R help - Oct 2003 - What is the definition of curve continuity and smoothness

Dear R-listers,

I am now using principal curves for data analysis.
The definition of it required the accurate concept
of curve continuity (C0, C1, ..., CK) and curve
smoothness.

So if anyone can introduce the exact definition
of continuous for curves and what is the most
popular textbooks for me?

Thanks for ur time and kind attention.

Fred

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