Loop Subdivision with Curvature Control

Ginkel, I.; Umlauf, G.

Loop Subdivision with Curvature Control

Files

163-171.pdf (482.75 KB)

Date

2006

Authors

Ginkel, I.
Umlauf, G.

Publisher

The Eurographics Association

Abstract

In this paper the problem of curvature behavior around extraordinary points of a Loop subdivision surface is addressed. A variant of Loop s algorithm with small stencils is used that generates surfaces with bounded curvature and prescribed elliptic or hyperbolic behavior. We present two different techniques that avoid the occurrence of hybrid configurations, so that an elliptic or hyperbolic shape can be guaranteed. The first technique uses a symmetric modification of the initial control-net to avoid hybrid shapes in the vicinity of an extraordinary point. To keep the difference between the original and the modified mesh as small as possible the changes are formulated as correction stencils and spread to a finite number of subdivision steps. The second technique is based on local optimization in the frequency domain. It provides more degrees of freedom and so more control over the global shape.

        @inproceedings{:10.2312/SGP/SGP06/163-171
,
booktitle = {Symposium on Geometry Processing
},
editor = {Alla Sheffer and Konrad Polthier
},
title = {{Loop Subdivision with Curvature Control
}},
author = {Ginkel, I. and 
Umlauf, G.
},
year = {2006
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-24-X
},
DOI = {/10.2312/SGP/SGP06/163-171
}
}