I've been poking around the stkr.waveshaping tools and finding a lot of useful content in it (although the GenExpr content in the codeboxes is still eluding my attempts to properly understand it).
Unfortunately, it seems like most flavors of distortion are still limited to the same tricks: dc offset, variations of soft/hard clipping, possibly wave folding, and the like. Inevitably, the results never impress me much, and I find it particularly disappointing that, apart from folding the wavefrom (which is always a bit too aggressive), the only other alternative seems to be an ultimately flat, horizontal clipping.
A while back, I remember testing an amp with an oscilloscope at a friend's place, and just kind of watching the sine wave distort. It seemed that, not only was the clipping not flatly horizontal, but the sine wave itself seemed to skew ever-so-slightly like a saw wave. I've cooked up a makeshift image to sort of illustrate my point and posted it at the end of this post (sorry it's kind of blurry; I had to resize it so I could upload it).
In short, my question is what other approaches there are to achieving a more natural sounding analog-like distortion without simply resorting to LP/shelving filters to tame the distortion's harmonics?