THREE-DIMENSIONAL COMPOSITION MATRICES AND THEIR APPLICATIONS FOR CREATION OF COMPOSITIONAL GEOMETRIC MODELS OF VOLUME OBJECTS OF ANY ARBITRARY FORM

Abstract

In the research the geometrical way of creation of models of dynamics in space of discretely presented separate states of process on the basis of use of methods of compositional geometry is offered.

The definition of basic states, three-dimensional composite matrices is introduced, the rules of designation of indexing of elements of three-dimensional composite matrices (compomatrices) are offered.

It is pointed out that a three-dimensional composite cannot be presented in the form of a single table, so it is proposed to provide them in the form of a set of tables in the areas of parameterization of the geometric figure for which this three-dimensional computer matric is compiled.

Examples of their general and detailed presentation are given.

It is reminded that in composite geometric modeling (CGM) each initial geometric figure (GF), before solving the problem, must be unified, ie lead to a form suitable for its use in composite geometric modeling.

The geometric component of the unified GF is presented in the form of point matric matrices in parametric directions.

The parametric component of the unified GF is presented in the form of parametric compomatrices.

It is emphasized that all calculation operations are carried out through the use of three-dimensional coordinate matrices (calculated), which are compiled according to the scheme of the corresponding point compomatrices.

It is pointed out that the initially formed three-dimensional computer matric is parametric, almost always, non-harmonized, in the sum of all its elements is not equal to one.

An algorithm for harmonizing a parametric three-dimensional computer matric is provided.

The sequence of operations in the compomatric form concerning obtaining a compomatrices of three-dimensional for a three-dimensional geometric figure of arbitrary form is given.

Keywords: three-dimensional compomatrices, composite model, harmonized point polynomial, geometric method of interpolation, basis state, types of compomatrices, designation of compomatrices, compomatrices point, compomatrices parametric, compomatrices coordinate.