ISO standards on geometrical product specifications and verification (GPS) define several geometrical operations, such as extraction, partitioning, filtration, and association. These operations are required for obtaining ideal or non-ideal features and acts at both specification and verification domains. Recently, another operation called reconstruction has become an important topic of discussion in the ISO GPS standards committee ISO/TC 213. The operation of reconstruction produces a continuous surface from a finite number of points. Different from association, which is an operation used to fit pre-defined ideal features to non-ideal features or point-cloud, the main challenge of reconstruction is to guarantee that the topology of the underlying surface is preserved and its boundaries are well defined. This paper takes some initial steps toward a mathematical definition of the reconstruction operation and explores fundamental concepts for specification and verification. Challenges and future research are also highlighted.
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