In my previous question I have asked about an effect on how to visualize light spheres. The question resulted in a very nice formulated answer which described pretty well how to achieve this by adding some fog to the scene and using some factor to weight different light samples on the rays from the camera to the scene.
However, since performance was too bad when testing it on the Xbox when taking shadows in account (
texCUBElod lookups seem to be expensive) in split-screen multiplayer, I wanted to solve the resulting integral (which is currently approximated by a Riemann's sum) analytically without taking shadows into account.
I could reduce the pixel shader code to some formula, but was unable to solve it. So, I've put up another question on the mathematics stackexchange. It was answered fast, but the responder could not come up with any way I could use to solve this in an efficient way.
The question remains, how the performance could be increased without losing awesomeness of the lighting effect. (It does not have to be physically correct, so, if there are methods to increase performance but take away realism, I would like to hear about them.)