Abstract We present a novel approach for rendering volumetric data including the Doppler effect of light. Similar to the acoustic Doppler effect, which is caused by relative motion between a sound emitter and an observer, light waves also experience compression or expansion when emitter and observer exhibit relative motion. We account for this by employing spectral volume rendering in an emission–absorption model, with the volumetric matter moving according to an accompanying vector field, and emitting and attenuating light at wavelengths subject to the Doppler effect. By introducing a novel piecewise linearear representation of the involved light spectra, we achieve accurate volume rendering at interactive frame rates. We compare our technique to rendering with traditional point‐based spectral representation, and demonstrate its utility using a simulation of galaxy formation.

In this paper, we present Gaia Sky, a free and open-source multiplatform 3D Universe system, developed since 2014 in the Data Processing and Analysis Consortium framework of ESA's Gaia mission. Gaia's data release 2 represents the largest catalog of the stars of our Galaxy, comprising 1.3 billion star positions, with parallaxes, proper motions, magnitudes, and colors. In this mission, Gaia Sky is the central tool for off-the-shelf visualization of these data, and for aiding production of outreach material. With its capabilities to effectively handle these data, to enable seamless navigation along the high dynamic range of distances, and at the same time to provide advanced visualization techniques including relativistic aberration and gravitational wave effects, currently no actively maintained cross-platform, modern, and open alternative exists.

We present a technique to visualize the streamline-based mapping between the boundary of a simply-connected subregion of arbitrary 3D vector fields. While the streamlines are seeded on one part of the boundary, the remaining part serves as escape border. Hence, the seeding part of the boundary represents a map of streamline behavior, indicating if streamlines reach the escape border or not. Since the resulting maps typically exhibit a very fine and complex structure and are thus not amenable to direct sampling, our approach instead aims at topologically consistent extraction of their boundary. We show that isocline surfaces of the projected vector field provide a robust basis for stream-surface-based extraction of these boundaries. The utility of our technique is demonstrated in the context of transport processes using vector field data from different domains.

Special relativistic visualization offers the possibility of experiencing the optical effects of traveling near the speed of light, including apparent geometric distortions as well as Doppler and searchlight effects. Early high-quality computer graphics images of relativistic scenes were created using offline, computationally expensive CPU-side 4D ray tracing. Alternate approaches such as image-based rendering and polygon-distortion methods are able to achieve interactivity, but exhibit inferior visual quality due to sampling artifacts. In this paper, we introduce a hybrid rendering technique based on polygon distortion and local ray tracing that facilitates interactive high-quality visualization of multiple objects moving at relativistic speeds in arbitrary directions. The method starts by calculating tight image-space footprints for the apparent triangles of the 3D scene objects. The final image is generated using a single image-space ray tracing step incorporating Doppler and searchlight effects. Our implementation uses GPU shader programming and hardware texture filtering to achieve high rendering speed.

Abstract We present a methodical new approach to visualize the aspects of general relativity from a self‐centered perspective. We focus on the visualization of the Gödel universe, which is an exact solution to Einstein's field equations of general relativity. This model provides astounding features such as the existence of an optical horizon and the possibility of time travel. Although we know that our universe is not of Gödel type, we can – using this solution to Einstein's equations – visualize and understand the effects resulting from the theory of relativity, which itself has been verified on the large scale in numerous experiments over the last century. We derive the analytical solution to the geodesic equations of Gödel's universe for special initial conditions. Along with programmable graphics hardware we achieve a tremendous speedup for the visualization of general relativity. This enables us to interactively explore the physical aspects and optical effects of Gödel's universe. We also demonstrate how the analytical solution enables dynamic lighting with local illumination models. Our implementation is tailored for Gödel's universe and five orders of magnitude faster than previous approaches. It can be adapted to manifolds for which an analytical expression of the propagation of light is available.

This paper describes methods for explanatory and illustrative visualizations used to communicate aspects of Einstein's 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.

In this application paper, we report on over fifteen years of experience with relativistic and astrophysical visualization, which has been culminating in a substantial engagement for visualization in the Einstein Year 2005 - the 100/sup th/ anniversary of Einstein's publications on special relativity, the photoelectric effect, and Brownian motion. This paper focuses on explanatory and illustrative visualizations used to communicate aspects of the difficult theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. We discuss visualization strategies, motivated by physics education and 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. Although our visualization tools build upon existing methods and implementations, these techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, 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.