Tobias Schafhitzel

GPU-Based Nonlinear Ray Tracing

In this paper, we present a mapping of nonlinear ray tracing to the GPU which avoids any data transfer back to main memory. The rendering process consists of the following parts: ray setup according to the camera parameters, ray integration, ray‐object intersection, and local illumination. Bent rays are approximated by polygonal lines that are represented by textures. Ray integration is based on an iterative numerical solution of ordinary differential equations whose initial values are determined during ray setup. To improve the rendering performance, we propose acceleration techniques such as early ray termination and adaptive ray integration. Finally, we discuss a variety of applications that range from the visualization of dynamical systems to the general relativistic visualization in astrophysics and the rendering of the continuous refraction in media with varying density.

Point-based stream surfaces and path surfaces

We introduce a point-based algorithm for computing and rendering stream surfaces and path surfaces of a 3D flow. The points are generated by particle tracing, and an even distribution of those particles on the surfaces is achieved by selective particle removal and creation. Texture-based surface flow visualization is added to show inner flow structure on those surfaces. We demonstrate that our visualization method is designed for steady and unsteady flow alike: both the path surface component and the texture-based flow representation are capable of processing time-dependent data. Finally, we show that our algorithms lend themselves to an efficient GPU implementation that allows the user to interactively visualize and explore stream surfaces and path surfaces, even when seed curves are modified and even for time-dependent vector fields.

Topology-preserving λ 2 -based vortex core line detection for flow visualization

We propose a novel vortex core line extraction method based on the λ2 vortex region criterion in order to improve the detection of vortex features for 3D flow visualization. The core line is defined as a curve that connects λ2 minima restricted to planes that are perpendicular to the core line. The basic algorithm consists of the following stages: (1) λ2 field construction and isosurface extraction; (2) computation of the curve skeleton of the λ2 isosurface to build an initial prediction for the core line; (3) correction of the locations of the prediction by searching for λ2 minima on planes perpendicular to the core line. In particular, we consider the topology of the vortex core lines, guaranteeing the same topology as the initial curve skeleton. Furthermore, we propose a geometry‐guided definition of vortex bifurcation, which represents the split of one core line into two parts. Finally, we introduce a user‐guided approach in order to narrow down vortical regions taking into account the graph of λ2 along the computed vortex core line. We demonstrate the effectiveness of our method by comparing our results to previous core line detection methods with both simulated and experimental data; in particular, we show robustness of our method for noise‐affected data.

Explanatory and illustrative visualization of special and general relativity

This paper describes methods for explanatory and illustrative visualizations used to communicate aspects of Einsteins theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. Our illustrations target a general audience of laypersons interested in relativity. We discuss visualization strategies, motivated by physics education and the didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Our primary approach is to adopt an egocentric point of view: the recipients of a visualization participate in a visually enriched thought experiment that allows them to experience or explore a relativistic scenario. In addition, we often combine egocentric visualizations with more abstract illustrations based on an outside view in order to provide several presentations of the same phenomenon. Although our visualization tools often build upon existing methods and implementations, the underlying techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, special relativistic 4D ray tracing for accelerating scene objects, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.

Real-time advection and volumetric illumination for the visualization of 3D unsteady flow

This paper presents an interactive technique for the dense texture-based visualization of unsteady 3D flow, taking into account issues of computational efficiency and visual perception. High efficiency is achieved by a novel 3D GPU-based texture advection mechanism that implements logical 3D grid structures by physical memory in the form of 2D textures. This approach results in fast read and write access to physical memory, independent of GPU architecture. Slice-based direct volume rendering is used for the final display. A real-time computation of gradients is employed to achieve volume illumination. Perception-guided volume shading methods are included, such as halos, cool/warm shading, or color-based depth cueing. The problems of clutter and occlusion are addressed by supporting a volumetric importance function that enhances features of the flow and reduces visual complexity in less interesting regions.

