We present a method for the hierarchical representation of vector fields. Our approach is based on iterative refinement using clustering 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 approximation levels by measuring the discrepancy between streamlines generated 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 connectivity information. It is possible to generate multiresolution representations of vector fields using this approach.

The visualization and analysis of complex fields often requires identifying and extracting domain specific features. Through a collaboration with geophysicists we extend previous work on crease surfaces with a new and complimentary definition: extremas in principal surface curvature rather than scalar value. Using this definition, we visualize the resulting surfaces which correspond to individual wave fronts. As these wave fronts propagate through a control structure (medium), they undergo changes in intensity, shape and topology due to reflection, refraction and interference. We demonstrate our ability to effectively visualize these phenomena in complex data sets including a large-scale simulation of a hypothetical earthquake along the San Andreas fault in Southern California.