Ah, yes, that should do. Thank you! (If you want, feel free to share this as answer.)

I should have specified that I want to look hat very large radii, not like $r=3$ as in this linked question but more like $r=100$. Which doesn't mean that I want to look at $10,000$ samples, but I look for a nice way to approximate the result from fewer samples.

I mean that I want no steps, even at high resolution. The reason for this is that I use the result as some kind of bump map, which reflects a texture, so small discontinuities would be far more visible that if I look only at the blurred image. Will look at your link, many thanks!

Wow, thanks so much for the comprehensive answer! I'll sure need a few days to work through all of this, but really appreciate it!

Rotations would be interesting but translation are fine for now. Ideally it would work with SVG paths, but pixels are fine as well.