Geometric Interoperability With Epsilon Solidity

Geometric data interoperability is critical in industrial applications where geometric data are transferred (translated) among multiple modeling systems for data sharing and reuse. A big obstacle in data translation lies in that geometric data are usually imprecise and geometric algorithm precisions vary from system to system. In the absence of common formal principles, both industry and academia embraced ad hoc solutions, costing billions of dollars in lost time and productivity. This paper explains how the problem of interoperability, and data translation in particular, may be formulated and studied in terms of a recently developed theory of $ε$-solidity. Furthermore, a systematic classification of problems in data translation shows that in most cases $ε$-solids can be maintained without expensive and arbitrary geometric repairs.