Curves with chord length parameterization

Motivated by the recent work (Farin, G., 2006. Rational quadratic circles are parameterized by chord length, Computer Aided Geometric Design 23, 722–724), we identify a family of curves that can be parameterized by chord length. The α- and (α,β)-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.