question to to Eq.4

[yuedajiong]

"diagonal matrix with only one nonzero value on the diagonal (the other two being much smaller)"
@ #2

‘flat’: only-one nonzero OR “at-most-two nonzero” ?

at-most-two nonzero includes:
2-nonzero: flat / plane
1-nonzero: thin / line

for example, a single Gaussian point, the scaling is x_y_z: [0.1, 0.2, 0.3]
In Eq.4, does the s_g mean 0.1, and n_g mean 0 : x-axis?

Thanks

[XOURTNEY]

I think the author means Sg is really small, then 1/Sg would be bigger than the others.
When considering to the scale matix, 1/sg would be the only number while others are ≈0.
So the Sg means the scale along z-axis and Sg is 1e-5 or even smaller, ng means z-axis, and ng would be the 3rd roll of rotation matirx.
not sure if i get the author right.