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continuity within a multi-segment spline-II

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In a previous thread,  and  gave very helpful comments on the topic of continuity within a multi-segment spline.
 
For a multi-segment spline, there is:
 
 Contituity (intenal continuity?) = m (degree) - r (multiplicity)
 
In most splines without shrinked segments, the multiplicity of middle knots should be 2. Therefore it's easy to judge the internal continuities C1, C2, C3 ... with the equation above.
 
If a spline is divided at its middle knots, the continuity between the reulting B-curves is often like G1, G2, G3 ...
 
Is there any definite relationship between these two types of continuity Cx vs. Gx?
 
Thanks!
 
Image.pngA 2-degree and 2-segment spline. Continuity at the middle knot: C1.
Image.pngThe spline is divided at the middle knot. Continuity between the resulting two B-curves: G1.

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