Chapter 6

Spline Basics

Carl de Boor

This chapter promotes, details and exploits the fact that (univariate) splines, i.e., smooth piecewise polynomial functions, are weighted sums of B-splines.

6.1 PIECEWISE POLYNOMIALS

A piecewise polynomial of order k with break sequence ξ (necessarily strictly increasing) is, by definition, any function f that, on each of the half-open intervals [ξj image ξj+1), agrees with some polynomial of degree < k. The term ‘order’ used here is not standard but handy.

Note that this definition makes a piecewise polynomial function right-continuous, meaning that, for any x, f(x) = f(x+):= limh↓0 f(x + h). This choice is ...

Get Handbook of Computer Aided Geometric Design now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.