In this article, we use the knowledge of positive definite tensors to develop a concept multi-kernels construct kernel-based interpolants scattered data. By techniques reproducing kernel Banach spaces, optimal recoveries and error analysis are shown for special class strictly multi-kernels.

The construction of a range restricted bivariate C ( or G ) interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising cubic Bézier triangular patches are always positive and satisfy C ...

We investigate the performance of DEI, an approach [2] that computes off-mesh approximations of PDE solutions, and can also be used as a technique for scattered data interpolation and surface representation. For the general case of unstructured meshes, we found it necessary to modify the original DEI. The resulting method, ADEI, adjusts the parameter of the interpolant, obtaining better perform...

where α = (α1, . . . , αn) is an n-tuple of nonnegative integers and |α| = ∑n j=1 |αj |. If every polynomial p ∈ πm−1(R) is determined by its values on X, then we will say that the data set X is unisolvent (for πm−1(R )). This condition can also be rephrased in terms of matrices. Order the monomials x in some convenient way. Form the matrix P for which the rows are an x evaluated at xj , j = 1,...

Isosurface extraction is a standard visualization method for scalar volume data and has been subject to research for decades. Nevertheless, to our knowledge, no isosurface extraction method exists that directly extracts surfaces from scattered volume data without 3D mesh generation or reconstruction over a structured grid. We propose a method based on spatial domain partitioning using a kd-tree...

Given a surface in 3-space or scattered points from a surface, we present algorithms for fitting the data by a surface which can be generated by a one–parameter subgroup of the group of similarities. These surfaces are general cones and cylinders, surfaces of revolution, helical surfaces and spiral surfaces.

A generalization of scattered data interpolation for arbitrary sets of data is presented that allows better interpolation in situations where non-punctulate constraints are present. A generalized point{set{metric is introduced which allows adaption of distance weighted interpolation methods to the described generalization. The usefulness of the approach is demonstrated by examples.

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