CHAPTER 7

B-Spline Approximation and the de Boor Algorithm

B-splines are generalizations of Bernstein polynomials and share many of their analytic and geometric properties. A spline is a piecewise polynomial whose pieces fit together smoothly at the joins. B-spline curves and surfaces have two advantages over polynomial curves and surfaces. For a large collection of control points, a Bezier curve or surface approximates the control polygon or polyhedron with a single polynomial of high degree. But high-degree polynomials take a long time to compute and are numerically unstable. Splines provide low-degree approximations, which are faster to compute and numerically more tractable. We could, of course, manufacture splines by forming piecewise Bezier ...

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