One-sided smoothness-increasing accuracy-conserving filtering for enhanced streamline integration through discontinuous fields

The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. One of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an inter-element level while allowing discontinuities between elements. This flexibility, however, generates a plethora of difficulties when one attempts to use DG fields for feature extraction and visualization, as most post-processing schemes are not designed for handling explicitly discontinuous fields. This work introduces a new method of applying smoothness-increasing, accuracy-conserving filtering on discontinuous Galerkin vector fields for the purpose of enhancing streamline integration. The filtering discussed in this paper enhances the smoothness of the field and eliminates the discontinuity between elements, thus resulting in more accurate streamlines. Furthermore, as a means of minimizing the computational cost of the method, the filtering is done in a one-dimensional manner along the streamline.United States. Army Research Office (Grant no. W911NF-05-1-0395)National Science Foundation (U.S.) (Career Award NSF-CCF0347791

New techniques for the scientific visualization of three-dimensional multi-variate and vector fields

Volume rendering allows us to represent a density cloud with ideal properties (single scattering, no self-shadowing, etc.). Scientific visualization utilizes this technique by mapping an abstract variable or property in a computer simulation to a synthetic density cloud. This thesis extends volume rendering from its limitation of isotropic density clouds to anisotropic and/or noisy density clouds. Design aspects of these techniques are discussed that aid in the comprehension of scientific information. Anisotropic volume rendering is used to represent vector based quantities in scientific visualization. Velocity and vorticity in a fluid flow, electric and magnetic waves in an electromagnetic simulation, and blood flow within the body are examples of vector based information within a computer simulation or gathered from instrumentation. Understand these fields can be crucial to understanding the overall physics or physiology. Three techniques for representing three-dimensional vector fields are presented: Line Bundles, Textured Splats and Hair Splats. These techniques are aimed at providing a high-level (qualitative) overview of the flows, offering the user a substantial amount of information with a single image or animation. Non-homogenous volume rendering is used to represent multiple variables. Computer simulations can typically have over thirty variables, which describe properties whose understanding are useful to the scientist. Trying to understand each of these separately can be time consuming. Trying to understand any cause and effect relationships between different variables can be impossible. NoiseSplats is introduced to represent two or more properties in a single volume rendering of the data. This technique is also aimed at providing a qualitative overview of the flows

New techniques for the scientific visualization of three-dimensional multi-variate and vector fields

Volume rendering allows us to represent a density cloud with ideal properties (single scattering, no self-shadowing, etc.). Scientific visualization utilizes this technique by mapping an abstract variable or property in a computer simulation to a synthetic density cloud. This thesis extends volume rendering from its limitation of isotropic density clouds to anisotropic and/or noisy density clouds. Design aspects of these techniques are discussed that aid in the comprehension of scientific information. Anisotropic volume rendering is used to represent vector based quantities in scientific visualization. Velocity and vorticity in a fluid flow, electric and magnetic waves in an electromagnetic simulation, and blood flow within the body are examples of vector based information within a computer simulation or gathered from instrumentation. Understand these fields can be crucial to understanding the overall physics or physiology. Three techniques for representing three-dimensional vector fields are presented: Line Bundles, Textured Splats and Hair Splats. These techniques are aimed at providing a high-level (qualitative) overview of the flows, offering the user a substantial amount of information with a single image or animation. Non-homogenous volume rendering is used to represent multiple variables. Computer simulations can typically have over thirty variables, which describe properties whose understanding are useful to the scientist. Trying to understand each of these separately can be time consuming. Trying to understand any cause and effect relationships between different variables can be impossible. NoiseSplats is introduced to represent two or more properties in a single volume rendering of the data. This technique is also aimed at providing a qualitative overview of the flows

Shape deformations based on vector fields

This thesis explores applications of vector field processing to shape deformations. We present a novel method to construct divergence-free vector fields which are used to deform shapes by vector field integration (Chapter 2). The resulting deformation is volume-preserving and no self-intersections occur. We add more controllability to this approach by introducing implicit boundaries (Chapter 3), a shape editing method which resembles the well-known boundary constraint modeling metaphor. While the vector fields are originally defined in space, we also present a surface-based version of this approach which allows for more exact boundary selection and deformation control (Chapter 4). We show that vectorfield- based shape deformations can be used to animate elastic motions without complex physical simulations (Chapter 5). We also introduce an alternative approach to exactly preserve the volume of skinned triangle meshes (Chapter 6). This is accomplished by constructing a displacement field on the mesh surface which restores the original volume after deformation. Finally, we demonstrate that shape deformation by vector field integration can also be used to visualize smoke-like streak surfaces in dynamic flow fields (Chapter 7).In dieser Dissertation werden verschiedene Anwendungen der Vektorfeldverarbeitung im Bereich Objektdeformation untersucht. Wir präsentieren eine neuartige Methode zur Konstruktion von divergenzfreien Vektorfeldern, welche mittels Integration zum Deformieren von Objekten verwendet werden (Kapitel 2). Die so entstehende Deformation ist volumenerhaltend und keine Selbstüberschneidungen treten auf. Inspiriert von etablierten, auf Randbedingungen beruhenden Methoden, erweitern wir diese Idee hinsichtlich Kontrollierbarkeit mittels impliziten Abgrenzungen (Kapitel 3). Während die ursprüngliche Konstruktion im Raum definiert ist, präsentieren wir auch eine oberflächenbasierte Version, welche ein genaueres Festlegen der Abgrenzungen und bessere Kontrolle ermöglicht (Kapitel 4). Wir zeigen, dass vektorfeldbasierte Deformationen auch zur Animation von elastischen Bewegungen benutzt werden können, ohne dass komplexe Simulationen nötig sind (Kapitel 5). Des weiteren zeigen wir eine alternative Möglichkeit, mit der man das Volumen von Dreiecksnetzen erhalten kann, welche mittels Skelett-Animation deformiert werden (Kapitel 6). Dies erreichen wir durch ein Deformationsfeld auf der Oberfläche, das das ursprüngliche Volumen wieder hergestellt. Wir zeigen außerdem, dass Deformierungen mittels Vektorfeld-Integration auch zur Visualisierung von Rauch in dynamischen Flüssen genutzt werden können(Kapitel 7)