Sort of like a more advanced version of this question.
Given a continuous 2D or higher function $f(x, y)$ corresponding to speed of getting through that point and two points $\vec{a}, \vec{b}$ to travel between, find the quickest route through.
For simplicity, assume that the metric of speed is meters per second and the unit of distance meters.
Note: The amount of time this will take isn't needed as a result. If it can be obtained though, all the better.
This is for a programming project of an alternative to A* search for GPS navigation. (Not a school project, just a personal project.)
Example: Imagine a pool full of oil and water that somehow are able to not move at all and fill the space from the top to the bottom. What is the quickest way to get through it, assuming that swimming through oil is only half as fast?