Lagrangian methods assume a central role in the analysis and visualization of vector fields resulting from simulation and measurement across many application domains. These methods provide key insight into vector field structures and dynamics, but are based on the expensive computation of integral curves. Applied to large-scale problems and data sets, they are burdened heavily by enormous computational cost.
To improve this situation, the problem-specific computation of integral curves employed in vector field visualization techniques is replaced by a two-stage process consisting of an adaptive pre-computation of integral curve sets and methods for interpolation within these sets, effectively transferring the vector field representation to the Lagrangian domain. Hence, the computational burden is isolated into a pre-computation stage. The obtained Lagrangian representation is stored into efficient out-of-core data structures. Integration-based visualization algorithms can leverage the resulting fast interpolation of integral curves, whose approximative characteristics are examined in detail, from this pre-computed data. This generic framework permits enhancement of existing integration-based visualization methods to become interactive and provides a basis for research into novel efficient and interactive vector field visualization for very large vector fields. Taking advantage of these properties, new visualization tools are developed to study transport processes in vector fields using Lagrangian analysis.
To increase the impact of this research and distribute it to a large community of scientists and engineers, the developed algorithms are integrated with an open-source visualization package. These new techniques are integrated into coursework and student projects that enable students to study new methods of analysis of flow computations. Information concerning these new methods are found on the project website (http://idav.ucdavis.edu/~joy/NSF-IIS-0916289).
