filename     : Gue07a.pdf
entry        : article
conference   : SIGGRAPH 2007, San Diego, USA, 5-9 August 2007
pages        : 23-9
year         : 2007
month        : August
title        : Algebraic Point Set Surfaces
subtitle     :
author       : Gael Guennebaud, Markus Gross
booktitle    : ACM Transaction on Graphics (Proceedings of SIGGRAPH 2007)
ISSN/ISBN    :
editor       : 
publisher    : ACM Press / ACM SIGGRAPH
publ.place   : New York, NY, USA
volume       : 26
issue        : 3
language     : english
keywords     : surface representation, moving least squares, sharp features
abstract     : In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.