Parallel geodesics on an egg-carton surface, alternately focused and scattered by changing curvature
A family of initially parallel geodesics is computed on a surface defined by z=a(sin(bπx/3)+sin(bπy/3)), which has alternating regions of positive and negative Gaussian curvature like an egg carton. The geodesics are computed by parallel transport of tangent vectors along the surface, and rendered as metallic tubes on a wooden board.
The curvature of the surface causes initially parallel geodesics to converge (in regions of positive curvature) and diverge (in regions of negative curvature), illustrating the Jacobi equation J¨+KJ=0 governing geodesic deviation. The wood-grain shader and board geometry give the piece a physical, sculptural quality.
Controls: Click and drag to orbit, scroll to zoom.
