Texture prefiltering for Linearly Transformed Cosines

I’m implementing Real-Time Polygonal-Light Shading with Linearly Transformed Cosines from Siggraph 2016.

I’m stuck on the texture prefiltering (section 5.3).

As I understand they use Gaussian Blur on the texture, but clamp and normalize kernel to fragments that intersect the original texture.

But how do they create the margin? I have tried proper Gaussian with 2D kernel and 2 pass Gaussian but neither seems similar to what is in the paper.

Also how should weight of Gaussian be chosen?

Or maybe I’m totally wrong and it is something more than simple Gaussian?

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