Interpolation-Based Pathline Tracing in Particle-Based Flow Visualization

Particle tracing in time-varying flow fields is traditionally performed by numerical integration of the underlying vector field. This procedure can become computationally expensive, especially in scattered, particle-based flow fields, which complicate interpolation due to the lack of an explicit neighborhood structure. If such a particle-based flow field allows for the identification of consecutive particle positions, an alternative approach to particle tracing can be employed: we substitute repeated numerical integration of vector data by geometric interpolation in the highly dynamic particle system as defined by the particle-based simulation. To allow for efficient and accurate location and interpolation of changing particle neighborhoods, we develop a modified k-d tree representation that is capable of creating a dynamic partitioning of even highly compressible data sets with strongly varying particle densities. With this representation we are able to efficiently perform pathline computation by identifying, tracking, and updating an enclosing, dynamic particle neighborhood as particles move overtime. We investigate and evaluate the complexity, accuracy, and robustness of this interpolation-based alternative approach to trajectory generation in compressible and incompressible particle systems generated by simulation techniques such as Smoothed Particle Hydrodynamics (SPH).