I am not sure if this question is more maths, physics, or computer science, but here we go.
Let's say we have a scalar field $\phi(\vec{x}): \mathbb{R}^2 \rightarrow \mathbb{N}$ but we only have information of some points of $\vec{x}$, although we consider that the field is smooth everywhere. Given two points $A$ and $B$, is it possible to calculate (or obtain, it doesn't have to be theoretically) the path that minimizes the line integral between them?
If the field had an analytical form, this would be straightforward, I would use any of the integration methods (Euler, RK...). In the case I have here, I could devise something similar to the Euler method transforming the field to a vector field in some way and making it continuous. But before I start doing anything, has this problem been tackled before? If so, what keywords should I search for?
