In computer graphics, many ray tracers approximate the Rendering Equation up to a specific depth. Intuitively, this is okay because the deeper a path is, the more energy it will absorb. As I cannot find any online resource that proves this mathematically, I have tried to do so myself using the rendering equation, but without luck. I would like some help in proving it, and I think others can benefit from having a reference to such a proof.
- The question is too mathematical for the Computer Graphics forum. (These questions are more about graphics, not so much about their mathematical foundations. There doesn't even exist a tag named rendering-equation :(.)
- The question is too physical for the Mathematics forum. (The rendering equation and the property I would like to proof have a physical foundation. Also "It's just integrals? Ask a physicist!")
- The question is too computer-sciency for the Physics forum. (I cannot find any tags that would be related to my question. Although the rendering equation is based on physics, it is actually nowhere to be found in the branch of physics itself.)
Which one of these sites would then be the most appropriate?
As a side note, I actually posted my question on the Graphics forum, but without reaction for the reason I mentioned, and because this forum is still in beta.
As asked by @RobertLongson, I posted the question here on the Meta Mathematics Exchange.