Marco Mazzetti’s research while affiliated with Polytechnic University of Turin and other places

Constructive solid geometry (CSG) defines objects as Boolean combinations of primitive solids, and usually stores them in binary trees. A bounding entity is an upper estimate of the extent of a CSG object. One of the problems in CSG is the search for the smallest bounding box of an object with the bounding boxes of the leaves as input. A method is presented that finds the smallest bounding box of the root; only prismatic boxes are considered. The method, called the canonical-form method, introduces an algebra of boxes which is shown to be a lattice. The lattice properties are then used to prove that the algorithm that computes the bounding boxes achieves a better approximation than the others. Some hints on implementation are then presented, and the efficiency of the method is compared with the S-bound method.