# How to (efficiently) find intersection of two polyhedral cones?

I have two polyhedral cones represented by their rays. I am looking to find their intersection, which would also be a polyhedral cone, hopefully efficiently. Does anybody know a way to do that?

Thanks

Deepanshu

• More details would help. Are you trying to find the intersection numerically or give a simple description in some sense? What kind of an answer would be acceptable? What space are you working in? – Joonas Ilmavirta Aug 19 '14 at 19:43
• At an REU in 2010, I was a part of a team that designed and implemented an algorithm along these lines as a part of a project to visualize piecewise flat manifolds. The relevant section of our paper begins at the bottom of page 8 at this link: math.arizona.edu/~asp/2010/… Hope something there is useful! – Justin Lanier Aug 19 '14 at 22:41

Presumably you are working in $\mathbb{R}^d$ for $d > 3$. There are specialized algorithms in $d=2,3$.