A method for B-spline filtration of data measured on a very precisely manufactured sphere is described in this paper. The method has been developed to decrease the uncertainty of measurement which can be obtained by least squares method commonly used when processing the measured data. The B-spline filtration is realised as a B-spline surface approximating the data measured on 3D coordinate measuring machine and transformed into the parametric space of the sphere. This transformaton eliminates the undesirable consequences of convex hull property of B-spline surfaces when processing convex data. Furthermore, the B-spline representation of the measured sphere can be considered as a certain replacement of the original sphere. Subsequently, the B-spline representation can be used for a new more precise measuring strategy in iterative measuring process. and Obsahuje seznam literatury
In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval error. We formalize the estimation problem of parameters of the interval function so as to minimize the sum of square/absolute interval errors. Introducing suitable interpretation of minimization of an interval function, each estimation problem is well-formulated as a quadratic or linear programming problem. It is shown that the proposed methods have close relation to both traditional and interval linear regression methods which are formulated in different manners.