The problem we seek to solve is a 3-dimensional fitting problem (placing a shape inside a free space, such that the size and "quality" of the placement is as good as we can make it). It is complicated by the facts that the free space is highly non-convex, that the shape has parameters beyond placement that can be varied, within bounds, to produce a bigger or better fit, and that some aspects of the quality of a fit are difficult to capture in a precise objective function.