G2Tensor Product Splines over Extraordinary Vertices Academic Article uri icon


  • We present a second order smooth filling of an n-valent Catmull-Clark spline ring with n biseptic patches. While an underdetermined biseptic solution to this problem has appeared previously, we make several advances in this paper. Most notably, we cast the problem as a constrained minimization and introduce a novel quadratic energy functional whose absolute minimum of zero is achieved for bicubic polynomials. This means that for the regular 4-valent case, we reproduce the bicubic B-splines. In other cases, the resulting surfaces are aesthetically well behaved. We extend our constrained minimization framework to handle the case of input mesh with boundary. 2008 The Eurographics Association and Blackwell Publishing Ltd.

published proceedings

  • Computer Graphics Forum

author list (cited authors)

  • Loop, C., & Schaefer, S.

citation count

  • 40

complete list of authors

  • Loop, Charles||Schaefer, Scott

publication date

  • July 2008