Distance on an Ellipsoidal ERM
• The red curve A to B is the normal section at A.
• The red curve B to A is the normal section at B.
• The green dotted curve, the minimum distance path on the surface of an ellipsoid, is called a geodesic.
• There is no plane that contains the geodesic.
• The length of a geodesic is an incomplete elliptic integral.
• The curvature in the figure is exaggerated for the purpose of exposition.
– For short distances all three curves have nearly the same length.
• When an environmental model is added, e.g., terrain, minimum distance paths on an ellipsoid are almost never geodesics.