Loop, CharlesSchaefer, Scott2015-02-212015-02-2120081467-8659https://doi.org/10.1111/j.1467-8659.2008.01277.xWe 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.10.1111/j.1467-8659.2008.01277.x1373-1382