Planar G1 Hermite interpolation with spirals Original Research Article

A method for creating an extended planar spiral from a segment of a given planar spiral is described. Spirals that satisfy certain conditions are used here so that the following important result holds. The main result of this paper is that there is a unique segment of the given spiral or unique extended spiral that matches very general given G1 Hermite data. The slight restriction on the G1 Hermite data is that it can be represented as a triangle and the unit tangent vector turns through an angle of less than π. This paper shows how to find a G1 Hermite interpolating curve where the segments joining each pair of interpolation points are spirals.