Interesting problem. I imagine the juicy part is that there is no clear cut formula for determining the rotation from the area needed. Thus the task is to com

Interesting problem. I imagine the juicy part is that there is no clear cut formula for determining the rotation from the area needed. Thus the task is to come up with a fast approximation algorithm to work backwards. So brute force way: If area_needed > area_cast: rotate_cube(delta) delta=/2 else similar rotation on -delta Now, my 3d geometry is rusty, so maybe rotation on 2 axis is enough but still optimizing 2 arguments is not going to be easy. Maybe you can max one rotation then max 2nd one.