langbein.org: Quadratic Approximation to Plane Parametric Curves and its Application in Approximate Implicitization

Contents

M. Li, X.-S. Gao, S.-C. Chou

The Visual Computer: Int. J. Computer Graphics, 22(9-11):906-917, 2006.
ISSN 01782789.

Expressing complex curves with simple parametric curve segments is widely used in computer graphics, CAD and so on. This paper applies rational quadratic B-spline curves to give a global C1 continuous approximation to a large class of plane parametric curves including rational parametric curves. Its application in approximate implicitization is also explored. The approximated parametric curve is first divided into intrinsic triangle convex segments which can be efficiently approximated with rational quadratic Bezier curves. With this approximation, we keep the convexity and the cusp (sharp) points of the approximated curve with simple computations. High accuracy approximation is achieved with a small number of quadratic segments. Experimental results are given to demonstrate the operation and efficiency of the algorithm.

@ARTICLE{Li2006a,
  author =       {Ming Li and Xiao-Shan Gao and Shang-Ching Chou},
  title =        {Quadratic approximation to plane parametric curves
                  and its application in approximate implicitization},
  journal =      {The Visual Computer: Int. J. Computer Graphics},
  year =         2006,
  volume =       22,
  pages =        {906-917},
  number =       {9-11},
  issn =         01782789,
  doi =          {10.1007/s00371-006-0075-6},
  url =          {http://www.langbein.org/research/solids/borg/li2006a/},
  abstract =     {Expressing complex curves with simple parametric curve
                  segments is widely used in computer graphics, CAD and
                  so on. This paper applies rational quadratic B-spline
                  curves to give a global C1 continuous approximation
                  to a large class of plane parametric curves including
                  rational parametric curves. Its application in
                  approximate implicitization is also explored. The
                  approximated parametric curve is first divided into
                  intrinsic triangle convex segments which can be
                  efficiently approximated with rational quadratic
                  Bezier curves. With this approximation, we keep
                  the convexity and the cusp (sharp) points of the
                  approximated curve with simple computations. High
                  accuracy approximation is achieved with a small
                  number of quadratic segments. Experimental results
                  are given to demonstrate the operation and efficiency
                  of the algorithm.},
}

Cite as Quadratic Approximation to Plane Parametric Curves and its Application in Approximate Implicitization, http://www.langbein.org/research/solids/did/li2006a by Frank C Langbein [27/October/2008, 21:23].

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