Introduction

Einstein's theory of special relativity is widely regarded as a difficult and hardly comprehensible theory, even today - more than ninety years after its publication in 1905. One important reason for this is that the properties of space, time, and light in relativistic physics are totally different from those in classical, Newtonian physics. In many respects, they are contrary to human experience and everyday perception, which is based on low velocities.

In the real world, mankind is limited to very small velocities compared to the speed of light. For example, the speed of light is a million times faster than the speed of an airplane and 40,000 times faster than the speed at which the Space Shuttle orbits the Earth. Even in the long term future, there is no hope of achieving velocities comparable to the speed of light.

Therefore, computer simulations are the only means of visually exploring the realm of special relativity. They enable us to experience special relativistic phenomena such as Lorentz contraction, time dilation, aberration, and finite speed of light. Thus they can help to establish a more intuitive approach to special relativity.

Visualization Techniques

Today, there exist two well-known techniques for rendering of fast moving objects. The first is an extension of normal three-dimensional ray-tracing. The second is a relativistic extension of polygon-rendering.

Relativistic ray-tracing can generate very accurate images of fast moving objects. It is very well suited for the production of high-quality pictures and movies. However, like normal ray-tracing, it has high computational costs and cannot be used for real-time visualization of special relativity (it least not on widely available hardware).

Relativistic polygon-rendering makes use of modern computer graphics hardware and allows special relativistic visualization in real-time. Based on relativistic polygon-rendering, the project Virtual Relativity deals with the implementation of a virtual environment for special relativity. Another field of research is the consideration of special relativistic effects on illumination.

A more detailed presentation of the theoretical background of both rendering techniques can be found in our Vismath 97 paper[1] and WSCG 2000 paper[4].

In our Vis 99 paper[2] and VisSym 00 paper[5], a texture mapping approach to special relativistic visualization is introduced. This novel rendering technique makes use of modern computer graphics hardware, in particular texture mapping and advanced per-pixel operations, and allows the visualization of the relativistic aberration of light, the Doppler effect, and the searchlight effect at interactive frame rates.

In our Vis 2000 paper[7], another novel rendering technique for special relativity is proposed. It is an image-based method which allows to render high speed flights through real-world scenes filmed by a standard camera. Here, the relativistic effects are taken into account by a modification of the so-called plenoptic function. Therefore, all known image-based non-relativistic rendering methods can easily be extended to incorporate relativistic rendering.

Pictures and Movies

Check out the picture and movie gallery !

Contact

Contact: Daniel Weiskopf

References

[1] R. Rau, D. Weiskopf, H. Ruder: Special Relativity in Virtual Reality, Mathematical Visualization, H.-C. Hege, K. Polthier (eds.), Springer 1998, 269-279.

[2] D. Weiskopf: A Texture Mapping Approach for the Visualization of Special Relativity, IEEE Visualization '99 Late Breaking Hot Topics Proceedings, A. Varshney, C.M. Wittenbrink, H. Hagen (eds.), ACM Press, October 1999, 41-44.

[3] D. Weiskopf, U. Kraus, H. Ruder: Searchlight and Doppler Effects in the Visualization of Special Relativity: A Corrected Derivation of the Transformation of Radiance, ACM Transactions of Graphics, Vol. 18, No. 3, July 1999, 278-292.

[4] D. Weiskopf: An Immersive Virtual Environment for Special Relativity, WSCG Conference Proceedings, V. Skala (ed.), University of West Bohemia, Pilsen, February 2000, 337-344.

[5] D. Weiskopf: Fast Visualization of Special Relativistic Effects on Geometry and Illumination, Data Visualization 2000 (Proceedings of the EG/IEEE TCVG Symposium on Visualization), W. de Leeuw, R. van Liere (eds.), Springer 2000, Wien, 219-228.

[6] D. Weiskopf, U. Kraus, H. Ruder: Illumination and Acceleration in the Visualization of Special Relativity: A Comment on Fast Rendering of Relativistic Objects, Journal of Visualisation and Computer Animation, 2000, Vol. 11, 185-195.

[7] D. Weiskopf, D. Kobras, H. Ruder: Real-World Relativity: Image-Based Special Relativistic Visualization, IEEE Visualization 2000 Proceedings, T. Ertl, B. Hamann, A. Varshney (eds.), ACM Press, October 2000, 303-310.