Hermite interpolation with Tschirnhausen cubic spirals Original Research Article

A method to create planar G1 curves by joining spiral segments is described. The spiral segments are either spirals taken from the Tschirnhausen cubic curve or spirals created by joining circular arcs to segments of the Tschirnhausen cubic in a G3 fashion. The above mentioned spirals can match geometric Hermite data in all cases where that data can be matched with a general spiral. The use of spirals gives the designer excellent control over the shape of curve that is produced because there are no internal curvature maxima, curvature minima, inflection points, loops, or cusps in a spiral segment.