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A vector sum operator is used to determine regions of the configuration space of the machine tool which correspond to undesired collisions, cavity access and material removal. Some indication of how cutter paths are generated is given and a practical implementation for the case of machining two and a half dimensional components under two and a half axis control is discussed in more detail.<\/jats:p>","DOI":"10.1017\/s0263574700008547","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:25:53Z","timestamp":1236691553000},"page":"83-91","source":"Crossref","is-referenced-by-count":3,"title":["The geometry of machining for computer-aided manufacture"],"prefix":"10.1017","volume":"4","author":[{"given":"T. W.","family":"Stacey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. E.","family":"Middleditch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700008547_ref011","unstructured":"11. Cameron S.A. , \u201cModelling Solids in Motion\u2019 PhD Thesis, Edinburgh University (1984)."},{"key":"S0263574700008547_ref012","unstructured":"12. Middleditch A.E. , Morris A.C. , \u201cThe Representation and Manipulation of Convex Polygons\u2019 CAE Technical Memo ITM84: 1, PCL (1984)."},{"key":"S0263574700008547_ref015","unstructured":"15. Middleditch A.E. , Tor S.B. \u2018Convex Decomposition of Simple Polygons\u2019 (to be published in ACM Transactions on Graphics)."},{"key":"S0263574700008547_ref013","unstructured":"13. \u2018Numerical Control of Machines \u2014 Axis and Motion Nomenclature\u2019 ISO 841, International Organisation for Standardisation."},{"key":"S0263574700008547_ref014","first-page":"169","article-title":"N.C. 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Armstrong G.T. , \u2018A Study of Automatic Generation of Non-invasive NC Machine Paths from Geometric Models PhD Thesis, Leeds University (1982)."},{"key":"S0263574700008547_ref002","volume-title":"Encyclopaedia"},{"key":"S0263574700008547_ref008","unstructured":"8. Grayer A.R. , \u2018Machining with Volumes\u2019 Ph.D. Thesis Cambridge University (1976)."},{"key":"S0263574700008547_ref010","doi-asserted-by":"publisher","DOI":"10.1145\/359156.359164"},{"key":"S0263574700008547_ref006","first-page":"1","volume-title":"Proc. 1981 SAE Int. 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