Edited sentence: The point P1 is the midpoint of the geodesic segment X0A1.thumb|250px|right|A curve in M, along with a vector X0 at A0, identified here as a geodesic segment.thumb|250px|right|Select A1 on the original curve.thumb|250px|right|The point X1 is obtained by following the geodesic X0P1 for twice its parameter length