CONSTRUCTION METHODS OF 4D MATHEMATICAL MODELS 3D BODIES ON A BASIS INTERLINEATION, INTERFLATATION, BLENDING APPROXIMATION AND WAVELETS

Abstract

In work the new method of the description of changes which occur in object changing in time, on the basis of use of the tomograms received during the various moments of time on system of planes which cross object is offered. Systems parallel or mutually perpendicular, or even crossed not under right angles of planes are supposed. The analysis of methods of construction of the tomograms based on use wavelets, interlineation functions of two variables, and approximation by Fourie and Fejer sums are given. During each moment of time we build 3D mathematical model on the basis of the constructed tomograms with the help: interflatation, the blending approximation, using of two or three x-ray pictures. On the basis of constructed 3D models during the various moments of time the four-dimensional mathematical model of the three-dimensional body changing in time is construction. Examples are considered.