Computer Laboratory

NURBS-compatible subdivision surfaces

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

Tom Cashman, Ursula Augsdörfer, Neil Dodgson and Malcolm Sabin


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.


MPG (88.0MB), MP4 (45.2MB)


PDF (7.0 MB)

Precomputed tables containing bounded curvature solutions (68.6 KB)


Binaries for Windows (5.4 MB)

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


  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}

© ACM, 2009. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Graphics, {28, 3, (August 2009)}