On geometric Lagrange interpolation by quadratic parametric patches

In the paper, the geometric Lagrange interpolation by quadratic parametric patches is considered. The freedom of parameterization is used to raise the number of interpolated points from the usual 6 up to 10, i.e., the number of points commonly interpolated by a cubic patch. At least asymptotically, the existence of a quadratic geometric interpolant is confirmed for data taken on a parametric surface with locally nonzero Gaussian curvature and interpolation points based upon a three-pencil lattice. Also, the asymptotic approximation order 4 is established. Key words: Interpolation, Approximation, Parametric surface.

• Type: Journal
• Year: 2008
• Where: CAGD
• Authors: Gasper Jaklic, Jernej Kozak, Marjeta Krajnc, Vito Vitrih, Emil Zagar
• Keywords: CAGD 2008, Geometric Lagrange Interpolation, Parametric Surface, Quadratic Geometric Interpolant