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
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Sign up to join this communityI 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
Presumably you are working in $\mathbb{R}^d$ for $d > 3$. There are specialized algorithms in $d=2,3$.
Here is one route. You have, essentially, what is known as the V-representation of your polytopal cones, V=vertex. An alternate representation is the H-representation, H=halfspace, the intersection of halfspaces. If you convert each cone's V-representation to an H-representation, then you have reduced your problem to intersecting all the halfspaces defining both cones.
One can convert between V- and H-representations via a variety of software packages. E.g., it can be accomplished in R; see this link. Perhaps a better place to start is polymake; see this web page.
The intersection of halfspaces can be accomplished by a wider variety of software, including polymake and qhull.
Another code you may wish to try is 4ti2's rays-function. It can also be called via polymake.