Approximate approximations from scattered data

Approximate approximations from scattered data

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by ...

Scattered data approximation of fully fuzzy data by quasi-interpolation

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...

Direct Isosurface Extraction from Scattered Volume Data

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...

Reconstruction of Kinematic Surfaces from Scattered Data ∗

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.

Reconstruction of Multivariate Functions from Scattered Data