How to check whether a point is inside the black regions or not?

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I have a huge map which is similar to bellow, enter image description here

Problem:

I want to find feasible path between two points in the map. Since size of map is huge it takes enormous time to calculate the path. The knowledge I have is that black regions are defined by a set of polytopes.

Is there faster way to determine whether a given point is inside a black regions or not? I am asking this because path path planning algorithm takes time to decide given point is obstacle-free or not due size of map.