create curve based on curvature attribute

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Hi everyone,
it's possible generate shape of curve based on curvature of surface?
I attach a scene.I need a generate curve on the white areas of surface.
Thanks !

Attachments:
curve_based_on_curvature.hipnc (112.7 KB)

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If geometry have hard edge you'll get sharp curvature, I mean higher curvature value.
Your geometry doesn't have that so I think it's not possible to get continuous curve using my approach.
If I use sharper version of your geometry, my approach is very accurate but on final geometry it gives discontinuous curve.
Change switch inputs, you will get the idea.

It's not very good approach, but it's only I could come up with.

Attachments:
curve_based_on_curvature_187.hipnc (129.7 KB)

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The problem is that i have a mesh with triangulated topology,
but even so i thank you for your idea and scene.
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