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Synonyms for Geodesic (same or very similar meaning)

WordNet sense 1 ((mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)):
geodesic line

WordNet sense 2 (of or relating to or determined by geodesy):
geodetic, geodesical

From the ODE community, based on WordNetadd/edit