Under the hood, the Mapping Toolbox’s distance (and the related geodetic functions) solve the “inverse geodesic” problem on the reference ellipsoid using the classic Vincenty algorithm. When you supply a sphere, it simply falls back to the great‐circle formula.
Key points:
- Ellipsoid mode: Vincenty’s inverse formula (1975)—accurate to a few tenths of a millimeter over most distances but known to fail or stall for nearly antipodal points.
- Sphere mode: Standard spherical law of cosines or haversine.
Because it really is Vincenty’s routine, you will see the documentation’s warning about degrading accuracy at long distances and breakdown at antipodes. Karney’s 2012 “modern” algorithm (available via his MATLAB file exchange code) fixes those edge‐cases and is numerically more robust, but the built-in Mapping Toolbox hasn’t switched over to it.
If you need guaranteed convergence for any two lat/lon pairs, you should plug in Karney’s routines (or another robust inverse‐geodesic solver) instead of relying on distance(). For most everyday use within a few thousand kilometers, the toolbox’s Vincenty‐based distance() is perfectly adequate.
— Follow me so you can message me anytime with future questions. If this helps, please accept the answer and upvote it as well.
