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Localization of rational B-spline surfaces

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Abstract

Localization of curved surfaces is an important problem in the manufacturing and inspection of mechanical elements and in the simulation of manufacturing processes. The objective of this paper is to provide an efficient method for accurate localization of a single free-form surface of the rational B-spline form. Our approach is based on the following components—first, representation of position tolerances in terms of a ball offset tolerance region around the ideal rational spline surface; to facilitate interrogation and data exchange, this is followed by approximation of the bounding surfaces of the tolerance region with rational B-splines; next, optimal positioning of the target surface with respect to the ideal surface by minimizing a distance-based norm; finally, verification of compliance with position tolerance constraints. Examples illustrate our technique.

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Authors and Affiliations

  1. Department of Ocean Engineering, Design Laboratory, Massachusetts Institute of Technology, Room 5-428, 77 Massachusetts Avenue, 02139, Cambridge, MA, USA

    N. M. Patrikalakis

  2. Department of Naval Architecture and Marine Engineering, National Technical University of Athens, Athens, Greece

    L. Bardis

Authors
  1. N. M. Patrikalakis
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  2. L. Bardis
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Patrikalakis, N.M., Bardis, L. Localization of rational B-spline surfaces. Engineering with Computers 7, 237–252 (1991). https://doi.org/10.1007/BF01206365

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