I heard about the importance of C1 and C2 continuity/smoothness of curves but every computer graphics text book I read ends on C2 continuity and does not mention continuity of higher degree than C2.
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3https://en.m.wikipedia.org/wiki/Jerk_(physics) says something about it – Coolwater Jul 23 '21 at 08:50
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1G3 continuity (not C3) is important in machine motion and aesthetics. See my answer to this question: https://math.stackexchange.com/questions/2496490/motivation-of-splines/2499704#2499704 – bubba Jul 30 '21 at 06:31