so me and a buddy have been working on a Black Hole render engine for quiet a while now. And at this point we have most of the technical stuff worked out. Which results in images like these; 
Note, the red coloration is just for testing purposes. Also, if anyone cares, the Render time on this is about 20minutes with 5 Supersamples, so the entire image is rendered 5 times with slight offsets to the initial conditions to achive Anti Alisasing. And if anyone wonders, the reason why the Einstein ring´s are darker is because the rays go straight through the disk in these areas. So the Optical depth is smaller.
Now, originally we had done Redshift & Doppler beaming on a 2D disk, which yielded results like these; 
Because it used to be a 2D disk, we were able to make some drastic assumptions about the Frequency shift. This was only possible because rays would simply terminate as soon as they hit the disk. I.e the integration stopped right then and there.
However, with a Volumetric disk this is no longer possible. Now, the only way for a ray to just stop integrating is if it either hits the Event Horizon or its displacement is larger than the drawing distance (150 units). If a ray wants to orbit the black hole for 100000 Steps and pass through the disk 10 times, it is free to do so.
For transparency sake, this is what happened when we used our 2D Algorithm on the Volumetric disk; 
Besides some pixels having infinit color values, it is rather clear what the issue is. It looks very unphysical and a lot of the color spectical is gone.
As such, the question is if there is anything special to consider with this set up ? Do we, for example, have to take samples of the local Redshift each time a ray is inside a Volume and use these all together ? Or does only the last position a ray had before leaving the disk for good matter ? Atm we are working on the assumption that we have to sample the redshift (and blueshift) throughout the disk and use all of these values to arrive at a final Redshift factor for any given ray / pixel. We thing this is needed because of Gravitational Redshift, which would be a factor for all Rays not just the ones that meet the disk.
Lastly, and these are not the main questions, if any of you have good resources on the temperature / Density and velocity distribution in an accretion disk, those would be very welocome :D
So yeah, i hope i explained the issue enough. Thank you for reading !
