Hi rajznyolc -
If you make a closed curve using the Curve command with Sharp=Yes and Sharp=No you can see the difference between non-periodic and periodic - basically, periodic curves and surfaces have seams which cannot develop a kink - they are always smooth across the seam. Use MakePeriodic/MakeNonPeriodic to convert between the two. Periodic curves have ‘extra’ control points that wrap around the curve at the ends - the curve or surface overlaps itself in both directions- you don’t get to see these though - you only see and interact with the parts ending at the seam location.
Rational curves and surfaces have point weights that vary - use the Weight command to see and edit point weights on a circle (rational) and a curve from the curve command, (or a Circle modified using Rebuild).
The curvature of the Rhino surface appears to be continuous to me - it does drop to zero at the seam, but as far as I can see it remains continuous- that is, the outer graph line is not broken.
-Pascal