G2 Tensor Product Splines over Extraordinary Vertices

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dc.contributor.authorLoop, Charlesen_US
dc.contributor.authorSchaefer, Scotten_US
dc.date.accessioned2015-02-21T17:32:28Z
dc.date.available2015-02-21T17:32:28Z
dc.date.issued2008en_US
dc.description.abstractWe 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.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume27en_US
dc.identifier.doi10.1111/j.1467-8659.2008.01277.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1373-1382en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2008.01277.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleG2 Tensor Product Splines over Extraordinary Verticesen_US
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27-Issue 5
SGP08: Eurographics Symposium on Geometry Processing