Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Representation, evaluation and editing of feature-based and constraint-based design
Representation, evaluation and editing of feature-based and constraint-based design
Computational topology: ambient isotopic approximation of 2-manifolds
Theoretical Computer Science - Topology in computer science
An assessment of the current state of product data technologies
Computer-Aided Design
On the long-term retention of geometry-centric digital engineering artifacts
Computer-Aided Design
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Product data exchange requires exchanging geometrical shape data that may have to be represented differently in the sending and in the receiving system. Since the translation process thereby entailed can lead to errors, emerging exchange standards include numeric invariants computed from the shape. Agreement of these invariants in the sending and receiving system are then used to increase confidence in the translation process. In this paper we show that there are many classes of noncongruent solids for which all the invariants of volume, surface area, moments and products of inertia agree. Thus these quantities alone are insufficient to exclude many translation errors. We also consider whether the examples are realistic and find that in today's constraint-based shape constructions the examples are not unlikely to occur.