Covering planar shapes with same size disks

I'm working on algorithm to cover given shapes with same sized, overlapping disks to cover the whole area. The shape is represented by the set of points and i'm struggling to convert givent points to a shape that i could work with. I'm looking for anything that could help me represent and analize given area so i can start working on executing given conditions. Is only a smart part of what i'm working at and i don't have any expirience with space covering algorithms so any usefull functions or scripts would be highly appreciated. I tried triangulations, boundary, alphaShape but those are not considerating all given points and i don't know how exactly start covering shapes represented by those functions.