TY - JOUR

T1 - Pythagorean hodograph spline spirals that match G3 Hermite data from circles

AU - Li, Zhong

AU - Ait-Haddou, Rachid

AU - Biard, Luc

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/4

Y1 - 2015/4

N2 - 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 solution is of degree 7 and is the involute of a G2 convex curve, referred to as the evolute solution, with prescribed length, and composed of two PH quartic curves. Conditions for G3 continuous contact with circles are then studied and it turns out that an ordinary cusp at each end of the evolute solution is required. Thus, geometric properties of a family of PH polynomial quartics, allowing to generate such an ordinary cusp at one end, are studied. Finally, a constructive algorithm is described with illustrative examples.

AB - 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 solution is of degree 7 and is the involute of a G2 convex curve, referred to as the evolute solution, with prescribed length, and composed of two PH quartic curves. Conditions for G3 continuous contact with circles are then studied and it turns out that an ordinary cusp at each end of the evolute solution is required. Thus, geometric properties of a family of PH polynomial quartics, allowing to generate such an ordinary cusp at one end, are studied. Finally, a constructive algorithm is described with illustrative examples.

UR - http://hdl.handle.net/10754/564114

UR - https://linkinghub.elsevier.com/retrieve/pii/S0377042714004440

UR - http://www.scopus.com/inward/record.url?scp=84908441422&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2014.10.005

DO - 10.1016/j.cam.2014.10.005

M3 - Article

VL - 278

SP - 162

EP - 180

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -