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.