Geometric Ambiguities in Boundary Representations
Hoffmann, Christoph M.; Hopcroft, John E.
Boundary representations are usually separated into two components, a topological component and a geometric component. The conditions necessary to insure that the topological component is unambiguous are well understood. However, in algebriac modeling systems (as opposed to polyhedral modeling systems), an unambiguous topological structure can have noncongruent geometric interpretations with identical vertex coordinates, face equations and edge descriptions using the usual representation of edges as the intersection of faces along with tangent vectors at vertices. This means that the conversion of a CSG tree that unambiguously describes a solid can lead to an ambiguous boundary representations unless additional information is retained in the boundary representation. This paper examines the source of these ambiguities and presents one method for their elimination.
computer science; technical report
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