Pythagorean hodograph spline spirals that match G3 Hermite data from circles
Résumé
A construction is given for a G3 piecewise rational Pythagorean hodograph convex spiral which interpolates two G3 Hermite data associated with two non-concentric circles, one being inside the other. The spiral comprises the involute of two PH quartic curves with G2 contact. For this purpose, conditions for G3 contact with circles are studied together with geometric properties of a family of PH polynomial quartics with an ordinary cusp at one extremity, so as to generate a point with zero curvature radius.