Approximation of discontinuous 3D functions by discontinuous interflatation splines
Abstract
The paper develops a method of approximating a three-dimensional body, which is described by a discontinuous 3D function, using a discontinuous spline interflatation operator. The case is considered when the studied body is completely covered by a system of elementary rectangular elements (parallelepipeds). A function describing a three-dimensional body can have discontinuities of the first kind on the lines or planes of a given system of parallelepipeds. In the article, a discontinuous spline is constructed - an interfletant, which uses one-sided function traces along a given partition system as experimental data; a theorem on the approximation error of the constructed discontinuous spline is presented. This method of approximation can be used in remote methods of studying objects.
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