Institute for Data Analysis and Visualization

We present a method for the hierarchical representation of vector fields. Our approach is based on iterative refinement using cluster-ing and principal component analysis. The input to our algorithm is a discrete set of points with associated vectors. The algorithm generates a top-down segmentation of the discrete field by splitting clusters of points. We measure the error of the various approxima-tion levels by measuring the discrepancy between streamlines gen-erated by the original discrete field and its approximations based on much smaller discrete data sets. Our method assumes no particular structure of the field, nor does it require any topological connectiv-ity information. It is possible to generate multiresolution represen-tations of vector fields using this approach.