1
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Thanks! Could you recommend a good introduction to $B$-splines? I liked the "practical" approach by Gerald Farin (Curves and Surfaces for Computer-AIded Geometric Design) but now I'd like something with theoretical slant. $\endgroup$ – blazs Sep 15 '15 at 7:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.