Abstract
There are several ways to define smoothness. Stark’s simple C r condition establishes a very simple construction of a smooth curve continuation. More generally, a curve is said to be GC r if it has an r times continuously differentiate parametrization. An even more general smoothness concept is based on the continuity of higher order geometric invariants. Piecewise polynomial curves with this general smoothness can be nicely studied using a geometric interpretation of symmetric polynomials.
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© 2002 Springer-Verlag Berlin Heidelberg
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Prautzsch, H., Boehm, W., Paluszny, M. (2002). Smooth curves. In: Bézier and B-Spline Techniques. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04919-8_7
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DOI: https://doi.org/10.1007/978-3-662-04919-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07842-2
Online ISBN: 978-3-662-04919-8
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