  We present here the first systematic treatment of the problems posed by the
visualization and analysis of large-scale, parallel adaptive mesh refinement
(AMR) simulations on an Eulerian grid. When compared to those obtained by
constructing an intermediate unstructured mesh with fully described
connectivity, our primary results indicate a gain of at least 80\% in terms of
memory footprint, with a better rendering while retaining similar execution
speed. In this article, we describe the key concepts that allow us to obtain
these results, together with the methodology that facilitates the design,
implementation, and optimization of algorithms operating directly on such
refined meshes. This native support for AMR meshes has been contributed to the
open source Visualization Toolkit (VTK). This work pertains to a broader
long-term vision, with the dual goal to both improve interactivity when
exploring such data sets in 2 and 3 dimensions, and optimize resource
utilization.
