# Continuity of composite Bézier curves

The composite curve S with pieces

where c0 = (−1, 1), c1 = (−1, 0), c2 = (0, 0), and d0 = (0, 0), d1 = (1, 0), d2 = (2, 1). What is the order of continuity of s at (0, 0)?

• It is C1 continuous at (0,0) – fang Oct 20 '14 at 6:29
• How did you find it, can you explain it? Thanks – Hanna Oct 20 '14 at 9:04
• The man's name was Bézier, not Bezier. – bubba Oct 20 '14 at 11:06

Calculate the first derivatives of $\mathbf{p}$ and $\mathbf{q}$ at $t=1$. You get $$\mathbf{p}'(1) = 2(\mathbf{c}_2 - \mathbf{c}_1) = (2,0)$$ $$\mathbf{q}'(1) = 2(\mathbf{d}_1 - \mathbf{d}_0) = (2,0)$$ The first derivatives agree, so the composite curve is $C_1$.
Do the same sort of calculation with second derivatives, and you will find that they do not agree, so the curve is not $C_2$.