Second Order Smoothness over Extraordinary Vertices

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Date
2004
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
Catmull & Clark subdivision is now a standard for smooth free-form surface modeling. These surfaces are everywhere curvature continuous except at points corresponding to vertices not incident on four edges. While the surface has a continuous tangent plane at such a point, the lack of curvature continuity presents a severe problem for many applications. Topologically, each n-valent extraordinary vertex of a Catmull & Clark limit surface corresponds to an n-sided hole in the underlying 2-manifold represented by the control mesh. The problem we address here is: How to fill such a hole in a Catmull & Clark surface with exactly n tensor product patches that meet the surrounding bicubic patch network and each other with second order continuity. We convert the problem of filling the hole with n tensor product patches in the spatial domain into the problem of filling the hole in the n frequency modes with a single bidegree 7 tensor product patch.
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@inproceedings{
:10.2312/SGP/SGP04/169-178
, booktitle = {
Symposium on Geometry Processing
}, editor = {
Roberto Scopigno and Denis Zorin
}, title = {{
Second Order Smoothness over Extraordinary Vertices
}}, author = {
Loop, Charles
}, year = {
2004
}, publisher = {
The Eurographics Association
}, ISSN = {
1727-8384
}, ISBN = {
3-905673-13-4
}, DOI = {
/10.2312/SGP/SGP04/169-178
} }
Citation