Relativistic Ray Tracing

Frederick Akalin

The goal of this project is to extend the pbrt renderer to handle special relativity. That is, the velocities of the camera and the objects in the scene will be taken into account when ray-tracing.

Whether this project falls under the heading of physically-based rendering is debatable; on one hand, special relativity provides a more accurate physical model of the world, yet on the other hand it is unlikely that, aside from the relativistic doppler shifting of objects in space, one will be able to see the more exotic effects predicted by relativity, like length contraction, in real life. However, since one would not be able to see relativistic effects in real life, it would be interesting for a program to be able to render such scenes, and perhaps useful to gain an intuition for relativity.

A more practical reason for picking this project is that it is easily adaptable to difficulty or time constraints; there are many independent relativistic effects that can be implemented, like the velocity of the camera, the velocity of the objects, Terrel rotation, relativistic abberation, and relativistic doppler shift. Therefore it is almost guaranteed that I will have something to show at the end of the quarter, even if it is a relatively (no pun intended) simple effect.

The main technical challenge would be to gain enough familiarity with the pbrt system to be able to modify it to handle relativity. For starters, instead of light rays in 3-d space, light rays in 4-d space-time would have to be ray-traced instead. Some of the more low-level aspects of pbrt, which we haven't studied in detail, would have to be modified. Also, understanding the mathematics behind relativity--that is, the modern 4-d formalism--would be non-trivial.

The main paper I will use for reference (at least in the beginning) is Relativistic ray-tracing: simulating the visual appearance of rapidly moving objects. It describes the extended model which takes into account the motion of the camera. If this is not challenging enough, this page provides more examples of effects to render, and the accompanying paper describes some of the effects of relativity. A possible plan after the above has been implemented would be: 1) take into account the motion of the objects; 2) implement relativistic abberation; 3) and implement relativistic doppler shift.

Below are some images from the abovementioned site which demonstrates relativistic effects. (Shamelessly leeched from the original site, but only a few people are going to see this.)

Static A tram at rest.	Warped A tram in motion appears to be Terrel rotated, or equivalently, shortened and sheared.	Darkened With all relativistic effects visible, the light from the tram is Doppler-shifted to higher frequencies (blueshifted) and darkened due to time dilation and geometrical effects.
Newton A desert highway scene.	+Aberration The scene corrected for aberration at 0.76c.	+Doppler The scene corrected for aberration and Doppler shift.
+Intensity The scene with all relativistic effects, including head-lighting / intensity effects.	Terrel Rotation A Terrel-rotated cube.	Static Flying inside a cube at 0.99c.
Earth Objects that present a circular outline, like the Earth, present a circular outline regardless of velocity - but can still appear distorted.	Starfield The starfield appears bunched and is Doppler shifted.	Speed Limit A close-up of the speed sign.