You could connect the two endpoints with a 
[cubic Bézier curve](https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Cubic_B%C3%A9zier_curves),
which achieves 1st- and 2nd-derivative continuity
at the endpoints ($P_0$ and $P_3$ in the illustration below).
<hr />
&nbsp; &nbsp; &nbsp; 
[![Bezier][1]][1]
<br />
&nbsp; &nbsp; &nbsp; 
<sup>
(Image from [CartouCHe](http://www.e-cartouche.ch/content_reg/cartouche/graphics/en/html/Curves_learningObject2.htmlrl).)
</sup>
<hr />

  [1]: https://i.sstatic.net/XF8De.jpg