Texture-Based Visualization of Unsteady 3D Flow by Real-Time Advection and Volumetric Illumination

This paper presents an interactive technique for the dense texture-based visualization of unsteady 3D flow, taking into account issues of computational efficiency and visual perception. High efficiency is achieved by a 3D graphics processing unit (GPU)-based texture advection mechanism that implements logical 3D grid structures by physical memory in the form of 2D textures. This approach results in fast read and write access to physical memory, independent of GPU architecture. Slice-based direct volume rendering is used for the final display. We investigate two alternative methods for the volumetric illumination of the result of texture advection: First, gradient-based illumination that employs a real-time computation of gradients, and, second, line-based lighting based on illumination in codimension 2. In addition to the Phong model, perception-guided rendering methods are considered, such as cool/warm shading, halo rendering, or color-based depth cueing. The problems of clutter and occlusion are addressed by supporting a volumetric importance function that enhances features of the flow and reduces visual complexity in less interesting regions. GPU implementation aspects, performance measurements, and a discussion of results are included to demonstrate our visualization approach.

Applications of Texture-Based Flow Visualization

Abstract Flow visualization is a classic sub-field of scientific visualization. The task of flow visualization algorithms is to depict vector data, i.e., data with magnitude and direction. An important category of flow visualization techniques makes use of textures in order to convey the properties of a vector field. Recently, several research advances have been made in this special category, of dense, texture-based techniques. We present the application of the most recent texture-based techniques to real world data from oceanography and meteorology, computational fluid dynamics (CFD) in the automotive industry, and medicine. We describe the motivations for using texture-based algorithms as well as the important recent advancements required for their successful incorporation into industry grade software. Our goal is to appeal to practitioners in the field interested in learning how these recent techniques can help them gain insight into problems that engineers and other professionals may be faced with on a daily basis. Many of these applications have only recently become possible.

Employing Complex GPU Data Structures for the Interactive Visualization of Adaptive Mesh Refinement Data

We present a framework for interactively visualizing volumetric Adaptive Mesh Renement (AMR) data. For this purpose we employ complex data structures to map the entire AMR dataset to graphics memory. This allows to apply hardware accelerated visualization algorithms previously only operating on uniform cartesian grids. For mapping the data to graphics memory we consider two approaches, a space-efcient, texture-based octree and a fast method based on page table address translation. We demonstrate the utility of our approach by extending an existing GPU raycasting implementation to render AMR data. As a r st step to vector eld visualization techniques we successfully integrated our framework into a commercial CFD postprocessing tool and visualized scalar properties of the vector eld.

Visualizing the Evolution and Interaction of Vortices and Shear Layers in Time-Dependent 3D Flow

In this paper, we present a visualization and tracking system for coherent structures. For this purpose, we propose to consider shear stress-the stretching and shear of particles inside a flow-in vortex dynamics. Based on a discussion and comparison of recent methods for computing shear stress, we introduce visualization techniques in order to provide a representation of shear layers according to their physical interpretation. This paper contributes a combination of theory in fluid mechanics and the corresponding visualization: 1) shear layer criteria are assessed according to how well they can be combined with common vortex identification criteria; 2) sheets of maximal shear are introduced as an appropriate visual representation of shear layers; 3) a visualization method is described for simultaneous tracking of vortices and shear layers as well as their interaction; and 4) the relevance of shear layers in vortex dynamics is demonstrated by means of several examples. We have implemented these new techniques in an interactive visualization system for time-dependent 3D flow. The system is used by fluid mechanics experts in their research of shear-vortex interaction.

Panorama maps with non-linear ray tracing

We present a framework for the interactive generation of 3D panorama maps. Our approach addresses the main issue that occurs during panorama map construction: non-linear projection or deformation of the terrain in order to minimize the occlusion of important information such as roads and trails. Traditionally, panorama maps are hand-drawn by skilled illustrators. In contrast, our approach provides computer support for the rendering of non-occluded views of 3D panorama maps, where deformations are modeled by nonlinear ray tracing. The deflection of rays is influenced by 2D and 3D force fields that directly consider the shape of the terrain. In addition, our framework allows the user to further modify the force fields to have fine control over the deformations of the panorama map. User interaction is facilitated by our real-time rendering system in terms of linked multiple views of both linear and non-linear projected terrain and the deformed view rays. Fast rendering is achieved by GPU-based non-linear ray tracing. We demonstrate the usefulness of our modeling and visualization method by several examples.