I looked at the examples of this library but couldn't get an idea which part of this library is a solution for my problem. Could you point me more direct to what you meant? 

i think you may find that "uniform distribution" isn't as well-defined as you might imagine.

 

take the simplest case:  your shape is a triangle, and N=1.

 

where, exactly, would you expect that point to occur?  centroid/incenter/excenter/elsewhere?  what properties would it have?  bisects angles or edges?  equidistant to vertices?  equidistanct to edges?  resulting areas of subdivided triangles formed between that point and vertices (or bisected edges) are equal?  (etc, there are lots of "triangle centers" with varying geometric properties)

 

once you've determined what N=1 in a triangle means, N=2,3,4 might be easier.  then (perhaps) doing arbitrary N for an arbitrary polygon might just involve triangulating it first, then apportioning some amount of N per triangle based on triangle area vs overall area, thus breaking it into a more manageable triangle-based problem.

 

it's quite possible that a purely analytical solution won't exist, and you might just have to find an iterative solution - modelling with spring forces or such, then running until a "best compromise" of all constraint criteria is achieved.

 

EDIT: thinking about it twice: It might not just be as easy as feeding a bunch of points into a spring force scenario. but maybe voronoi and spring forces in combination will do the job.