Abstract
Work on the installation of suspended ceilings requires very accurate calculations and precise cutting. When creating the appropriate design systems are based on geometric calculations and key formulas describing the surface. The aim of the work was to develop a subsystem for the design of stretch ceilings, which would minimize the time and material costs that inevitably arise during the organization of production, installation of this type of structures. The classification of approaches related to geometric modeling is carried out. There are two main approaches to geometric modeling of design objects: the approach of structural geometry and the boundary approach. Constructive geometry is to create a library of geometric primitives (elementary objects), on the basis of which by means of regularized Boolean operations (intersection, Union, etc.) is to build a model. The boundary approach is based on the capabilities of piecewise analytical description of the object, description of its boundary elements (faces, edges, vertices of features and contours, nodal point of plane objects) based on algebraic equations. Geometric models have a hierarchical structure that results from the bottom-up construction. An element of a geometric structure can be: a coordinate system, a point, a curve (flat, spatial), a surface, a geometric body. For the two-dimensional case, the objects of modeling are planar contours, which consist of segments of planar curves. The elements of the topological structure of the contours are node points, line segments. The curve can be represented by a set of points, provided that they are close enough to each other. In the scatter method of geometric simulation model is used, the basis of which is the point. The use of mathematical description of the curve complicates the model, but has a number of advantages, for example, there is no need for an interpolation scheme to find intermediate points. The program is designed "Europalace" allows you to quickly build a shape with the specified parameters. There are tools to rotate the selected objects and enable the step-by-step construction mode in order to carefully consider the geometric modeling process and adjust it if necessary. The created system of design of stretch ceilings has the following features: execution of construction on the basis of the table of input data with coordinates and angles; execution of construction of an ellipse; execution of construction of a half-ellipse; execution of construction of a rectangle; execution of construction of a triangle; functions of rotation of the selected edges; feature construction steps; the function print project.

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