  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.
