 
Summary: Eurographics Symposium on PointBased Graphics (2004)
M. Alexa, S. Rusinkiewicz, (Editors)
The Domain of a Point Set Surface
Nina Amenta and Yong J. Kil
University of California at Davis
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 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.
Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Curve, surface, solid, and
object representations
1. Introduction
The idea of modeling surfaces with clouds
of points is becoming increasingly popu
lar [Lin01, ABCO03, ZPKG02, PKKG03, MVdF03, AK04],
