You have reached the End of the Evolving Visualization Sequence. This and following pages contain notes to myself.

- Don

Biblio Timeline: Chronological list of relativistic papers.

Don's sphere animations.

Best of Breed: 4D Ray Tracing w/ oversampling (>= x2 wavelength) at endpoints of wave.

Acceleration: "...relativistic rendering is not sensitive to acceleration of the camera" - Weiskopf.

These are Visualization Resources for upcoming projects (State of the Art in SR & GR Visualization).

1) Visualization Software

a) Newtonian Physics


b) Special Relativity

Werner: Light++

Weiskopf: Virtual Relativity, Tübingen

Hale: Einstein Explorer, University of London (SourceForge)

Joachim Diepstraten, Daniel Weiskopf, Thomas Ertl:
Automatic Generation and Non-Photorealistic Rendering of 2+1D Minkowski Diagrams

c) General Relativity

Werner: Light++ Blackhole Visualization

2) Visualization of Relativistic Objects in Flat Space. (SR)

a) Images

b) Videos

Black: Reflections

Van Devender: Relativistic Starflight, University of Oregon

Searle: Relativistic Optics, Australian National University

Walker: John Walker's C-ship, Independent

Weiskopf: Visualization of Relativity, Tübingen

Weiskopf: Virtual Relativity Gallery, Tübingen

3) Visualization of Relativistic Objects in Curved Space. (GR)

a) Images

b) Videos

Benger: International Numerical Relativity Group, NCSA

Nemiroff: Black Holes and Neutron Stars, Goddard

Hamilton: Falling Into a Black Hole, U of Colo, Boulder

Zahn: Vierdimensionales Ray-Tracing in einer gekrümmten Raumzeit,Tübingen

c) Courses

Norlund: Relativistic Dynamics and Visualization, Niels Bohr Institute

4) Visualization of Objects with Relativistic Rotations. (GR)

Zahn: Rollende Räder,Tübingen

Weiskopf: Rigidly rotating disk of dust

Hamilton: Cartwheel & Hypercubes U. of Colo, Boulder



Institute of Astronomy and Astrophysics Tübingen
Theoretical Astrophysics & Computational Physics

University of Colorado at Boulder
Center for Astrophysics and Space Astronomy

NASA Goddard Space Flight Center
Laboratory for High Energy Physics


1. M. Boas, Apparent shape of large objects at relativistic speeds, Amer J. Phys. 29 (1961), 283.

2. M.C. Chang, F. Lai, and W.C. Chen, Image shading taking into account relativist effects. ACM Transactions on Graphics, 15 (1996), 265-30.

3. W. Gekelman, J. Maggs, and L. Xu, Real-time relativity, Computers in Physics (1991), 372-385.

4. P.K. Hsiung, R.H.P Visualizing relativistic effects in spacetime, Proceedings of Supercomputing '89 Conference, 1989, pp 597-606.

5. R. Penrose, The apparent shape of a relativistic moving sphere, Proc. Cambr. Phil. Soc. 55 (1959), 137.

6. G. Scott and M. Driel, Geometrical appearances at relativistic speeds, Amer. J. Phys. 38 (1970), 971.

7. G. Scott and R. Viner,The geometrical appearance of large objects moving at relativistic speeds, Amer. J. Phys. 33 (1965), 534.

8. J. Terrel, Invisibility of the Lorentz contraction, Phys. Rev. 116 (1959), 1041.

9. P.-K. Hsiung, R.H. Thibadeau, C.B. Cox and R.H.P. Dunn, Time Dilation and Visualization in Relativity, In Proceedings of the Supercomputing '90 Conference, pages 835-844, 1990.

10. P.-K. Hsiung, R.H. Thibadeau, C.B. Cox, R.H.P. Dunn, M. Wu and P.A. Olbrich, Wide-Band Relativistic Doppler Effect Visualization, In Proceedings of the Visualization '90 Conference, pages 83-92, Oct. 1990.

11. P.-K. Hsiung, R.H. Thibadeau and M. Wu, Fast visualization of Relativistic Effects in Spacetime, Computer Graphics (1990 Symposium on Interactive 3D Graphics), 24 (2): (1990), 83-88.

12. V. F. Weiskopf, The Visual Appearance of Rapidly Moving Objects, Physics Today, 13 (9): (1960) 24-27.

13. Albert Einstein, Relativity, The Special and General Theory,1920

14. Daniel Weiskopf, Visualization of Four-Dimensional Spacetimes, Dissertation, University of Tübingen, 2001

15. D. Weiskopf, Four-Dimensional Non-Linear Ray Tracing as a Visualization Tool for Gravitational Physics, IEEE Visualization 2000 Proceedings, T. Ertl, B. Hamann, A. Varshney (eds.), ACM Press, October 2000, 445-448.

15. Andrew J. Hanson (Indiana University) and Daniel Weiskopf (University of Stuttgart), Further Reading - A List of Weiskopf's Papers, SIGGRAPH 2001 Course #15: "Visualizing Relativity" .

16. Max Born, Einstein's Theory of Relativity, 1924, Dover Publications, 1962

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