Why Quasi-Interpolation onto Manifold has Order 4
2020
We consider approximations of functions from samples where the functions take values on a submanifold of $\mathbb{R}^n$. We generalize a common quasi-interpolation scheme based on cardinal B-splines by combining it with a projection $P$ onto the manifold. We show that for $m\geq 3$ we will have approximation order $4$. We also show why higher approximation order can not be expected when the control points are constructed as projections of the filtered samples using a fixed mask.
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