Metamodel for Mathematical Modelling Surfaces of Celestial Bodies on the Base of Radiolocation Data

The paper proposes for the mathematical modelling surfaces of celestial bodies by the given radar data use the models, produced from the geometrical metamodel G. The metamodel G consists of the corresponding to the dimensions of a space geometrical objects (points, lines, surfaces), the mathematical methods of interpolation, interlinations, interflatation, and the set of rules for producing mathematical models. Using the metamodelling approach allows us to consider from a unique point of view the different methods for the modelling surfaces of bodies and also to develop a computer tool which accelerates and simplify the modelling process, starting from the problem specification and finishing visualization and interpretation of the obtained solution. The correctness of the derived from the metamodel G the set of the models M1, M2 ... MN results from the correspondence of the structure of the model objects of G to the structure of experimental data, recorded in the process of radiolocation as values of the functions in the points, and traces of the functions on the given lines and surfaces. Widely used in cartography Digital Elevation Model (DEM), can be also produced from G by using for the description of the bodies the surfaces in the form of triangles. Using the metamodel G allows us to integrate the DEM method for the data specification with setting data in points and on lines (which are the basic objects of the metamodel G) and so apply more precise (comparatively with the classical interpolation) methods of interlination and interflatation of functions. Another advantage of the proposed metamodelling approach is a possibility of development of complex geometrical models by composition of the basic elements of the metamodel. As an example, the paper proposes a new method for the reconstruction of the surface of a celestial body by the data, given on the system of strips – interstripation (form the inter – in between – of the strips).