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Data approximation using polyharmonic radial basis functions

Segeth, Karel (2021)

Programs and Algorithms of Numerical Mathematics

The paper is concerned with the approximation and interpolation employing polyharmonic splines in multivariate problems. The properties of approximants and interpolants based on these radial basis functions are shown. The methods of such data fitting are applied in practice to treat the problems of, e.g., geographic information systems, signal processing, etc. A simple 1D computational example is presented.

Data compression with Σ Π -approximations based on splines

Olga E. Baklanova, Vladimir A Vasilenko (1993)

Applications of Mathematics

The paper contains short description of Σ Π -algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation problems and colour image processing are described and discussed.

Development and Implementation of NURBS Models of Quadratic Curves and Surfaces

G. Petkov, Emiliyan (2009)

Serdica Journal of Computing

This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess...

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