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.
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Rovenski, V. (2010). Piecewise Curves and Surfaces. In: Modeling of Curves and Surfaces with MATLAB®. Springer Undergraduate Texts in Mathematics and Technology. Springer, New York, NY. https://doi.org/10.1007/978-0-387-71278-9_9
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DOI: https://doi.org/10.1007/978-0-387-71278-9_9
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