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