3
$\begingroup$

I was reading a paper about voxel cone tracing and came across this term. So, what is a Gaussian Lobe or a Lobe in general?

I am asking in the context of Computer Graphics, BRDF and NDF.

$\endgroup$

2 Answers 2

2
$\begingroup$

In a BRDF or NDF this most likely refers to a spherical Gaussian distribution, also known as a von Mises–Fisher distribution.

It's similar to the usual Gaussian, but using the dot product between two unit vectors as a measure of distance to the mean:

$$ p(\hat v) = a \exp(\lambda(\hat \mu \cdot \hat v))$$

where $a$ is a normalization factor, $\lambda$ is a number controlling the width of the lobe (roughly corresponds to $1/2\sigma^2$ in the usual Gaussian), $\hat \mu$ is the unit direction vector for the mean of the lobe, and $\hat v$ is the unit direction vector at which we're evaluating the lobe.

(You'll also sometimes see it defined with $\lambda(\hat \mu \cdot \hat v - 1)$ in the exponent, but the $-1$ term can be pulled out and rolled into the normalization factor.)

$\endgroup$
1
$\begingroup$

Having a gaussian lobe usually means that your ndf is one or a weighted sum of gaussian distributions. Instead of your ndf, you can define your brdf in the same way.

A gaussian distribution is a function of the form $$\frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$

It has a hat shape common to many ndfs; this is good because it mimicks how normals align in most real world materials

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.