On the variety of planar spirals and their applications in computer aided design

Abstract: In this paper we discuss the variety of planar spiral segments and their applications in objects in both the real and artificial world. The discussed curves with monotonic curvature function are well-known in geometric modelling and computer aided geometric design as fair curves, and they are very significant in aesthetic shape modelling. Fair curve segments are used for two-point G1 and G2 Hermite interpolation, as well as for generating aesthetic splines.