Node smoothing algorithm

I’m on vacation, so naturally I have spent the past few hours thinking intensely about math.

Mostly what I’ve been thinking is, gosh I am even worse at geometry now than I was when I was a teenager and actually knew math.

Update, the next day: This is what I was working on yesterday. Trying to understand the vector math behind Inkscape’s node smoothing algorithm (the thing that gives you automatic control nodes on bezier curves.) I think I understand it now but it’s still weird.

a sine wave looking curve, and beneath it, a zig-zag with a mess of triangles drawn around it

Updated