I don’t think this is a transformation that can be performed by only stretching and deforming the surface (e.g., the maps of a city with time units vs distance units aren’t homomorphic).

Imagine starting on the far south end of a congested city surrounded by a circular, relatively low-traffic highway. Points on the northern end of the city would be “closer” on such a map than points directly in the center.

You could certainly define a transformation that accounts for this, but I think it would necessarily defy most people’s intuitive interpretation of such a map.

You could resolve it by cutting the circular highway att the furthest point, and let the surrounded are baloon out. The map would still make sense close to the user.