Vector Field Analysis and Visualization through Variational Clustering

Abstract

Scientic computing is an increasingly crucial component of research in various disciplines. Despite its potential, exploration of the results is an often laborious task, owing to excessively large and verbose datasets output by typical simulation runs. Several approaches have been proposed to analyze, classify, and simplify such data to facilitate an informative visualization and deeper understanding of the underlying system. However, traditional methods leave much room for improvement. In this article we investigate the visualization of large vector elds, departing from accustomed processing algorithms by casting vector eld simplication as a variational partitioning problem. Adopting an iterative strategy, we introduce the notion of vector ieproxiesln to minimize the distortion error of our simplifiation by clustering the dataset into multiple best-fitting characteristic regions. This error driven approach can be performed with respect to various similarity metrics, offering a convenient set of tools to design clear and succinct representations of high dimensional datasets. We illustrate the benefits of such tools through visualization experiments of three-dimensional vector fields.