Geodesics on a Gaussian bump surface, showing convergence and divergence due to curvature
Geodesics are the shortest paths between points on a curved surface, generalizing straight lines to Riemannian geometry. This program computes geodesics on a surface shaped like a Gaussian bump by numerically integrating the geodesic equation derived from the induced metric. The resulting curves reveal how the positive curvature at the peak causes nearby geodesics to converge and then diverge, illustrating the relationship between curvature and the behavior of geodesics.
Controls: Click and drag to orbit, scroll to zoom.
