A two-point \(G^1\) Hermite interpolating family of spirals (Q953374)

A one-parameter family of spirals that can match planar, two-point \(G^1\) Hermite data, called \(i\)-spiral [cf. \textit{H. Pottmann}, Comput. Aided Geom. Des. 12, No.~2, 175--192 (1995; Zbl 0872.65011)] is presented. These spirals can be used as an alternative to the biarc, which is also a one- parameter family of curves that can match two-point \(G^1\) Hermite data. It is also shown that there is a unique \(G^1\) Hermite interpolating spiral that passes through a given point in an allowable region. Some examples of use of these spirals are also given. The \(i\)-spiral has been used by \textit{T. N. T. Goodman} et al. [a paper submitted to Comput. Aided Geom. Des.] for \(G^2\) Hermite interpolation.