Design of C2 algebraic-trigonometric pythagorean hodograph splines with shape parameters

Cindy González (1) , Gudrun Albrecht (1, 2) , Marco Paluszny (2) , Marianela Lentini (2)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 Universidad Nacional de Colombia Sede Medellín

In this paper, we construct C2 Algebraic-Trigonometric Pythagorean Hodograph (ATPH) splines by solving a non-linear system of equations in complex variables. We compare these splines, which depend on several shape parameters, with their polynomial PH counterpart as well as with the well-known C2 cubic B-splines. We finally present criteria for choosing the free shape parameters based on the minimization of certain fairness functionals.

Mots clés: Algebraic-Trigonometric Pythagorean Hodograph curves; C2 interpolating splines; Newton–Raphson method; fairness measure

Domaines: Mathématiques [math]

Cindy González, Gudrun Albrecht, Marco Paluszny, Marianela Lentini. Design of C2 algebraic-trigonometric pythagorean hodograph splines with shape parameters. Computational & Applied Mathematics, 2016, 37 (2), pp.1472-1495. ⟨10.1007/s40314-016-0404-y⟩. ⟨hal-03164878⟩