It could be done, but like bezier curves, bezier splines and nurbs can be self-intersecting, which makes finding intersection points non-trivial. Representing o

It could be done, but like bezier curves, bezier splines and nurbs can be self-intersecting, which makes finding intersection points non-trivial. Representing objects with surfaces is called BREP (Boundary REPresentation), but CSG (Constructive Solid Geometry) is much easier when you are representing shapes with solids. In fact, typically csg on vertexes is done by treating each vertex as half-solid (one side of space is solid, other is not) and then combining them into single solid. When your dividing shape can self-intersect you can have two independent solids which wreaks havoc on equations. Some newer CSG systems use signed distance functions now, which represent 3d shapes mathematically and for many cases it works wonderfully without nurbs.