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Item Inertial Steady 2D Vector Field Topology(The Eurographics Association and John Wiley & Sons Ltd., 2016) Günther, Tobias; Theisel, Holger; Joaquim Jorge and Ming LinVector field topology is a powerful and matured tool for the study of the asymptotic behavior of tracer particles in steady flows. Yet, it does not capture the behavior of finite-sized particles, because they develop inertia and do not move tangential to the flow. In this paper, we use the fact that the trajectories of inertial particles can be described as tangent curves of a higher dimensional vector field. Using this, we conduct a full classification of the first-order critical points of this higher dimensional flow, and devise a method to their efficient extraction. Further, we interactively visualize the asymptotic behavior of finite-sized particles by a glyph visualization that encodes the outcome of any initial condition of the governing ODE, i.e., for a varying initial position and/or initial velocity. With this, we present a first approach to extend traditional vector field topology to the inertial case.Item General Projective Maps for Multidimensional Data Projection(The Eurographics Association and John Wiley & Sons Ltd., 2016) Lehmann, Dirk J.; Theisel, Holger; Joaquim Jorge and Ming LinTo project high-dimensional data to a 2D domain, there are two well-established classes of approaches: RadViz and Star Coordinates. Both are well-explored in terms of accuracy, completeness, distortions, and interaction issues. We present a generalization of both RadViz and Star Coordinates such that it unifies both approaches. We do so by considering the space of all projective projections. This gives additional degrees of freedom, which we use for three things: Firstly, we define a smooth transition between RadViz and Star Coordinates allowing the user to exploit the advantages of both approaches. Secondly, we define a data-dependent magic lens to explore the data. Thirdly, we optimize the new degrees of freedom to minimize distortion. We apply our approach to a number of high-dimensional benchmark datasets.Item Stylized Caustics: Progressive Rendering of Animated Caustics(The Eurographics Association and John Wiley & Sons Ltd., 2016) Günther, Tobias; Rohmer, Kai; Rössl, Christian; Grosch, Thorsten; Theisel, Holger; Joaquim Jorge and Ming LinIn recent years, much work was devoted to the design of light editing methods such as relighting and light path editing. So far, little work addressed the target-based manipulation and animation of caustics, for instance to a differently-shaped caustic, text or an image. The aim of this work is the animation of caustics by blending towards a given target irradiance distribution. This enables an artist to coherently change appearance and style of caustics, e.g., for marketing applications and visual effects. Generating a smooth animation is nontrivial, as photon density and caustic structure may change significantly. Our method is based on the efficient solution of a discrete assignment problem that incorporates constraints appropriate to make intermediate blends plausibly resemble caustics. The algorithm generates temporally coherent results that are rendered with stochastic progressive photon mapping. We demonstrate our system in a number of scenes and show blends as well as a key frame animation.