G2 tensor 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 Author(s) Journal compilation 2008 The Eurographics Association and Blackwell Publishing Ltd.

published proceedings

  • Eurographics Symposium on Geometry Processing

author list (cited authors)

  • Loop, C., & Schaefer, S.

complete list of authors

  • Loop, C||Schaefer, S

publication date

  • December 2008