We examine the representation of geometric tolerances in solid-geometric models from the perspective of two classes of functional requirements. The first class deals with positioning of parts with respect to one another in an assembly, and the second with maintaining material bulk in critical portions of parts. Both are directly relatable to the geometry of the parts. Through examples, we demonstrate that these functional requirements can be captured in a specific form of tolerances designated as virtual boundary requirements (VBRs). We further demonstrate that the only proposed theory of tolerances in solid models, and the current dimensioning and tolerancing standards in industrial practice, are both inadequate for dealing with VBRs. Accordingly, we develop a theoretical basis for the rigorous statement and interpretation of VBRs.
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