On interpolation by Planar cubic 𝐺² pythagorean-hodograph spline curves

Jaklič, Gašper; Kozak, Jernej; Krajnc, Marjeta; Vitrih, Vito; Žagar, Emil

doi:10.1090/S0025-5718-09-02298-4

On interpolation by Planar cubic $G^2$ pythagorean-hodograph spline curves
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by Gašper Jaklič, Jernej Kozak, Marjeta Krajnc, Vito Vitrih and Emil Žagar PDF

Math. Comp. 79 (2010), 305-326 Request permission

Abstract:

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic $G^2$ Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is confirmed.

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