Opacity Optimization and Inertial Particles in Flow Visualization
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Vector field visualization is a major discipline of scientific visualization that helps to push the frontiers of research in fluid mechanics, medicine, biology, astrophysics and many more. In particular, vector field visualization is concerned with the discovery of relationships in possibly large and complex vector fields, which serve as general descriptors of air and fluid flows, magnetic fields and dynamical systems. The visualization community found a number of different ways to assist in the analysis and exploration of these fields. Two major classes of approaches are the so-called geometry-based and feature-based / topology-based techniques. The first and second part of this thesis introduce techniques that reside in these two classes, respectively. The third part of the thesis addresses the analysis of inertial particles, i.e., finite-sized objects carried by fluid flows. When it comes to 3D flow visualization, we often encounter occlusion problems when displaying dense sets of lines or multiple surfaces. A vital aspect is the careful selection of the primitives that best communicate the relevant features in a data set. In the first part of the thesis, we present optimization-based approaches that adjust the opacity of lines and surfaces to strive for a balance between the presentation of relevant information and occlusion avoidance. The second part of the thesis is dedicated to novel rendering techniques for the visualization of unsteady flows. For this, we will apply techniques from light transport in heterogeneous participating media to the unbiased rendering of Lagrangian scalar fields, namely finite-time Lyapunov exponents. Further, we propose a new class of vortex definitions for flows that are induced by rotating mechanical parts, such as stirring devices, hydrocyclones, centrifugal pumps or ventilators. In the third part of this thesis, we introduce inertial particles as a new application domain to the flow visualization community. Recent research in flow visualization focused on the analysis of massless particles. However, in many application scenarios, the mass of particles and their resulting inertia are essential, such as when sand particles interact with aircraft. The governing ODE of even simple inertial flow models is up to seven dimensional, which makes feature extraction a challenging task. We abstract the description of mass-dependent particle trajectories and apply existing flow visualization methods to the mass-dependent case. In particular, we extract and visualize integral geometry, study the vortical motion and separation behavior of inertial particles, extend traditional vector field topology to the inertial case and present a new approach to the source inversion problem, i.e., the recovery of the source of dispersed pollutants. We demonstrate the usefulness of our methods by applying them to a variety of synthetic and real-world data sets.