NURBS with Extraordinary Points: High-degree, Non-uniform, Rational Subdivision Schemes

We present a subdivision framework that adds extraordinary vertices to NURBS of arbitrarily high degree. The surfaces can represent any odd degree NURBS patch exactly. Our rules handle non-uniform knot vectors, and are not restricted to midpoint knot insertion. In the absence of multiple knots at extraordinary points, the limit surfaces have bounded curvature.

Video

Precomputed tables containing bounded curvature solutions (68.6 KB)

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Source code: ZIP (960.4 KB), TGZ (885.3 KB)

Doxygen documentation

@article{Cashman:2009:NEP,
  title   = {{NURBS with Extraordinary Points:
              High-degree, Non-uniform, Rational Subdivision Schemes}},
  author  = {Thomas J. Cashman and Ursula H. Augsd{\"o}rfer and
              Neil A. Dodgson and Malcolm A. Sabin},
  journal = {ACM Transactions on Graphics},
  year    = {2009},
  volume  = {28},
  number  = {3},
  pages   = {\#46, 1--9}
}