Abstract
Asymmetric tensor fields have found applications in many science and engineering domains, such as fluid dynamics. Recent advances in the visualization and analysis of 2D asymmetric tensor fields focus on pointwise analysis of the tensor field and effective visualization metaphors such as colors, glyphs, and hyperstreamlines. In this paper, we provide a novel multi-scale topological analysis framework for asymmetric tensor fields on surfaces. Our multi-scale framework is based on the notions of eigenvalue and eigenvector graphs. At the core of our framework are the identification of atomic operations that modify the graphs and the scale definition that guides the order in which the graphs are simplified to enable clarity and focus for the visualization of topological analysis on data of different sizes. We also provide efficient algorithms to realize these operations. Furthermore, we provide physical interpretation of these graphs. To demonstrate the utility of our system, we apply our multi-scale analysis to data in computational fluid dynamics.
Highlights
Asymmetric tensor fields have found a wide range of applications such as fluid mechanics [26, 35, 36]
We describe our algorithms to extract the eigenvector and eigenvalue graphs from a given asymmetric tensor field T defined on a triangular mesh M that is associated with an underlying mesh
We develop a novel multi-scale topology-driven analysis framework for asymmetric tensor fields on surfaces
Summary
Asymmetric tensor fields have found a wide range of applications such as fluid mechanics [26, 35, 36]. Their work is limited to planar datasets, at a single scale, and without physical interpretation This makes the impact of their work rather limited as many datasets from fluid mechanics involve vector and tensor fields on curved surfaces, such as the diesel engine and cooling jacket simulations [19]. We provide a multi-scale topological representation using these graphs for data in the plane or on curved surfaces. To enable a multi-scale topological representation, we identified a set of atomic operations with which nodes in the graphs (corresponding to feature regions and points in the data) can be merged. The utility of our approach is demonstrated with a number of application datasets
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