Stack blur is a fast, discrete tent filter (weights are 1, 2, 3, 2, 1, normalize, it makes a triangle/tent shape). You can find tent filter blurs all over, including in Apple's own image processing library:
Does that actually look good? I would have thought it would have really obnoxious diagonal artifacts.
Unless it can be tuned to behave like a repeated box blur (and therefore approximate a true Gaussian). A tent shape would just be two box blurs, right?
The convolution of a box filter with a box filter is a tent filter. So yes, a tent filter blur can be done with two box filter blurs.
And repeated box filters asymptotically approach a Gaussian filter, though in practice it converges very quickly. A single box filter can be thought of as a piece-wise constant approximation of a Gaussian filter. Two passes of box filters produce a piece-wise linear approximation (the tent). And three passes of box filters produce a piece-wise quadratic approximation. Four passes for a cubic approximation, etc. Usually, just the three box filters are used since they are close enough.
I'd need to look at the math in detail here, but I suspect that it's ultimately just cleverly interleaving the running sums for the two box filter to perform them in a single pass.
If so, it might be an interesting challenge to see if the idea can be extended to compute the higher quality three box filter approximation in a single pass.
https://developer.apple.com/documentation/accelerate/vimage/...