filename : Ozt10.pdf entry : toappear conference : SIGGRAPH ASIA 2010, Seoul, Republic of Korea, 16-18 December, 2010 pages : year : 2010 month : December title : Spectral Sampling of Manifolds subtitle : author : A. Cengiz Oztireli, Marc Alexa, Markus Gross booktitle : ISSN/ISBN : editor : publisher : ACM publ.place : volume : issue : language : English keywords : Sampling, Laplace-Beltrami, Heat Kernel, Poisson Disk Sampling abstract : A central problem in computer graphics is finding optimal sampling conditions for a given surface representation. We propose a new method to solve this problem based on spectral analysis of manifolds which results in faithful reconstructions and high quality isotropic samplings, is efficient, out-of-core, feature sensitive, intuitive to control and simple to implement. We approach the problem in a novel way by utilizing results from spectral analysis, kernel methods, and matrix perturbation theory. Change in a manifold due to a single point is quantified by a local measure that limits the change in the Laplace-Beltrami spectrum of the manifold. Hence, we do not need to explicitly compute the spectrum or any global quantity, which makes our algorithms very efficient. Although our main focus is on sampling surfaces, the analysis and algorithms are general and can be applied for simplifying and resampling point clouds lying near a manifold of arbitrary dimension.