<p>In a BRDF or NDF this most likely refers to a <a href="https://mynameismjp.wordpress.com/2016/10/09/sg-series-part-2-spherical-gaussians-101/" rel="nofollow noreferrer">spherical Gaussian</a> distribution, also known as a <a href="https://en.wikipedia.org/wiki/Von_Mises%E2%80%93Fisher_distribution" rel="nofollow noreferrer">von Mises–Fisher distribution</a>.</p>

<p>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>

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

<p>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.</p>

<p>(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.)</p>

CC BY-SA 3.0
2018-02-22T18:22:44.773Z
2018-02-22T18:22:44.773Z
Nathan Reed
<p>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.</p>

<p>A <a href="https://en.m.wikipedia.org/wiki/Normal_distribution" rel="nofollow noreferrer">gaussian distribution</a> is a function of the form $$\frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$</p>

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

CC BY-SA 3.0
2018-02-22T16:49:56.507Z
2018-02-22T18:25:04.567Z
2018-02-22T18:25:04.567Z
Sebastián Mestre
<p>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?</p>

<p>I am asking in the context of Computer Graphics, BRDF and NDF.</p>

<mathematics><brdf><ndf>
What is a Gaussian Lobe concerning BRDF and NDF?
user1006274
# What is a Gaussian Lobe concerning BRDF and NDF?

(Asked by: username_0 on 2018-02-22)

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.

**Tags:** mathematics, brdf, ndf


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## 2 answers

### Answer by username_1 on 2018-02-22. Score: 2

In a BRDF or NDF this most likely refers to a [spherical Gaussian](https://mynameismjp.wordpress.com/2016/10/09/sg-series-part-2-spherical-gaussians-101/) distribution, also known as a [von Mises–Fisher distribution](https://en.wikipedia.org/wiki/Von_Mises%E2%80%93Fisher_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.)


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### Answer by username_2 on 2018-02-22. Score: 1

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](https://en.m.wikipedia.org/wiki/Normal_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


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