# Knots and B-Splines

phiby
I have been reading about B-Splines for a couple of days now, but I just can't get what a knot is!!! I have referred multiple books & websites. Can someone explain knots to me a in a simple language?

Homework Helper
If you have read about splines, then presumably you know that they are piecewise polynomial functions. "Knots" are the points where the "pieces" change. That is, where the formula changes.

If f(x) is the "quadratic spline" that is given by
$f(x)= x^2$ for $0\le x\le 2$, $f(x)= 2x^2- 4x+ 4$ for $2\le x\le 3$, etc. then x= 2 or, more properly, the point (2, 4) is a "knot".

Typically one wants a spline that interpolates given values. Often the knots are chosen at the "interpolation points" but not always.

phiby
"Knots" are the points where the "pieces" change. That is, where the formula changes.

Assume a B-spline with n+1 control points (0 to n) & d control points per curve(polynomial of degree (d-1)). The text says that B-Splines are defined only in the interval from knot value ud-1 to un+1. So what are the extra knots at the beginning and end of the knot vector for?