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.

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@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}
}