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Abstract
Preventing any overlap of the elements that compose a structure is an essential test in CAD applications. The elements are usually convex polygons and ellipses in 2D, and convex polyhedra, frusta of cones and cylinders, ellipsoids, and tori in 3D. Overlapping surfaces have at least one common volume characterized by a set of inequalities. The function Reduce in Mathematica can determine if such a set exists or not. It is described within the context of Magnetica, a program used to compute magnetic fields. The elements are then the various polygons or polyhedra that define the contour of the magnet pole and the curves or surfaces of the conductors that create the magnetic field. They are numbered in a list and, in case two elements intersect, a message is issued indicating which elements are incorrectly entered. The components of the magnet are built using the algebraic surfaces of Geometrica.
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