Abstract
In this paper, we construct \(C^2\) 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 \(C^2\) cubic B-splines. We finally present criteria for choosing the free shape parameters based on the minimization of certain fairness functionals.
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