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I'm slightly confused by this. A point on a polyline doesn't have a single normal, as it's incident to two edges, and in general those edges have two different normals. If you push out the edge by the offset amount, that's what Tiller and Hanson proposed in 1984, and one of the things I found is that it performs surprisingly badly. It is in common use though.

If you're talking about a variation of that where you choose some other concept of "normal" relevant to the point, I'd be interested to learn more.

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Yes, I'm using the term normal in the usual graphics sense of a vertex normal, as the average of the normals of the incident edges. It's the Tiller & Hanson 1984 approach.

Gotcha gotcha. I just coded this up, and averaging the two incident normals performs about the same as OG Tiller-Hanson, slightly worse. The original version (and my implementation) displaces the edge, which basically means computing the new control point as the intersection of the two displaced edges. I believe there are a bunch of T-H variations out there, but haven't collected any evidence yet that they significantly improve matters.