Testing whether a tetrahedron lies inside Linear cell complex

In this post I want to discuss a practical issue which I am facing right now while implementing an adaptive tetrahedral mesh generator. The problem is straightforward to cast and you can see my StackExchange question on the same for better visual understanding. As of today, that question remains unanswered, but I am at a point in my implementation where it cannot be avoided anymore.

So, lets get right into the middle of it without further ado. Given a convex three-dimensional Linear cell complex(or LCC) and a surface mesh representing region of interest in that LCC, we need to label 3-cells of LCC as either inside or outside that region of interest.

Written on 11 Mar 2015