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edited Sep 4, 2018 at 0:55

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You could connect the two endpoints with a cubic Bézier curve cubic Bézier curve, which achieves 1st- and 2nd-derivative continuity at the endpoints ($P_0$ and $P_3$ in the illustration below).

[![Bezier][1]][1]
^{(Image from [CartouCHe](http://www.e-cartouche.ch/content_reg/cartouche/graphics/en/html/Curves_learningObject2.htmlrl).)}

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created Sep 4, 2018 at 0:06

Joseph O'Rourke

150.9k
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You could connect the two endpoints with a cubic Bézier curve, which achieves 1st- and 2nd-derivative continuity at the endpoints ($P_0$ and $P_3$ in the illustration below).

[![Bezier][1]][1]
^{(Image from [CartouCHe](http://www.e-cartouche.ch/content_reg/cartouche/graphics/en/html/Curves_learningObject2.htmlrl).)}