Pythagorean hodograph spline spirals that match G3 Hermite data from circles

Zhong Li (1) , Rachid Ait-Haddou (2) , Luc Biard (3)

1 Department of Mathematics and Science, Zhejiang Sci-Tech University
2 Geometric Modeling and Scientific Visualization Center
3 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

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.

Mots clés: G3 Hermite interpolation; transition curve; rational spiral; PH curves; path planning; highway designing

Domaines: Géométrie différentielle [math.DG]

Zhong Li, Rachid Ait-Haddou, Luc Biard. Pythagorean hodograph spline spirals that match G3 Hermite data from circles. Journal of Computational and Applied Mathematics, 2015, 278, pp.162-180. ⟨10.1016/j.cam.2014.10.005⟩. ⟨hal-00985241⟩