Instant visitation maps for interactive visualization of uncertain particle trajectories

Abstract

Visitation maps are an effective means to analyze the frequency of similar occurrences in large sets of uncertain particle trajectories. A visitation map counts for every cell the number of trajectories passing through this cell, and it can then be used to visualize pathways of a certain visitation percentage. In this paper, we introduce an interactive method for the construction and visualization of high-resolution 3D visitation maps for large numbers of trajectories. To achieve this we employ functionality on recent GPUs to efficiently voxelize particle trajectories into a 3D texture map. In this map we visualize envelopes enclosing particle pathways that are followed by a certain percentage of particles using direct volume rendering techniques. By combining visitation map construction with GPU-based Monte-Carlo particle tracing we can even demonstrate the instant construction of a visitation map from a given vector field. To facilitate the visualization of safety regions around possible trajectories, we further generate Euclidean distance transform volumes to these trajectories on the fly. We demonstrate the application of our approach for visualizing the variation of stream lines in 3D flows due to different numerical integration schemes or errors introduced through data transformation operations, as well as for visualizing envelopes of probabilistic fiber bundles in DTI tractography.