Q:

Does the blending matrix change between calculating various curve segments in a uniform cubic B-splines approximation?

I would like to ask about uniform (periodic) cubic B-splines (approximation, no interpolation).
$$B=1/6\begin{bmatrix}-1&3&-3&1\\3&-6&3&0\\-3&0&3&0\\1&4&1&0\end{bmatrix}$$ 
$B$ is the matrix of coefficients that allows calculating a single curve segment with the formula:
$$ Q_i(u)=[u^3 u^2 u^1 1]B \begin{bmatrix}P_{i-3}\\P_{i-2}\\P_{i-1}\\P_{i}\end{bmatrix} $$
When $i=3$ I calculate the first segment of the curve. My question is when $i=4$ and I want to calculate the second segment of the curve I must change the $4$ control points but does $B$ change or not? 

A:

No, the $B$ matrix (basis coefficient matrix) does not change from one segment to the next. It is a property of the type of spline you're using, in this case cubic B-splines. If you used Bézier splines or Hermite splines instead, you'd have a different $B$ matrix.

