How do i determine if one point can be connected to another through a line that doesnt intersect with any objects on a binary image

Hi, so im trying to programm an exact cell decomposition algorithm for trajectory planning, and i already found the middle points of every cell, now, for the search algorithm part i need to find which points are next to the one im currently evaluating. I've already tried finding the equation of the line that connects them and seeing if in any point along the line there's a 0 in the image matrix. The thing is with points that are too close on one axis (i.e (40,204) and (41,29)) there can be an 'obstacle' between them even though each point is in 'free' space. Another thing, is that i just need the very next ones, something like what the image shows.