Lagrangian-based Simplification and Feature Estimation for Flow Visualization



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Vector fields are commonly used in various engineering and scientific applications for the study of different dynamical systems. Their analysis and visualization is of paramount importance to those applications. There are two different representations of vector field (or flow) data, i.e., the Eulerian representation and the Lagrangian representation. Recently, the Lagrangian-based flow representation is getting increasing attention from the computational fluid dynamics (CFD) community, especially for particle-based flow simulation (PFS) and large-scale flow simulation, due to its storage efficiency. However, most existing analysis and visualization techniques are for Eulerian-based (or mesh-based) flow data. There exists little work on the analysis of Lagrangian-based flow data, which motivates this dissertation work.

The flow information represented by the Lagrangian way can be either very sparse or with complex, time-varying spatial configurations, making their analysis for feature detection challenging. In addition, directly visualizing Lagrangian-based flow data (i.e., rendering the particle trajectories or integral curves provided by the data) will easily lead to clutter and occlusion.

To address the aforementioned challenges, this dissertation makes three contributions. First, to analyze PFS data, a least square fitting framework for the estimation of the flow separation behavior and a Lagrangian accumulation framework for analyzing the average (or overall) physical behaviors of flow particles are introduced. Second, to reduce the clutter and occlusion issue when visualizing the Lagrangian flow data, a new and efficient geometry-based similarity metric is introduced combined with the k-means clustering algorithm to achieve a reduced representation. A comparative evaluation is also performed on the clustering algorithms with similarity measures to assess their effectiveness in generating desired clustering results and reduced representations. Finally, two separation estimate strategies are introduced to identify strong separation-like behaviors from sets of integral curves, which provides the first direct solution to locating separation regions from sparse input of integral curves without reconstructing the entire vector field. We have applied the above three techniques to a number of 2D and 3D Lagrangian flow data to demonstrate their effectiveness.



Lagrangian-based representation, Flow visualization, Feature estimation


Portions of this document appear in: Shi, Lieyu, Lei Zhang, Wei Cao, and Guoning Chen. "Analysis enhanced particle-based flow visualization." Electronic Imaging 2017, no. 1 (2017): 12-21. And in: Shi, Lieyu, Robert S. Laramee, and Guoning Chen. "Integral Curve Clustering and Simplification for Flow Visualization: A Comparative Evaluation." IEEE Transactions on Visualization and Computer Graphics (2019).