GEOMETRIC MODELING OF THE RECONSTRUCTION OF SOME OBJECTS BASED ON THEIR SHADOW PROJECTIONS

Abstract

There are many tools for constructing images and processing graphic information, which today are perfectly operated by a modern experienced engineer, who must be able to find new solutions to technical problems based on a combination of originality, mathematics, updated methods, applied scientific knowledge and professionally approach new implementations.

In the course of descriptive geometry, the direct problem is the study of methods for constructing images. In this case, a solution can be obtained regardless of the projection task and the type of object being displayed. The inverse problem can be considered the problem of recognizing the depicted images, finding their positional and metric characteristics. It is precisely such a problem that cannot always be solved. Restoring information about a geometric object is an important necessity.

The relevance of the topic is determined by the need for research in finding and indentifying general tecniques that often arise when applying various aspects of the reconstruction of geometric objects from their shadow proections.

The work defines the concept of «еllipsoid» as a common object of research. It is noted that in some implementations the problem of reconstructing an «ellipsoid» from its orthogonal shadow projections arises, which are used, for example, in nuclear technology to determine the energy parameters of microfuels, with stereological control to determine the parameters of inclusion domains. In this case, it is assumed that the surface of a granule or domain can be approximated with sufficient accuracy by an «ellipsoid».

There are many problems from various branches of science and technology, in the solution of which it is possible to apply the method of reconstructing geometring objects from their sufficiently informative shadow projections, for example, in aerial photography as a means of qualitatively improving X-ray images, in the field of plasma diagnostics, and especially in experiments on controlled thermonuclear fusion.

Key words: geometric objct; shadow projection; ellipsoid; reconstruction; stereology; granule; doman.