Unroll for surface new idea

I saw the idea for unrolling the surfaces and decided to implement.

Lines to the surface edges are created from the center point on the surface. Then, a point is created on the plane from which the lines originate at the same angles. Distances are measured on the lines and a curve is created at the end points.
Faced with the problem of creating the shortest curves from the center point to the edge of the surface at a given angle.
Please help.

Lines.gh (5.2 KB)
Cerves.3dm (48.0 KB)

Something like this?

Lines_re.gh (15.3 KB)

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That’s cool. Thanks. I studied grasshopper not so long ago and you really helped me. Tell, How you appropriated a plane this parameter by default?

Right click on the component -> set one plane

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