The Domain of a Point Set Surface

Amenta, Nina; Kil, Yong J.

The Domain of a Point Set Surface

Files

139-147.pdf (5.48 MB)

Date

2004

Authors

Amenta, Nina
Kil, Yong J.

Publisher

The Eurographics Association

Abstract

It is useful to be able to define a two-dimensional point-set surface determined by a point cloud. One popular definition is Levin's MLS surface. This surface is defined on a domain which is a three-dimensional subset of R3, a narrow region around the input point cloud. If we were to extend the definition outside the domain, we would produce components of the surface which are far from the point cloud. This is important in practice, since when moving points onto the MLS surface, we need to begin with an initial guess which is within the domain. We visualize the domain in two dimensions, and explain why it is so narrow. We also consider two MLS variants which can be defined on a wider domain without producing spurious surface components. One is efficient and works well except near sharp corners. The other is computationally expensive but seems to work well everywhere.

        @inproceedings{:10.2312/SPBG/SPBG04/139-147
,
booktitle = {SPBG'04 Symposium on Point - Based Graphics 2004
},
editor = {Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon Rusinkiewicz
},
title = {{The Domain of a Point Set Surface
}},
author = {Amenta, Nina and 
Kil, Yong J.
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1811-7813
},
ISBN = {3-905673-09-6
},
DOI = {/10.2312/SPBG/SPBG04/139-147
}
}