How to divide a 2d space with given segments(lines)

I'm looking for an general algorithm to solve following problem:

There is an flat (2d) space in form of rectangle, by given dimensions axb. Divide the space with given m- lines that takes given n-lengths. Lines can meet in nodes but can not be more lines in one node then given k.

Let's assume that i.e. n2 is equal to another n2 etc -i know that on the picture lengths are not the same. 

Or...from other side how to create such sketch randomly a then by some algorithm decrease the number of segments (lines)?