[Freetype] New paper on curve representation [relevant to font rendering]

[Nelson H. F. Beebe]

The new paper noted below on curve representation may be relevant to
discussions several weeks ago on the Metafont list.  I'm cc'ing it to
the freetype list because of the subject overlap.

The second author, a former colleague of mine, has written several
major books in the field of CAGD.  

Because of its properties with respect to circle representation, this
algorithm seems worthy of study by people implementing fontware.

@String{j-J-GRAPHICS-TOOLS      = "Journal of Graphics Tools: JGT"}

@Article{Nasri:2001:SAG,
  author =       "Ahmed Nasri and Gerald Farin",
  title =        "A subdivision algorithm for generating rational
                 curves",
  journal =      j-J-GRAPHICS-TOOLS,
  volume =       "6",
  number =       "1",
  pages =        "35--47",
  year =         "2001",
  CODEN =        "JGTOFD",
  ISSN =         "1086-7651",
  bibdate =      "Wed Feb 06 11:23:34 2002",
  bibsource =    "http://www.acm.org/jgt/issues.html";,
  URL =          "http://www.acm.org/jgt/papers/";,
  abstract =     "The well-known Chaikin algorithm generates uniform
                 quadratic B-spline curves by repeating the process of
                 cutting off the corners of a polygon. One disadvantage
                 of this algorithm is the incapability of generating
                 circles. This paper proposes a modification of this
                 algorithm to produce piecewise rational curves; in
                 particular a circle is produced from a given square.
                 For a general control polygon, every two subsequent
                 polygon legs of equal length will correspond to a
                 circular arc. Such an arc will be parameterized by arc
                 length and will remain circular under affine
                 transformations. Both properties are not shared by the
                 standard rational quadratic form.",
  acknowledgement = ack-nhfb,
}

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- Nelson H. F. Beebe                    Tel: +1 801 581 5254                  -
- Center for Scientific Computing       FAX: +1 801 585 1640, +1 801 581 4148 -
- University of Utah                    Internet e-mail: address@hidden  -
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- Salt Lake City, UT 84112-0090, USA    URL: http://www.math.utah.edu/~beebe  -
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