Adaptive quasi-interpolating quartic splines

We present an adaptive quasi-interpolating quartic spline construction for regularly sampled surface data. The method is based on a uniform quasi-interpolating scheme, employing quartic triangular patches with C1-continuity and optimal approximation order within this class. Our contribution is the adaption of this scheme to surfaces of varying geometric complexity, where the tiling resolution can be locally defined, for example driven by approximation errors. This way, the construction of high-quality spline surfaces is enhanced by the flexibility of adaptive pseudo-regular triangle meshes. Numerical examples illustrate the use of this method for adaptive terrain modeling, where uniform schemes produce huge numbers of patches.

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