Offset Curve on Surface: option

(Rhino 5) Why offset a polyline that has straight edges is performed by rounding all vertices?
(I do not know Rhino 6 as functions, but you could add an option “sharp edges” and “rounded corners” as the offest curves

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This one has been on the wish pile for a while… I nudged it for you.
http://mcneel.myjetbrains.com/youtrack/issue/RH-2130 for future reference

In the meantime, if you projected the original polyline, use Offset while it’s flat and you’ll have the corner options. Then project that crv to the surface.