Distance and distance-like quantity concept

[asinghvi17]

On both the planar and the spherical manifolds, pointwise distance operations involve a final, monotonic transformation (sqrt for planar, acos for spherical) which is a bit expensive, but is unnecessary for comparison.

Given that a distance computation requires finding the nearest point we should have this hierarchy:

nearest_point -> distancelike -> distance

(name up for review)
but basically distancelike is guaranteed to be monotonic in distance, so you can use it for comparisons, and there should be a simple conversion function to go from a distancelike value to a distance value. Note this doesn't mean that the distancelike needs to be separable, in fact for spherical and geodesic it will not be separable..

On the plane this is squared Euclidean distance, on the sphere this is Cartesian distance.

Does that make sense @rafaqz @skygering?

[rafaqz]

Makes perfect sense. So distance would just call distancelike then do the final transformation.

[asinghvi17]

Exactly. Except you might want to use hypot for planar distance but that's really an implementation detail.