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An exact solution is presented to the following inspection problem in two dimensions. A manufactured part is desired to have a polygonal shape E/sub d/. Tolerances are given in terms of two polygons, one, called E/sup -/ lying within E/sub d/, and the other, called E/sup +/, lying outside E/sub d/. A vision system yields a description of each manufactured part as a polygon I. It is desired to determine whether I can be translated and rotated to lie between the tolerance polygons E/sup -/ and E/sup +/, in which case the part is considered to conform to the desired tolerances.>

A general and simple algorithm is presented which computes the set FP of all free configurations for a polygonal object I (with m edges) which is free to translate and/or to rotate but not to intersect another polygonal object E. The worst-case time complexity of the algorithm is O(m/sup 3/n/sup 3/ log mn), which is close to optimal. FP is a three-dimensional curved object which can be used to find free motions within the same time bounds. Two types of motion have been studied in some detail. Motion in contact, where I remains in contact with E, is performed by moving along the faces of the boundary of FP. By partitioning FP into prisms, it is possible to compute motions when I never makes contact with E. In this case, the theoretical complexity does not exceed O(m/sup 6/n/sup 6/ alpha (mn)) but it is expected to be much smaller in practice. In both cases, pseudo-optimal motions can be obtained with a complexity increased by a factor log mn.>

Article Free Access Share on Simultaneous containment of several polygons Authors: F. Avnaim INRIA, Avenue Emile Hugues, 06565 VALBONNE INRIA, Avenue Emile Hugues, 06565 VALBONNEView Profile , J. Bsissonnat INRIA, Avenue Emile Hugues, 06565 VALBONNE INRIA, Avenue Emile Hugues, 06565 VALBONNEView Profile Authors Info & Claims SCG '87: Proceedings of the third annual symposium on Computational geometryOctober 1987 Pages 242–247https://doi.org/10.1145/41958.41984Published:01 October 1987Publication History 21citation325DownloadsMetricsTotal Citations21Total Downloads325Last 12 Months7Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF