Filling polygons automatically

How we can fill polygons automatically like in this example, we have two type of polygons(pink and black) , the first type the black polygons, should grow to occupy the void area between the black polygon and the pink one, but this expansion is limited by the second type (the pink polygon) so we cannot have an overlap, this grow occurs following the direction of the lines of black polygons towards pink polygon. if the black polygon is overlapping the pink one, the overlapping part should be cut from the black polygon.

in the initial state we could have void area between pink and black polygons or could be overlapped, but after processing we shouldn't have void area between all polygon and there's no overlapping area.

i wish i had given a good description of the problem, is this a mathematical problem ? what is the kind of this problem ?

i wish these drawings could explain more the problem