Computing CSG-tree boundaries as algebraic expressions

Abstract 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.

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