I have this problem. I tried a lot of options before to post this question.
By referencing the above, I have an object (the blue point) that is moving towards $a)$ where it finds a value of $n = 40$.
Edit: I know the coordinates when the object is on $a)$. Could be a problem where a greedy algorithm could give an approximation of the solution (the points where $n$ is constant)?
The goal is find a path like a circumference in order to keep the value of $n$ constant, like the point $b)$. If the blue dot move towards outside this circumference the value of $n$ could be as the cases $c)$ or $d)$.