20,000 words (plus interactive demos) on Bézier curves: http://pomax.github.io/bezierinfo/ by @TheRealPomax
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I think this normal/tan/bitan stuff would've been great for it. We didn't end up having time for it anyhow.
Reading through your answer, I would've been able to cheat on finding the normal because of how we controlled spline points.
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Basically control points were full xforms with rot, scale, etc. So tan at the control point was just the fwd vec.
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yeah, that's a good cheat.
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