## Description

Given four points and suppose it's necessary to fit a cubic through them.

Let $y(x)=ax^3+bx^2+cx+d$ in which

• $y(-3)=\alpha$
• $y(-1)=\beta$
• $y(1)=\gamma$
• $y(3)=\delta$
Then:
• $a=\frac{1}{48}((\delta-\alpha)-3(\gamma-\beta))$
• $b=\frac{1}{16}((\delta+\alpha)-(\gamma+\beta))$
• $c=\frac{1}{48}(27(\gamma-\beta)-(\delta-\alpha))$
• $d=\frac{1}{16}(9(\gamma+\beta)-(\delta+\alpha))$