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 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.

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