CubicInterpolation

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:

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

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