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A single-segment spline requires one more pole that its degree to define it.
So a 5 degree spline requires 6 poles.
A 5 degree spline with 7 poles has one-too-many to be single segment, so you now have two segments (both degree 5). If you were to increase the degree to 6, segments would reduce accordingly.
8 poles in yours gives you two segments.
Continuity is an indication of "smoothness" at the knot point, it's not related to poles and degree.
It is indeed correct that
Continuity (at a given knot) = degree - multiplicity of the knot.
Another important relationship is
Number of knots = number of poles + degree + 1
And the final useful fact is that, in most systems, the start and end knots of a degree m spline will have multiplicity m+1.
Your spline of degree 5 has 8 poles, so it must have 8 + 5 + 1 = 14 knots. The start and end knots will each have multiplicity 6 (=5+1), so that's 12 knots accounted for. The other two knots look like they are at roughly t = 0.3 and t =0.7. Those are the parameter values at which the inter-segment joins occur. Each of these knots has multiplicity 1, so the continuity there is 5 - 1 = 4. In other words, your spline is C4 at each internal knot.
OK, so why does NX say the joints are C2, rather than C4. I think the answer is that the NX Info function assumes you won't care about higher levels of continuity (most people don't). So, when it says "C2", I suspect it means "C2 or better".
Interactive NX doesn't give you any direct control over knot multiplicities (as far as I know). So, the easiest way to play with these concepts is to write little programs that use SNAP functions.
The output listing from Info-->Spline says:
Display symbols: C0= filled square with 2 rings C1= filled square with 1 ring C2= filled square Poles=o Defining Points=+
But, as before, "C2" probably means "C2 or better".
Hi @Yamada Thank you!