COMPOSITION MATRICES - GEOMETRIC FIGURE

Abstract

The definition of the composite matrix-geometric figure and its notation are given. The circle of geometric figures is defined - these are discretely specified curved lines, discretely specified surfaces and discretely specified geometric bodies, for which the compomatrix-geometric figure will be formed.

Records of the formation of a one-dimensional compomatrix-geometric figure for a separate curved line without taking into account and taking into account parametric directions are provided. At the same time, variants of both continuous and discrete curved lines are considered. Variants of notation of composite matrices-geometric figure for curves included in the composition of surfaces and geometric bodies, taking into account their parametric directions, have also been developed. Variants of designations of two-dimensional compomatrix-geometric figure for surfaces that are separate geometric formations and for surfaces that are part of a geometric body have been developed. At the same time, options for surfaces containing only continuous frames of lines or only discrete frames of lines, or a mixed version of both discrete and continuous in different parametric directions are considered. The notation of three-dimensional composite matrices-a geometric figure for a geometric body formed by three frames of only discrete lines or only frames of continuous lines, or a mixed version - a frame of continuous lines along one parametric direction, and a frame of discrete lines along the other, has been developed. Also developed is the notation of compomatrixes-a geometric figure for a geometric body formed by a continuous or discrete surface and a framework of continuous or discrete lines. Variants of notation of three-dimensional compomatrices have also been developed - a geometric figure for a geometric body given by a frame of points arranged in a frame of discrete lines. An explanation is provided for the formation of compomatrixes-a geometric figure for a geometric body that is continuously continuous. This compo-geometric matrix appears as the basis for the formation of a three-parameter point polynomial, which compositionally interpolates the points of a geometric body both on its surface and inside it.

Keywords: Compomatrix-geometric figure, point compomatrix, parametric compomatrix.