Geodesics in Nil geometry with an earth texture on the geodesic sphere, showing helical twisting
This program displays geodesics in Nil geometry, one of Thurston’s eight 3-dimensional model geometries based on the Heisenberg group. Geodesics emanate from a central point in all directions, and the resulting geodesic sphere is textured with an earth map to make the distortion caused by the non-Euclidean geometry visible. In Nil, geodesics twist helically due to the non-abelian group structure, causing the earth texture to warp in characteristic ways.
Controls: Click and drag to orbit, scroll to zoom.
