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Zbl 1205.65093
Lü, Wei
Curves with chord length parameterization. (English)
[J] Comput. Aided Geom. Des. 26, No. 3, 342-350 (2009). ISSN 0167-8396

Summary: Motivated by the recent work [{\it G. Farin}, Comput. Aided Geom. Des. 23, No. 9, 722--724 (2006; Zbl 1171.65330)], we identify a family of curves that can be parameterized by chord length. The $\alpha$- and $(\alpha ,\beta )$-schemes are presented for characterizing planar and spatial curves respectively. Rational chord-length parameterizations are thoroughly investigated. In particular, the low-degree rational curves such as cubics and quartics are studied and applied to geometric Hermite interpolation. The results advise that this new class of curves, subsuming straight lines and circular arcs, have several obvious advantages over general polynomial and rational curves.

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)

Keywords: chord-length parameterization; rational curve; Bézier control point; complex analysis; circular arc; Hermite interpolation

Citations: Zbl 1171.65330

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