Is cardinal $B$-spline of order $n$ really piecewise Bezier order $n$ curve? Is cardinal $B$-spline of order $n$ really piecewise Bezier curve $n$? I think I saw this in some lecture notes, but I can't recall where.
 A: Any b-spline curve is just a piecewise polynomial, i.e. a sequence of polynomial segments, joined end-to-end. And, in fact, in deBoor's well-known book on splines, he talks a lot about the piecewise polynomial representation of splines.
Each of the polynomial pieces can be represented as a Bézier curve (because every polynomial can be represented using the Bernstein basis).
So, yes, every parametric polynomial spline curve is just a sequence of Bézier curves strung together.
To compute the control points of the Bezier curves from the control points of the b-spline, you can use Boehm's algorithm, as outlined in this answer: Convert a B-Spline into Bezier curves
The book by Carl deBoor is an excellent account of both theory and practice. The title is "A Practical Guide to Splines". I'd give you a link, but my ability to insert links seems to be broken. It's a well-known book, and should be easy to find at Amazon or your local university library.
Another good one is "Bezier and B-Spline Techniques" by Hartmut Prautzsch and Wolfgang Boehm.
If you want something really theoretical, try "Spline Functions: Basic Theory" by Larry Schumaker.
