Displaying similar documents to “Data approximation using polyharmonic radial basis functions”

Curve reconstruction from a set of measured points

Hlavová, Marta

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In this article, a method of cubic spline curve fitting to a set of points passing at a prescribed distance from input points obtained by measurement on a coordinate measuring machine is described. When reconstructing the shape of measured object from the points obtained by real measurements, it is always necessary to consider measurement uncertainty (tenths to tens of micrometres). This uncertainty is not zero, therefore interpolation methods, where the resulting curve passes through...

Multivariate smooth interpolation that employs polyharmonic functions

Segeth, Karel

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We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational...

A particular smooth interpolation that generates splines

Segeth, Karel

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There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known...