

Title  The Domain of a Point Set Surfaces
(Article) 
in  Eurographics Symposium on Pointbased Graphics 
Author(s) 
Nina Amenta, Yong J Kil 
Editor(s) 
Markus Gross, Hanspeter Pfister, Marc Alexa, Szymon Rusinkiewicz 
Keyword(s)  pointsets, surfaces, domain, MLS surface 
Year 
June 2004

Location  ETH Zurich, Switzerland 
Date  June 24, 2004 
Volume  1 
Number  1 
Publisher  Eurographics Association 
Address  PO Box 16, CH1288 AirelaVille, Switzerland 
URL  http://graphics.cs.ucdavis.edu/~yjkil/pub/domain.html 
Pages  139147 
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Abstract 
It is useful to be able to define a twodimensional pointset surface determined by a point cloud. One popular definition is Levin's MLS surface. This surface is defined on a domain which is a threedimensional, 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.
