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I have a made a planet and wanted to make an atmosphere around it. So I was referring to this site:

Click to visit site

I don't understand this:

As with the lookup table proposed in Nishita et al. 1993, we can get the optical depth for the ray to the sun from any sample point in the atmosphere. All we need is the height of the sample point (x) and the angle from vertical to the sun (y), and we look up (x, y) in the table. This eliminates the need to calculate one of the out-scattering integrals. In addition, the optical depth for the ray to the camera can be figured out in the same way, right? Well, almost. It works the same way when the camera is in space, but not when the camera is in the atmosphere. That's because the sample rays used in the lookup table go from some point at height x all the way to the top of the atmosphere. They don't stop at some point in the middle of the atmosphere, as they would need to when the camera is inside the atmosphere.

Fortunately, the solution to this is very simple. First we do a lookup from sample point P to the camera to get the optical depth of the ray passing through the camera to the top of the atmosphere. Then we do a second lookup for the same ray, but starting at the camera instead of starting at P. This will give us the optical depth for the part of the ray that we don't want, and we can subtract it from the result of the first lookup. Examine the rays starting from the ground vertex (B 1) in Figure 16-3 for a graphical representation of this.

First Question - isn't optical depth dependent on how you see that is, on the viewing angle? If yes, the table just gives me the optical depth of the rays going from land to the top of the atmosphere in a straight line. How to find the optical depth in the case where the ray pierces the atmosphere and goes through it to the camera?

Second Question - What is the vertical angle it is talking about...like, is it the same as the angle with the z-axis as we use in polar coordinates? (I am having a very hard time understanding this angle)

Third Question - The article talks about scattering of the rays going to the sun..shouldn't it be the other way around? like coming from the sun to a point?

Any explanation on the article or on my questions will help a lot.

Thanks in advance!

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    \$\begingroup\$ For your third question, consider that any mathematical ray we trace from the camera to the sun is a path that a ray of light or photon can trace in reverse, from the sun to the camera. We don't care about the direction the ray is traversed, we care that there is a path for the light to take. \$\endgroup\$
    – DMGregory
    Jun 2 '20 at 11:58
  • \$\begingroup\$ Thanks! @DMGregory ....can you help me understand the angle in the second question since I think that it is the thing that is causing all the problems? \$\endgroup\$
    – Ridayesh
    Jun 2 '20 at 12:05
  • \$\begingroup\$ You already asked that question above. You don't need to repeat your question in the comments. When someone has an answer for you, they'll post it in the Answers section below. \$\endgroup\$
    – DMGregory
    Jun 2 '20 at 12:27

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