geodesic <differential geometry, geodesy>
geodesic line <differential geometry
curve on a surface with a zero-length tangential curvature vector
Note to entry: A geodesic's curvature vector is perpendicular the surface thus has the minimum curvature of any curve restricted to the surface. This is often defined as a minimal distance curve between two points, but this does not always suffice, since some points (especially on ellipsoids and spheres) are often joined by more than one geodesic. For example, on an ellipsoid the points with (φ, λ) = (0, 0) and (0, 180) are joined by four separate geodesic [2 polar (the shorter) and 2 equatorial]. The exponential map is only guaranteed to be one-to-one for a small area (depending on where the centre is and how the surface is curved).
ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)