Geodesic estimation for the bent plane from Figure 28; yellow points are closer to the source (marked with an arrow in the ground truth plot). (Top) Different views of the data in 3D, with points colored according to the heat geodesics computed from $G★$⁠. (Middle) Geodesics displayed on an unbent version of the data set: heat geodesics approximate well the true geodesics over $M$⁠, and graph geodesics computed from $G★$ follow closely. (Bottom) Graph geodesics computed from $k$-NN graphs using different choices of $k$⁠. Choosing $k$$=$ 16 gives near-perfect results, but $k$$=$ 4 shows distortions, and $k$$=$ 66 misses completely.