How can I find a $n$-th degree polynomial for a line with $n-1$ predetermined points?

35 Views Asked by At

Essentially, I have a set of points which I want to create a polynomial that passes through a set of points. This is within the context of having set locations on a line to set times. It is preferred that the time be between 0 and 1 at all times. For example, when I have 5 target points, the times would be x = $0, 0.25, 0.5, 0.75, 1$.