To determine the relative position of any two surfaces in a system, one
approach is to useoperations (Minkowski sum and intersection) on sets of
constraints. These constraints aremade compliant with half-spaces of R^n where
each set of half-spaces defines an operandpolyhedron. These operands are
generally unbounded due to the inclusion of degrees ofinvariance for surfaces
and degrees of freedom for joints defining theoretically
unlimiteddisplacements. To solve operations on operands, Minkowski sums in
particular, "cap" halfspacesare added to each polyhedron to make it compliant
with a polytope which is bydefinition a bounded polyhedron. The difficulty of
this method lies in controlling the influenceof these additional half-spaces on
the topology of polytopes calculated by sum or intersection.This is necessary
to validate the geometric tolerances that ensure the compliance of amechanical
system in terms of functional requirements
