The reason we choose to use BSP trees and used Algorithm 5 is because of the efficiency of merging the two trees. The operation of merging two trees take milliseconds, and can be done in O( n log n) efficiency in the best case and O (n2) in the worst case where we have a very unbalanced tree. The most computationally expansive portion of the Algorithm 5 comes from actually creating the trees. For convex polygons