CODEWITHSUNDEEP
mathgraphicsgaussiandeviation
sHeldON
sHeldON

Reputation: 11

How the length of averaged normal can be seen as a function of deviation of the angle?

Recently I read NVidia's Mipmapping_Normal_Maps which says we can used the un-renormalized averaged normal to compute the standard deviation of the angle between averaged normal and sample normals. By the first step, 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 length of averaged normal is represented by a function of Standard Deviation of the angle(original function of Gaussian distribution, red curve in the figure)?

Upvotes: 0

Views: 73

Answers (1)

OrangeWombat
OrangeWombat

Reputation: 315

I believe the answer to your question is equation (1) in the paper. It shows how the averaged normal is equal to the reciprocal of 1 + sigma^2. Sigma is the standard deviation. Sometimes sigma^2 is called the variance.

At any rate, if you know the standard deviation, that's your value for sigma in the equations. Square it to get the variance, sigma^2.

Upvotes: 1

Related Questions