Planar spirals that match G2 Hermite data Original Research Article

A method for creating an extended spiral from a segment of a given spiral is described. The extended spiral can match a wider variety of G2 Hermite data in the plane than the given spiral. The extended spiral is composed of a segment of the given spiral and circular arcs joined to it in a G2 manner. Extended spirals created from some given spirals, such as the clothoid, can match any given G2 Hermite data that can be matched by a general spiral. Extended spirals created from other spirals, such as the Tschirnhausen cubic, can match a restricted set of the G2 Hermite data that can be matched by a general spiral.