Analysis and synthesis of point distributions based on pair correlation

A. Cengiz Öztireli, Markus Gross
2012 ACM Transactions on Graphics  
Base simulation With synthesized particles Original 1 PCF r max Original (Photo) Synthesized 1 PCF r max Synthesized (Rendering) PCF Irregularity 1 5 r max r max 1 1 r max r max PCF Irregularity Figure 1: Left: Our analysis and synthesis methods offer a unified treatment of point distributions, middle: to understand and recreate complex structures such as turbulence, right: by generating distributions of possibly multiple classes of objects with pair correlation functions (PCF) precisely
more » ... g those of provided input examples, such as the distributions of these candies of four colors. 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.
doi:10.1145/2366145.2366189 fatcat:mrw36s5y7fbs5dty6ap4uspibi