G2 Tensor Product Splines over Extraordinary Vertices
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Date
2008
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd
Abstract
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.
Description
@article{10.1111:j.1467-8659.2008.01277.x,
journal = {Computer Graphics Forum},
title = {{G2 Tensor Product Splines over Extraordinary Vertices}},
author = {Loop, Charles and Schaefer, Scott},
year = {2008},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2008.01277.x}
}