A two-point G1G1 Hermite interpolating family of spirals

A one-parameter family of spirals that can match planar, two-point G1G1 Hermite data 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 G1G1 Hermite data. Some suggestions on choosing the free parameter of the family of spirals is given. It is shown that there is a unique G1G1 Hermite interpolating spiral that passes through a given point in an allowable region. Three examples of the use of these spirals are given: curve completion with spirals, design with spirals, and approximation of the clothoid by spirals.