Mathematical modelling of discontinuous processes in a computer tomography by means of discontinuous splines

O. M. Lytvyna, I. I. Pershynaa, O. O. Lytvyna, S. I. Kulykb

aUkrainian Engineering Pedagogical Academy, Universitetskaya street, 16, 61003, Ukraine

bKharkov National Technical University ?KhPI?, Frunze street, 21, 61002, Ukraine

Abstract

In work authors build for the first time and investigate mathematical methods of approach of discontinuous one- dimensional and two-dimensional objects by discontinuous interpolational and interlineational splines by means of rectangular and triangular elements. Two cases are considered: 1) when points of ruptures of approached function coincide or do not coincide with knots of approaching splines; 2) when the approaching spline has ruptures of the first kind on lines between various elements (rectangular or triangular). The problem of an optimum finding of knots of an approaching discontinuous spline and a problem of a finding of ruptures of the set function is investigated also.

Keywords: discontinuous function, discontinuous spline, a computer tomography