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Closest Point on a line segment for different distance metrics (i.e L1 norm, max norm)

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Does anyone have a good reference/suggestions for how to find the point on lineseg ab closest to some query point p, for non-euclidian distance metrics? (Specifically I'd like to know L1 norm and max norm).

I've been having a really hard time finding anything about this online.

Thanks! 🙂


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