Isometric embedding of a hyperbolic disk in Euclidean space with adjustable mesh parameters
The hyperbolic plane has curvature K=−1 and cannot be smoothly isometrically embedded in R3, but small regions can be approximated numerically. This program builds a triangular mesh whose intrinsic edge lengths match the hyperbolic metric ds2=dr2+sinh2(r)dθ2 on a disk of finite radius, then relaxes it in R3 using a spring-and-charge system: springs enforce the target edge lengths while Coulomb-like repulsive charges prevent self-intersection.
The resulting surface develops the characteristic ruffled saddle geometry of negative curvature. Parameters controlling the charge strength and spring stiffness can be adjusted in the GUI.
Controls: Click and drag to orbit, scroll to zoom.
