Hyperbolic tilings library

cults3d

New: I added an Instructable about how to use this to make cookies: https://www.instructables.com/id/Hyperbolic-Cookies/. This OpenSCAD library allows users to create customizable tilings of the hyperbolic plane, utilizing the Poincaré disk model and triangle groups. A triangle group is defined by a triplet (p,q,r) where 1/p + 1/q + 1/r < 1. It can be invoked as triangle_group(p,q,r). The number 0 represents the special value ∞. Any infinite numbers must precede finite numbers, such as in triangle_group(0,2,3), which is legal. Tessellation data is computed from the triangle group with tgroup_tessellation_data(group, depth), where depth is the number of consecutive reflections from the center tile. The modules building the 3D object use this tessellation data; a few modules are provided as examples, such as tessellation_simple and tessellation_cookie. It should be easy to build your own modules starting from these. Note that the same tiling (same triangle group) can give quite different objects depending on how you mark edges. Warning: Given the recursive, exponential complexity of these tilings, generating STLs is long (about 15 minutes on my laptop at depth 3), so it's best to use a very small depth parameter for tweaking (as in, 0 or 1). Only go up to depth 3 or 4 when you have a design you like. This library is basically a stress test for CGAL, and it might crash your computer or teleport you to some unpleasant place. I am not responsible for this.