Data-Driven Space-Filling Curves

TL;DR

This paper introduces a flexible, data-driven space-filling curve method for 2D and 3D visualization that better preserves spatial features by optimizing data coherency through Hamiltonian paths, supporting multiscale data.

Contribution

It presents a novel, data-driven approach to space-filling curves that improves feature preservation and supports multiscale data visualization, extending existing methods.

Findings

Outperforms existing techniques in preserving data features.

Supports multiscale data via quadtrees and octrees.

Effective in multivariate and ensemble visualization tasks.

Abstract

We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to existing methods. We achieve such data coherency by calculating a Hamiltonian path that approximately minimizes an objective function that describes the similarity of data values and location coherency in a neighborhood. Our extended variant even supports multiscale data via quadtrees and octrees. Our method is useful in many areas of visualization, including multivariate or comparative visualization, ensemble visualization of 2D and 3D data on regular grids, or multiscale visual analysis of particle simulations. The effectiveness of our method is evaluated with numerical comparisons to existing techniques and through examples of ensemble and multivariate datasets.