Ideas for Raytracing

Images rendered using Raytracing

A problem of making raytracing images using numerical geodesics is that raytracing requires to go backwards in time. For raytracing, an observer's position is given in space and time and the view direction (towards the screen pixel looked at). To do backward geodesic tracing one would have to complete a full numerical simulation and use the whole data set. This gives rise to the same problems as mentioned at the raytracing of free particles section, since the whole data set cannot be saved due to the large amount of data, whereby data subsets may be too inexact (but not necessarily, as Bernhard Schutz commented, because the demands of accuracy and stability for the set of pde's might be lower as that required to get a good null geodesic and the numerical metric to get required raytracing accuracy does not necessarily have the resolution of the numerical grid.).
This problem possibly has already been solved, since the same method of `backtracing in time' is used when event horizons determined. In this case light like geodesics are traced backwards to see if they meet at the same region, and if this is the case, this region has the properties of an event horizon. However this horizon finder currently only works for axisymmetric situations and not for generic 3D situations (Miguel Alcubierre), and it is optimized just to find null horizons, not to truly compute backwards lightlike geodesics (Paul Walker).

Currently, 50-10.000 time forward geodesics can be computed instaneously at simulation time without too much influence to the whole simulation process.

An idea which yet has to be discussed is the idea of doing a `time backward simulation'. At a first step, a complete GR simulation could be made whereby only the initial and the final data set are saved. Then the final data set could be used as initial data set and a new simulation process now can generate time backward geodesics as they are required for the raytracing process. This is similar as one would look at the white whole solution instead of looking at the black hole solution. The saved initial data set could then be used to compare the results of the final backward simulation data with the `initial initial' data as an accuracy test. Also various intermediate stages from the forward simulation stage could be used for the backward simulation, so that the backward simulation is just some kind of `interpolation' between various steps, which have been saved.

The achievable image quality is questionable. Special properties of the space time like the Photon Orbit of a static black hole could probably not be reveiled with numerical space times (P.Walker). E.g. a simulation using the exact solution used a resolution of 1E-16m to get a smooth output. So it would be of interest to get known to the limits of raytracing using numerical relativity data.

Special problems

A special problem to do raytracing within curved space times are the simulation of stars, as demonstrated in this frame from the simulation series The Black Earth:

Stars are too small to be resolved by physical detectors, but `blurr out' to appear as spheres due to the limited resolution (diffraction, filme coarseness etc.) of the detector. The current idea to solve this problem is to treat each star as an spherical gaussian intensity function at the background. This works good for flat space time and produces spherical stellar images. However in curved space time stellar images become distorted and appear as ellipsoids or large arcs of various size, as it should happen to galaxies due to gravitational lenses. But this is not what would happen to true stars, since even by gravitational lensing stars would not change their appearance in the sense that they would still be point sources, but with some different position and intensity as compared to flat space. This problem requires the computation of expansion, shear and twist along each backward-traced geodesic.

Static Raytracing