Multidimensional fields modelling based on b-spline technique with application in manufacturing errors monitoring

Abstract

In this paper we present methods for the assessment of B-spline functions for a given point, by means of tensor fields and methods for the selection of the initial data. On this basis, we developed different algorithms for testing the theoretical solutions we obtained. The assessment of a multivariable B-spline function is made by a two-steps algorithm, in each step being evaluated a B-spline function of one variable. In practice, the components of the vector or matrix of the control points are experimentally determined and, thereforetheir real value is not known except in a rough approximation. Considering the B-spline function depending on these values by minimizing operators as: f t2dt, xu,v2dudv,   xu,v,w2dudvdw, out of the minimum necessary conditions for a multivariable function, we get homogenous linear algebraic systems, out of whose analysis we can obtain useful information on the importance of points which measurements are made on.