[mediumfi]

One additional reason is that the projections of a Gaussian are also Gaussian (more generally any linear transform of a Gaussian is Gaussian). So if you have the parameters of a 3D Gaussian ellipsoid and a viewing angle, you can quite easily get the parameters of the corresponding 2D ellipse. So the ray marching algorithm turns into just blending a stack of 2D ellipses. For many other non Gaussian functions projection is trickier.

[enriquto]

Ah, that is a very good reason indeed! At least for projecting from 2D to 1D the gaussian is the only distribution with this property. The functional equation g(x)g(y)=g(√(x^2+y^2))g(0) determines the gaussian up to a constant.

[T-A]

Also, their derivative is just a multiplication (if normalized) or two (if not).

https://hannibunny.github.io/orbook/preprocessing/04gaussian...