I'll wave the flag for the curvature-controlled element. There should be no problem because curvature only goes to infinity at a sharp corner, which is actually not realizable as even the sharpest corner is at least the size of an atom; not zero. Curvature can be a constant or varied along the element. The main constraint would be that the element be curvature continuous; no sudden changes/discontinuities in the curvature.
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