About raw2alpha cuda code

[MinJunKang]

Hi, thanks for your great work. The code that calculates the alpha value from density uses this one :

alpha = 1 - (1 + exp(density + shift)) ^ (-interval)

However, I found that the original nerf uses the equation to calculate alpha from density as :

alpha = 1 - exp(-density * interval)

My question is

(1) What is the difference between those two representations?

(2) Why do we have to use a custom cuda kernel for calculating alpha instead of using torch library? I am curious about this in terms of the improvement of speed.

[MinJunKang]

Sorry my bad, I should have read section 4 of the manuscript, "Density voxel grid for volume rendering". But I am still curious about the second one.