2d space dividing by m lines

Question

It has been years since I wrote any program... so I need your help and advice.

I 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.

Here there is an example http://i.stack.imgur.com/YzJ4a.png

let's assume that ie n2 is equal to another n2 etc -i know that on the picture is not exactly

maybe you can recommend literature that help me to solve that problem?

Answer 1

That is an Euclidean graph problem. In particular, that graph is a planar straight line graph.

http://en.wikipedia.org/wiki/Planar_straight_line_graph

If you are looking for literature, Computational Geometry: An Introduction by Preparata and Shamos may helps you.

Good luck!