Parametric first-derivative join of Bézier curves
= Parametric first-derivative join of Bézier curves
{title2=$P_n=Q_0,\quad n(P_n-P_{n-1})/h=m(Q_1-Q_0)/k$}
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>.