This program numerically integrates the geodesic equation on a paraboloid z = x^2 + y^2. The paraboloid has everywhere positive Gaussian curvature that increases near the vertex, causing geodesics to curve and wrap around the surface. Geodesics on the paraboloid can be studied analytically via Clairaut’s relation for surfaces of revolution, but here they are computed numerically from the Christoffel symbols.
Controls: Click and drag to orbit, scroll to zoom.
