Algorithm to cover maximal number of points with one circle of given radius

Question

Let\'s imagine we have a plane with some points on it. We also have a circle of given radius.

I need an algorithm that determines such position of the circle that it

Answer 1

You could pixelize the whole area, then go to each point and increase the value of all pixels within the circle of the radius around that point. The pixels with the highest sum are good candidates.

Of course, you might lose some good areas or "hallucinate" good areas due to rounding errors. Perhaps you could try to do a rough pixellation first, then refine the promising areas.