Functional Decomposition for Bundled Simplification of Trail Sets

Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization.