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BibTeX entry

@Article{Chen:1993:SIS,
  author =       "Lin-Lin Chen and Shuo-Yan Chou and Tony C. Woo",
  title =        "Separating and Intersecting Spherical Polygons:
                 Computing Machinability on Three-, Four-, and Five-Axis
                 Numerically Controlled Machines",
  journal =      j-TOG,
  volume =       "12",
  number =       "4",
  pages =        "305--326",
  month =        oct,
  year =         "1993",
  CODEN =        "ATGRDF",
  ISSN =         "0730-0301",
  bibdate =      "Fri Jan 5 07:58:42 MST 1996",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0730-0301/159732.html",
  abstract =     "We consider the computation of an optimal workpiece
                 orientation allowing the maximal number of surfaces to
                 be machined in a single setup on a three-, four-, or
                 five-axis numerically controlled machine. Assuming the
                 use of a ball-end cutter, we establish the conditions
                 under which a surface is machinable by the cutter
                 aligned in a certain direction, without the cutter's
                 being obstructed by portions of the same surface. The
                 set of such directions is represented on the sphere as
                 a convex region, called the {\em visibility map} of the
                 surface. By using the Gaussian maps and the visibility
                 maps of the surfaces on a component, we can formulate
                 the optimal workpiece orientation problems as geometric
                 problems on the sphere. These and related geometric
                 problems include finding a densest hemisphere that
                 contains the largest subset of a given set of spherical
                 polygons, determining a great circle that separates a
                 given set of spherical polygons, computing a great
                 circle that bisects a given set of spherical polygons,
                 and finding a great circle that intersects the largest
                 or the smallest subset of a set of spherical polygons.
                 We show how all possible ways of intersecting a set of
                 $n$ spherical polygons with $v$ total number of
                 vertices by a great circle can be computed in $O(vn
                 \log n)$ time and represented as a spherical partition.
                 By making use of this representation, we present
                 efficient algorithms for solving the five geometric
                 problems on the sphere.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; performance",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages, and systems. {\bf
                 F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations. {\bf
                 J.6}: Computer Applications, COMPUTER-AIDED
                 ENGINEERING, Computer-aided manufacturing (CAM).",
}

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