Grasshopper implementation of http://www.cs.rpi.edu/~cutler/publications/planar_remeshing_gi07.pdf planar remeshing algorithm.
First we choose the number of faces required, then the mesh is broken down into that many clusters of faces. The clusters can be defined using euclidian distance or local curvature. Planes are then created at each cluster and intersected with the neighbouring planes (which we know from the cluster connectivity information). Finally, corrections are made if the adjacency of the neighbouring clusters is not the same as the adjacency of the planar mesh.
The resulting tri-valent mesh is the closest approximation of the original mesh and can be easily fabricated with planar materials such as plywood, glass, sheet metal or cardboard.
This was used in the development of the TRADA pavilion with Ramboll Computational Design, see vimeo.com/51055184 http://www.harrilewis.com/?p=302
I'm interested in using the software and techniques from the TRADA pavilion to create a structural frame to support sculpture, create internal meeting room pods, pop-up venues and large scale domes.
The forms are structurally efficient as they maintain the advantages of doubly curved surfaces. The tri-valent
mesh means connections between panels may be "pinned" as shown by the use of hinges in the TRADA pavilion.