Extruding Curves Radially - Grasshopper

Hello,
I made this diagrid of linear lines that are mapped to a surface with the intent of creating a reciprocal structure. I am struggling to extrude the curves in a radial fashion around the barrel vault and this was my attempt. Cant seem to get the vectors to remain perpendicular to the original curve of the barrel. Please help, much appreciated.


Pls share your current 3dm and gh file.

…and make sure to include the barrel surface (not used in the shown gh-definition).
I expect the surface normal is the vector you are looking for.

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Reciprocal Structure02.3dm (181.7 KB)
Reciprocal Structure02 GH.gh (17.0 KB)
Sorry about that. They are attached.

Yes, looking for surface normal. Unsure how to extrude the lines using those vectors.

what i had in mind :
Reciprocal Structure02_jvs.gh (29.2 KB)

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This is awesome thank you so much. Why couldn’t you just use “evaluate surface”? If you wouldn’t mind explaining the process before that it would be very helpful

the “evaluate Surface” asks you where to evaluate it. (point input)
BUT thats not a point in XYZ (3 dimensional) but in UV (the 2 Surface dimensions)
use a panel to have a look at the points I give to the evaluate node: Z =0 (third dimension not used)
To get that UV position I use “Surface closest point”. that is asking for a point in 3d and pulls it to the surface. and the midpoints of the curve are not on the surface since the curves are straight lines and the surface is bended.

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That makes sense. Thanks a ton.