Hyperbolic cylinder isometrically embedded in Euclidean space, with OBJ export for 3D printing
A cylinder with hyperbolic intrinsic geometry (metric ds2=dx2+cosh2(x)dy2 with periodic y) is discretized into a mesh and embedded into R3 using a spring-and-charge network. Spring rest lengths encode the hyperbolic distances, and Coulomb repulsion between vertices prevents self-intersection.
The embedding is computed via gradient descent on a composite energy functional that combines spring, shear, bending, and charge energies, with momentum-based optimization. The resulting surface displays the characteristic saddle-like ruffling of negatively curved geometry embedded in Euclidean space, with an OBJ export function for 3D printing.
Controls: Click and drag to orbit, scroll to zoom.
