Saddle connectors - an approach to visualizing the topological skeleton of complex 3D vector fields

Abstract

a) Iconic representation. (b) Due to the shown separation surfaces, the topological skeleton of the vector field looks visually cluttered. (c) Visualization of the topological skeleton using saddle connectors.Figure 1: Topological representations of the benzene data set with 184 critical points. AbstractOne of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that such topological structures contain a number of separating stream surfaces. Since these stream surfaces tend to hide each other as well as other topological features, for complex 3D topologies the visualizations become cluttered and hardly interpretable. This paper proposes to use particular stream lines called saddle connectors instead of separating stream surfaces and to depict single surfaces only on user demand. We discuss properties and computational issues of saddle connectors and apply these methods to complex flow data. We show that the use of saddle connectors makes topological skeletons available as a valuable visualization tool even for topologically complex 3D flow data.

Feature-Based Uncertainty Visualization

“…Figure 3.4 shows critical point classifications [27], [58]. show examples of 2D and 3D topologies which consist of critical points connected with separatrices.…”

“…(a) 2D critical points [27] (b) 3D critical points [58] This kind of uncertainty is neglected by most current methods but needs to be quantified so viewers are aware of the uncertainty.…”

Topological Methods for Visualizing Vortical Flows

“…Complete 3D topology has not been attempted yet, however there are authors that examine subsets, such as Globus et al [6] and Theisel et al [17] using saddle connectors. Tricoche et al [18] describe how the time-tracking of singularities and the corresponding topological variations can be investigated for instationary 2D vector fields.…”

On the Role of Topology in Focus+Context Visualization

“…The dense and direct depiction of the flow is limited to just a small region of the data to avoid visual clutter. Further examples of topological visual representations of flow can be found in related works [6,8,13,14]. …”