Gaussian distribution of normals' angular deviation

Question

Recently I read NVidia's Mipmapping-Normal-Maps

In the "Estimating Normal Variation" section, it assumes a Gaussian distribution of the angular deviation and give a figure (sorry but I cannot post an image as a new user, please refer to Figure_2 in that paper).

Then my question is, how the Na is represented by a function of Standard Deviation?

Answer 1

The links doesn't work for me but I assume Na is what was represented normal distributed. The function for Na would be:

with:

• Na as the normal distributed value (x-axis value)
• sigma () as the standard variance
• f(Na) as the probability density (y-axis value)
• mu (µ) as the expected value (usually the average value)