Piecewise Curves and Surfaces

After an introductory section, in Section 9.2 we will consider Bézier curves. Then we will discuss the important notions of parametric C ^k- continuity and geometric C ^k-continuity of piecewise curves. Section 9.3 is devoted to (parametrically C ^k-continuous) Hermite interpolation and its applications to spline curves. In Section 9.4 we will study β-splines, which are geometrically C ^k-continuous. We will also briefly survey their particular case, B-splines, which are parametrically C ^k-continuous. In Sections 9.5 and 9.6 we will study similar problems for piecewise surfaces. Along the way we will create and apply several M-files that are given in Section A.4.