  We present an MPI-parallel algorithm for the in-situ visualization of
computational data that is built around a distributed linear forest-of-octrees
data structure. Such octrees are frequently used in element-based numerical
simulations; they store the leaves of the tree that are local in the curent
parallel partition.
  We proceed in three stages. First, we prune all elements whose bounding box
is not visible by a parallel top-down traversal, and repartition the remaining
ones for load-balancing. Second, we intersect each element with every ray
passing its box to derive color and opacity values for the ray segment. To
reduce data, we aggregate the segments up the octree in a strictly distributed
fashion in cycles of coarsening and repartition. Third, we composite all
remaining ray segments to a tiled partition of the image and write it to disk
using parallel I/O.
  The scalability of the method derives from three concepts: By exploiting the
space filling curve encoding of the octrees and by relying on recently
developed tree algorithms for top-down partition traversal, we are able to
determine sender/receiver pairs without handshaking and/or collective
communication. Furthermore, by partnering the linear traversal of tree leaves
with the group action of the attenuation/emission ODE along each segment, we
avoid back-to-front sorting of elements throughout. Lastly, the method is
problem adaptive with respect to the refinement and partition of the elements
and to the accuracy of ODE integration.
