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Selecting which polyline is displayed on top in case of segment overlaps seems to be quite a FAQ, however, I would like to find a way to display overlapping polyline segments side-by-side, i.e. as multiple lines separated by offsets, similar to how Google Transit displays branching transit services.

Google Transit

Is there a Leaflet library that does that?

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there appears to be one called Polyline Offset which should allow you to control the rendering of polylines.

There's a demo here and a screen shot of one of the other demos:-

enter image description here

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