Parametric first-derivative join of Bézier curves ($P_n=Q_0,n(P_n-P_{n-1})/h=m(Q_1-Q_0)/k$)

Two adjacent Bézier curves of degrees $n,m$ and interval lengths $h,k$ have a $C^1$ join precisely when their endpoint positions and their derivatives in the common parameter agree. Parallel endpoint polygon edges alone give tangent-direction agreement; their scaled vectors must be equal for parametric first-derivative continuity.