Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
A general framework for high-accuracy parametric interpolation
Mathematics of Computation
On geometric interpolation of parametric surfaces
Computer Aided Geometric Design
Geometric interpolation by planar cubic polynomial curves
Computer Aided Geometric Design
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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.