{\displaystyle \mathbf {S} (t)=\sum _{i=0}^{m-n-2}\mathbf {P} _{i}b_{i,n}(t){\mbox{ , }}t\in [t_{n},t_{m-n-1}]}.

{\displaystyle b_{j,0}(t):=\left\{{\begin{matrix}1&\mathrm {if} \quad t_{j}\leq tt_{j+1}\Θ&\mathrm {otherwise} \end{matrix}}\right.,\qquad j=0,\ldots ,m{-}2}{\displaystyle b_{j,n}(t):={\frac {t-t_{j}}{t_{j+n}-t_{j}}}b_{j,n-1}(t)+{\frac {t_{j+n+1}-t}{t_{j+n+1}-t_{j+1}}}b_{j+1,n-1}(t),\qquad j=0,\ldots ,m{-}n{-}2.}{\displaystyle b_{j,n}(t):={\frac {t-t_{j}}{t_{j+n}-t_{j}}}b_{j,n-1}(t)+{\frac {t_{j+n+1}-t}{t_{j+n+1}-t_{j+1}}}b_{j+1,n-1}(t),\qquad j=0,\ldots ,m{-}n{-}2.}

B-Spline 곡선인데 미분해서 기울기를 구해야 합니다