filename     : Ozt12b.pdf
entry        : toappear
conference   : ACM SIGGRAPH ASIA 2012, Singapore, 28 November-1 December, 2012
pages        : to appear
year         : 2012
month        : December
title        : Analysis and Synthesis of Point Distributions based on Pair Correlation
subtitle     :
author       : A. C. Oztireli and M. Gross
booktitle    : ACM Trans. Graph. (Proc. of ACM SIGGRAPH ASIA)
ISSN/ISBN    : 
editor       : 
publisher    : ACM
publ.place   : Singapore
volume       : 31
issue        : 6
language     : English
keywords     : Sampling, distributions, point processes, multi-class, blue-noise, Poisson-disk sampling, anti-aliasing
abstract     : Analyzing and synthesizing point distributions are of central importance for a wide range of problems in computer graphics. Existing synthesis algorithms can only generate white or blue-noise distributions with characteristics dictated by the underlying processes used, and analysis tools have not been focused on exploring relations among distributions. We propose a unified analysis and general synthesis algorithms for point distributions. We employ the pair correlation function as the basis of our methods and design synthesis algorithms that can generate distributions with given target characteristics, possibly extracted from an example point set, and introduce a unified characterization of distributions by mapping them to a space implied by pair correlations. The algorithms accept example and output point sets of different sizes and dimensions, are applicable to multi-class distributions and non-Euclidean domains, simple to implement and run in $O(n)$ time. We illustrate applications of our method to real world distributions.