Abstract
This paper is devoted to the topical issue of studying the shapes of geometric surfaces in terms of descriptive geometry and their computer modeling. Definitions of algebraic and geometric surfaces are given. The analysis of features and parameters of surfaces for their classification into the main groups that are most common in practice is performed. The main methods of setting surfaces used in practice, depending on the shape of the surface and the task are given. Analytical, kinematic and frame methods of setting surfaces have been studied. The analytical method is presented on the basis of a conical surface of rotation; the canonical equation of the surface is analyzed, its correspondence for the upper and lower cone cavities is shown. The conical surface is graphically displayed in the AutoCAD graphics system. The peculiarities of the kinematic method of surface formation, which is presented on the example of the surface of rotation, made in the graphics system AutoCAD, and the surface of a straight hyperboloid, the drawing of which is made in the system COMPASS-3D. Examples of practical use of simulated surfaces are given. Enough attention is paid to the study of frame surfaces. A complex drawing of the surface of a cylinder given by a linear framework is given. The three-line frame of the ship's surface, which is formed by waterlines, frames and buttocks, is presented in detail. Simulated frame surface of an axial gas turbine blade is presented in the AutoCAD system. Algorithms and methods of geometric modeling of surfaces in graphic systems AutoCAD and KOMPAS-3D are given. Geometric models of some surfaces have been developed: straight helicoid, single-cavity hyperboloid, hyperbolic paraboloid, surface with return edge, etc. Examples of practical implementation of simulated surfaces are given.
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