To make section along any curve, my algorithm is:
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Make CURVE (any, even Joined by couple fragments).
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Make cut SURFACE (by EXTRUDING curve).
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Use function IntersectTwoSets. As first set – select cutting surface, as second – objects to cut.
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After previous operation, new generated section curves are selected. Add to this selection cutting surface and Isolate them (or Move/Copy near).
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Make new flat surface with length and height the same as cutting surface.
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Use FlowAlongSrf. As base surface select cutting surface. Make sure, that Regid option is set to Yes.
As result: Your section will be made allong any curve, and then unroled on flat surface.