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.

In spring 1999, the Department for Theoretical Astrophysics of Tubingen University together with the Ministries of Science and of Education, Baden-Wurttemberg, started a global computing project called XPulsar@home. Its aim was to compute a large number of X-Ray Pulsar models with a Monte-Carlo-Simulation code. The simulation was implemented as a Java applet, later also as a Java application, running on private or school PCs of volunteer participants. The server structure consisted of one main server and several slave servers. The whole system, except for the Java virtual machines, was built from free software components. During the first four months, about 75 years of computation time was obtained, with several hundred clients. The major motivation to contribute was a competition among the high schools in Baden-Wurttemberg. The second objective of the competition was to make physics and astronomy more interesting and exciting for students through participation in a research project.

This paper describes a novel rendering technique for special relativistic visualization. It is an image-based method which allows to render high speed flights through real-world scenes filmed by a standard camera. The relativistic effects on image generation are determined by the relativistic aberration of light, the Doppler effect, and the searchlight effect. These account for changes of apparent geometry, color and brightness of the objects. It is shown how the relativistic effects can be taken into account by a modification of the plenoptic function. Therefore, all known image-based nonrelativistic rendering methods can easily be extended to incorporate relativistic rendering. Our implementation allows interactive viewing of relativistic panoramas and the production of movies which show super-fast travel. Examples in the form of snapshots and film sequences are included.

We address the issue of illumination and acceleration in special relativistic visualization. Betts (J. Visual. Comput. Animat. 1998; 9: 17–31) presents an incorrect derivation of the transformation of the Rayleigh–Jeans radiation, which we compare to the correct transformation of radiance in the framework of special relativity. His rendering algorithm can be modified to correctly account for the relativistic effects on illumination. Furthermore, we show how acceleration can be included in special relativistic visualization by calculating the trajectory of accelerating objects, which is a prerequisite for a physically based camera model. Therefore interaction and animation in special relativistic visualization are possible. Copyright © 2000 John Wiley & Sons, Ltd.

We demonstrate that a photo-realistic image of a rapidly moving object is dominated by the searchlight and Doppler effects. Using a photon-counting technique, we derive expressions for the relativistic transformation of radiance. We show how to incorportate the Doppler and searchlight effects in the two common techniques of special relativistic visualization, namely ray tracing and polygon rendering. Most authors consider geometrical appearance only and neglect relativistic effects on the lighting model. Chang et al. [1996] present an incorrect derivation of the searchlight effect, which we compare to our results. Some examples are given to show the results of image synthesis with relativistic effects taken into account.

This paper reports on progress we have made in modelling cosmic X-ray sources on supercomputers. The results we present are meant to serve as an example for the fact that sophisticated visualization techniques play a crucial role in scientific computing. Among the graphical methods we demonstrate, raytracing in curved space-time and a physically motivated 3D-volume rendering algorithm might be of interest to the graphics community in general.