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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.

Problem

  • 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.

EDIT

As asked by @RobertLongson, I posted the question here on the Meta Mathematics Exchange.

  • Seems more maths than anything, have you tried asking on maths (or physics) meta whether they think this question would be OK? – Robert Longson May 10 at 15:09
  • @RobertLongson I haven't yet. But if you think it's primarily maths, then I will also ask it on the meta there. We will see. – Safron May 10 at 15:26
  • "but without reaction for the reason I mentioned" It's only been 8 hours! – muru May 10 at 17:35
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This is an interesting question that requires cross-discipline knowledge.

In my opinion, it can be on-topic in several communities; therefore, you may want to choose where to post it using your judgment of whom you want it to be answered.

Currently, you posted it in Computer Graphics, and I would encourage you to give the community the chance to answer the question. It's been only several hours. If you don't see enough attention to your question, you certainly can post it to other community: Consult the cross-posting guidance, please, don't simply post it at as many places as possible without deleting/modifying your question.

This question would be also on-topic on Computational Science SE, which you may consider later.

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    Okay. For now, I will leave the question on the Computer Graphics exchange. When there is no attention there, I will follow the cross-posting guidance to move the question to another community. – Safron May 10 at 17:57

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