Second Order Smoothness over Extraordinary Vertices
| dc.contributor.author | Loop, Charles | en_US |
| dc.contributor.editor | Roberto Scopigno and Denis Zorin | en_US |
| dc.date.accessioned | 2014-01-29T09:19:51Z | |
| dc.date.available | 2014-01-29T09:19:51Z | |
| dc.date.issued | 2004 | en_US |
| dc.description.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. | en_US |
| dc.description.seriesinformation | Symposium on Geometry Processing | en_US |
| dc.identifier.isbn | 3-905673-13-4 | en_US |
| dc.identifier.issn | 1727-8384 | en_US |
| dc.identifier.uri | https://doi.org/10.2312/SGP/SGP04/169-178 | en_US |
| dc.publisher | The Eurographics Association | en_US |
| dc.subject | Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations | en_US |
| dc.title | Second Order Smoothness over Extraordinary Vertices | en_US |
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