Second Order Smoothness over Extraordinary Vertices

Loop, Charles

Second Order Smoothness over Extraordinary Vertices

Files

169-178.pdf (2.74 MB)

Date

2004

Authors

Loop, Charles

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.

        @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
}
}