Functional Decomposition for Bundled Simplification of Trail Sets

Abstract : 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.
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Christophe Hurter, Stéphane Puechmorel, Florence Nicol, Alexandru Telea. Functional Decomposition for Bundled Simplification of Trail Sets. IEEE Transactions on Visualization and Computer Graphics, Institute of Electrical and Electronics Engineers, 2017, PP (99), pp.1 - 1. ⟨10.1109/TVCG.2017.2744338⟩. ⟨hal-01587221⟩

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