Parallel geodesics on a sinusoidal wave surface, bunching and spreading with the curvature
A family of initially parallel geodesics is computed on a surface defined by z=asin(b(x+y)). Despite the visual waviness, this surface is a non-geodesic embedding of a flat (Euclidean) domain, meaning its Gaussian curvature is not identically zero but varies with the wave parameters. The geodesics demonstrate how the curvature of the ambient embedding affects the paths of shortest distance.
The surface is rendered as a wooden board with a procedural wood-grain shader, and the geodesics appear as metallic tubes. The wave geometry produces a distinctive pattern where geodesics alternately bunch together and spread apart as they traverse regions of varying curvature.
Controls: Click and drag to orbit, scroll to zoom.
