It doesn’t have to be a regular geometric shape. Any conceivable surface, no matter how awkward and lumpy — unless you have some infinitely rough mathematical object or other weird thing that doesn’t exist in real life — will permit the definition of geodesic curves.

But also, how much detail you account for is inherently a subjective decision tied to the level of precision you need for your specific application. Are you going to consider every whitecap and speck of foam when you describe your path? That depends! If your goal is to steer an ocean liner in a roughly straight line without hitting any landmasses, then probably not!

If you’re a satellite looking for sea-level defects due to gravitational anomalies, then you might need a little more precision.