Biarcs and bilens (Q1950209)

Following \textit{A. I. Kurnosenko} [Comput. Aided Geom. Des. 27, No. 3, 262--280 (2010; Zbl 1210.65039), ibid. 27, No. 6, 474--481 (2010; Zbl 1210.65040)], where the main concepts of the theory of spiral curves have been presented as the background to the solution of the two-point \(G^2\) Hermite interpolation problem, the author explores here further the properties of spirals, especially the simplest spirals, namely, biarc curves. Biarc formulation is applied to define the bilens, and to prove the bilens theorem, which is an important positional inequality for spiral arcs. This result improves the bounding region, constructed by \textit{M. Barton} et al. [Graph Models, 73, 50--57 (2011; Zbl 1266.65030)].