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It is also shown that surface approximations under different criteria and constraints can all be formulated as optimization problems with specified requirements on the residual errors represented by the signed distance functions, and that classical numerical optimization algorithms can be directly applied to solve them since the derivatives of the involved objective functions and constraint functions are all available. Examples of global cutter position optimization for flank milling of ruled surface with a cylindrical tool, which requires approximating the tool envelope surface to the point cloud on the design surface following the minimum zone criterion, are given to confirm the validity of the proposed approach.<\/jats:p>","DOI":"10.1115\/1.3510588","type":"journal-article","created":{"date-parts":[[2010,11,23]],"date-time":"2010-11-23T23:02:07Z","timestamp":1290553327000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":41,"title":["Geometry of Signed Point-to-Surface Distance Function and Its Application to Surface Approximation"],"prefix":"10.1115","volume":"10","author":[{"given":"Li Min","family":"Zhu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. 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