Problem $3$: Generate a normalized piecewise cubic spline curve through the four points with

position vectors $P1[1,1],P2[2,3],P3[4,-2],P4[5,1]$ with tangent vectors $P{1}^{\text{'}}=[01]$ and

P$4\text{'}=[-1-1].$ Take $50$ points on each segment.

Hermite basis functions or blending functions

$H=\left[\begin{array}{cccc}2& -2& 1& 1\\ -3& 3& -2& -1\\ 0& 0& 1& 0\\ 1& 0& 0& 0\end{array}\right],B=\left[\begin{array}{cccc}1& 0& 0& 0\\ 1& 4& 1& 0\\ 0& 1& 4& 1\\ 0& 0& 0& 1\end{array}\right]$

Write Matlab Code with logic flowchart