h-Blossoming: A new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves

  • Authors:

  • Plamen Simeonov;Vasilis Zafiris;Ron Goldman

  • Affiliations:

  • Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, TX 77002, United States;Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, TX 77002, United States;Department of Computer Science, Rice University, Houston, TX 77251, United States

  • Venue:
  • Computer Aided Geometric Design
  • Year:
  • 2011

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Abstract

A new variant of the blossom, the h-blossom, is introduced by altering the diagonal property of the standard blossom. The significance of the h-blossom is that the h-blossom satisfies a dual functional property for h-Bezier curves over arbitrary intervals. Using the h-blossom, several new identities involving the h-Bernstein bases are developed including an h-variant of Marsden@?s identity. In addition, for each h-Bezier curve of degree n, a collection of n! new, affine invariant, recursive evaluation algorithms are derived. Using two of these recursive evaluation algorithms, a recursive subdivision procedure for h-Bezier curves is constructed. Starting from the original control polygon of an h-Bezier curve, this subdivision procedure generates a sequence of control polygons that converges rapidly to the original h-Bezier curve.