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Comment by Filip Milovanović on How to translate points on a path relative to two other points?

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Is it OK if the curve moves as a sort of a rigid body attached to the line, or are there constraints that would prevent that? E.g., if you rotate the control line 180 degrees, do the endpoints of the curve rotate as well (flipping their left vs right relative orientation), or should they stay fixed, or at least close, to their original locations? Is the control line allowed to rotate arbitrarily (including extreme angles such as 180 deg), or are there limits?

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