, October 19, 2012

P, G, and D surfaces

I am planning to have a project with students and teachers of TFG (Taipei) school later this month to construct Gyroidal and D surfaces together. It could be a difficult task because the gyroidal structure is probably the most complicated bead structure Chern and I have ever made. A simple tutorial on the three-dimensional structure of a gyroidal surface and how it can be decomposed into several basic and easily weaved units seems to be useful. So I am now preparing some slides to make the project work out smoothly. Here is one of the slides about the famous P-, D- and G-types Triply Periodic Minimal Surfaces (TPMS) which I generated with matlab:
Additionally, Chern, Wei-Chi, Chia-Chin and I also have a paper jointly for the Bridges meeting last summer. Chern made the presentation. I didn't attend it, though. This paper describes the bead models of these three structures quite generally.

Chuang, C.; Jin, B.-Y.; Wei, W.-C.; Tsoo, C.-C. "Beaded Representation of Canonical P, D, and G Triply Periodic Minimal Surfaces", Proceedings of Bridges: Mathematical Connections in Art, Music, and Science, 2012, 503-506.


AGM said...

Your blog is great! ...very informative and useful.
With triaxial weaving, I have been making approximate representations of these surfaces
Deforming a woven mesh of hexagons and equilateral triangles, with pentagons, heptagons etc. produces these surfaces.
I appreciate all the work you publish; thanks
Alison Martin

Bih-Yaw Jin said...

I like the P surface you made with triaxial weaving.I have seen a presentation on making cage-like structure with the same kind of technique in the Bridges conference (Coimbra). But yours are about the hyperbolic structures. It is cool. I might consider to play with this technique someday.

Sharing is the way the world makes progress.

Julian de Mos said...

Your pictures of the P, G and D surfaces, with unit cell and assembly are really helpful to visualize cubic phases of lipid water mixtures as well! I want to ask if I could cite you and use them for the introductory part of my PhD thesis. Would be great! Have just used a D surface 3D model to render a lipidic cubic phase in Blender but cant make the others as I dont have matlab or mathematica...