Hello simin_sh
The truth is what is called "gaussian blur" is not exactly what is mathematically defined as a Gaussian function.
In BGRABitmap, the normal blur is in fact rather conic: the importance of neighbor pixels decreases linearly and at the radius it reaches zero. It is called "gaussian blur" in the menu of LazPaint, but that's not really. It is an approximation of it. We could however experiment, trying to generating a true Gaussian blur, and then see how it compares to other blur methods.
In Paint.NET, what is called "gaussian blur" is the fast blur of BGRABitmap. The importance of pixels decreases linearly as well, but both directions are accounted for separately, so it is does not give exactly a rounded shape, something more like a hyperbole. However that's good enough in most causes, and it is available in LazPaint as "fast blur".
A true Gaussian blur in fact does not have a radius, as it is based on the exp function. It has a standard deviation and it is likely that it's what you enter in Photoshop is the standard deviation. Still Photoshop probably does not do an actual Gaussian blur but an approximation of it. I read on a forum that it uses 3 different algorithms depending on the "radius". We could try and compare what Photoshop does with a true Gaussian blur.
So to answer your question specifically, I don't know the algorithm used in Photoshop, but it is worth investigating what a true Gaussian blur does and see how it compares to it, and determine if it is possible to compute it fast enough.
About the radius, as said above, in Photoshop, it is not the radius and probably the standard deviation. We could also compare with a true Gaussian blur to see if it is exactly the standard deviation, the double, half of it, etc. There may be a simple formula indeed like multiplying by a constant to go from one to the other.
I am curious if you can have a better match using the fast blur instead of the conic blur.
Regards
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