Abstract: A new algorithm is proposed for allowing one to adjust curvatures at the two endpoints of an interpolating spiral which matches G¹ Hermite data,respectively.Firstly,the formulae for involutes of a planar quartic PH curve are given as well as their geometric properties.Based on these results,an algorithm is proposed for planar G¹ Hermite interpolation with spirals.This algorithm derives a two-parameters family of interpolating spirals,and the endpoints’ curvatures are alternative as changing the two free parameters.Theoretically,the curvature at one endpoint can be arbitrary small.When the given G² Hermite data satisfies some conditions,a construction is given for the interpolant by choosing appropriate free parameters.Numerical examples show that this algorithm is efficient and satisfactory.