https://i.stack.imgur.com/rij3X.png
As in the image we can see that ray of light is bouncing off objects. Black ones are opaque objects and white ones are transparent objects. I want to calculate how many times a ray of light bounces to reach a particular point, "without tracing rays". I am looking for the mathematical equation(that takes scene and a point as its input and outputs the number of bounces) that tells how many times ray of light will bounce to reach a particular point.
Is this type of mathematical equation exists? If not, which area of mathematics should I study to find solution to this problem?
I don't see any way other than ray-tracing.
The rays reflect off the black rectangles and are refracted (presumably using Snell's law) by the white rectangles.
I noticed that either ray 2 or 3 near the bottom right seem to have been absorbed by a white rectangle.
It would be an interesting exercise to program this given a set of rectangles and the index of refraction of the white rectangles.
I wonder how much precomputation could be done, given the location and type of the rectangles, to speed up the ray tracing.