How to make the lines fall onto the object to create separate segments?

I am trying to get the highlighting lines fall onto the object behind so I could color it as a face silhouette, I got the top part where its flat, but it gets tricky where there are curves. Is there an easy way to do this?

I think it is possible to rotate both object and lines such a way that lines would lie parallel to an XY plane, then to use “Drape” tool of “Sandbox” toolbar. Then rotate everything back.

The most basic way would be to use the pencil tool to make the curve into a face by adding two edges to form a right angle. Then use push pull to extrude it through the shape. Delete all the extra leaving just the new curved face. Then intersect the new face with the shape.

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In addition to Boxs pushpull solution, if you have installed TIGs ExtrudeTools, you can use the Extrude Edges by Vector tool (EEbyV)…

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Thank you all!! I made it work!

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