Large-Scale Integration-Based Vector Field Visualization - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 313

integral curves emanating from all seed points. Parameters typically pertain to solver
accuracy and integration length. Assuming that the vector field data is decomposed
into connected regions or blocks , integral curves likely traverse multiple blocks, each
of which has to reside in main memory on the processor performing the integration
of the curve. Thus, the data access pattern is not only dependent on the data set, but
also influenced by the choice of seed points and integration parameters.
Studying the effectiveness of parallelization approaches to integral curve prob-
lems, Pugmire et al. [ 16 ] classified scenarios according to three categories with strong
implications on performance. We briefly recapitulate their description here.
Seed Set Size If the given problem requires only the computation of tens to hundreds
of streamlines, parallel computation takes a secondary place to optimal data distribu-
tion or loading; the corresponding seed set is referred to as small . This case is typically
encountered in exploratory visualization scenarios where comparatively few integral
curves are interactively seeded by a user. In contrast, a large seed set encompasses
thousands to millions of seed points for integral curves. For such problems, parallel
computation of integral curves must be employed.
Seed Set Distribution Similarly, the distribution of seed points is an important
problem characteristic. If seed points are concentrated, i.e. located densely , within a
small region of the vector field domain, it is likely that all integral curves will traverse
a relatively small amount of the overall data. For some applications such as integral
curve statistics, on the other hand, a sparse seed set covers the entire vector field
domain. This results in integral curves traversing the entire data set. Hence, the seed
set distribution determines strongly if performance stands to gain most from parallel
computation, data distribution, or both.
Vector Field Complexity The structure of a vector field can have a strong influence
on which parts of the data need to be taken into account in the integral curve com-
putation process. Critical points or invariant manifolds of strongly attracting nature
draw streamlines towards them, and the resulting integral curves seeded in or travers-
ing their vicinity remain closely localized. On the other hand, the opposite case of a
nearly uniform vector field requires integral curves to pass through large parts of the
data. This data dependency of integral curve computation is both counterintuitive and
hard to identify without conducting prior analysis to determine the field structure.
Overall, these problem characteristics determine to what extent an integration-
based problem can profit from a chosen parallel computation and data distribu-
tion. Jointly, they affect the three main cost factors inherent in parallel algorithms—
communication, I/O, and computation—that need to be balanced to achieve optimal
performance. We will next describe two basic approaches and briefly survey advanced
algorithms that provide improved performance and efficiency in certain cases.