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Abstract

This paper presents an efficient and robust algorithm for the geometric determination of swept volumes during the simulation of NC-milling (three-axis machining and five-axis machining). The boundary Y of the volume swept by a cutter F is represented polygonally by using instantaneous helical motions to exactly determine the line of contact between F and Y. Applying concepts of differential geometry allows a better and more efficient approximation of tool paths. Tool paths are explicitly calculated when a design surface G is to be milled along prescribed curves. We also describe how to quickly determine a polygonized representation of the truncated material during the milling process by means of 'G-buffering'. This polygon-oriented algorithm is perfectly suitable for Boolean subtractions and error assessment.

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@techreport{Glaeser-1997-EVG,
  title =      "Efficient Volume-Generation During the Simulation of
                NC-Milling",
  author =     "Georg Glaeser and Meister Eduard Gr{\"o}ller",
  year =       "1997",
  abstract =   "This paper presents an efficient and robust algorithm for
               the geometric determination of swept volumes during the
               simulation of NC-milling (three-axis machining and five-axis
               machining). The boundary Y of the volume swept by a cutter F
               is represented polygonally by using instantaneous helical
               motions to exactly determine the line of contact between F
               and Y. Applying concepts of differential geometry allows a
               better and more efficient approximation of tool paths. Tool
               paths are explicitly calculated when a design surface G is
               to be milled along prescribed curves. We also describe how
               to quickly determine a polygonized representation of the
               truncated material during the milling process by means of
               'G-buffering'. This polygon-oriented algorithm is perfectly
               suitable for Boolean subtractions and error assessment.",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  month =      apr,
  number =     "TR-186-2-97-10",
  keywords =   "G-Buffer, sweeps, solid modeling, NC-verification,
               NC-milling, computer aided manufacturing",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/1997/Glaeser-1997-EVG/",
}