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Recursive polynomial curve schemes and computer-aided geometric design

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Abstract

A class of polynomial curve schemes is introduced that may have widespread application to CAGD (computer-aided geometric design), and which contains many well-known curve schemes, including Bézier curves, Lagrange polynomials, B-spline curve (segments), and Catmull-Rom spline (segments). The curves in this class can be characterized by a simple recursion formula. They are also shown to have many properties desirable for CAGD; in particular they are affine invariant, have the convex hull property, and possess a recursive evaluation algorithm. Further, these curves have shape parameters which may be used as a design tool for introducing such geometric effects as tautness, bias, or interpolation. The link between probability theory and this class of curves is also discussed.

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Authors and Affiliations

  1. Computer Science Department, University of Minnesota, 55455, Minneapolis, Minnesota, USA

    Phillip J. Barry

  2. Computer Graphics Laboratory Computer Science Department, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Ronald N. Goldman

Authors
  1. Phillip J. Barry
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  2. Ronald N. Goldman
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Communicated by Klaus Höllig.

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Barry, P.J., Goldman, R.N. Recursive polynomial curve schemes and computer-aided geometric design. Constr. Approx 6, 65–96 (1990). https://doi.org/10.1007/BF01891409

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  • DOI: https://doi.org/10.1007/BF01891409

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