Topological extensions via boolean operations

Boolean operations between a given set of shapes allow the creation of an infinite number of shapes. Adding a single new primitive (for ex. a toroid) to the basic set of shapes, all the possible combinations with all the old shapes become moreover possible.

• UNION: the union of two volumes B and C is obtained positioning two overlapping ` MANY' daughters B and C inside the same mother A. To identify the result of the union as a single volume is enough to create a SET associated to the volumes B and C.
• SUBTRACTION: the subtraction of a volume B from a volume C is obtained positioning B as ` ONLY' and C as a ` MANY' overlapping B. The result of the subtraction is automatically what the tracking sees as the C volume, so GSPOS is the only user interface needed. The volume B can have the same material as the mother A or not. The normal positioning technique used for ` ONLYs' is a particular case of boolean subtraction (a volume is contained inside the other).
• INTERSECTION: the intersection of two volumes B and C is obtained positioning a protuding ` MANY' object C in a ` MANY' object B which is normally placed in a ` ONLY' mother A. A and B must have the same material, while C has the material asked for the intersection. The intersection is given by the part of C which is not protuding from B, therefore by what the new tracking sees as the volume C: again the only needed user interface is GSPOS. If not interacting with other daughters of A, B could also be ` ONLY'. Without any ambiguity, even further ` MANY' daughters of A can overlap the protuding part of C outside B, because it is really invisible to the new tracking.