# Void-and-Cluster Sampling of Large Scattered Data and Trajectories

## TL;DR

This paper introduces a novel void-and-cluster sampling method for large scattered datasets that ensures optimal spatial distribution, adapts to data density, supports progressive loading, and extends to time-dependent trajectories with quality evaluation.

## Contribution

It presents a new statistical sampling technique that achieves blue noise distribution, adapts to data complexity, and provides a continuous level-of-detail for large, dynamic datasets.

## Key findings

- Effective data reduction with blue noise properties
- Adaptive sampling based on data complexity
- Supports progressive data loading and quality assessment

## Abstract

We propose a data reduction technique for scattered data based on statistical sampling. Our void-and-cluster sampling technique finds a representative subset that is optimally distributed in the spatial domain with respect to the blue noise property. In addition, it can adapt to a given density function, which we use to sample regions of high complexity in the multivariate value domain more densely. Moreover, our sampling technique implicitly defines an ordering on the samples that enables progressive data loading and a continuous level-of-detail representation. We extend our technique to sample time-dependent trajectories, for example pathlines in a time interval, using an efficient and iterative approach. Furthermore, we introduce a local and continuous error measure to quantify how well a set of samples represents the original dataset. We apply this error measure during sampling to guide the number of samples that are taken. Finally, we use this error measure and other quantities to evaluate the quality, performance, and scalability of our algorithm.