SPATIAL TECHNICAL CURVES AS SMOOTH LINES OF THE ARCS NORMCURVES - Ivanov, G.; Dzhanabaev, Zh.; Umbetov, N.; Borovikov, I. (Academic Scientific Journal of Computer Science, 2020)
In solving applied problems one often encounters with the construction of spatial curves for a number of pre-set conditions. As a rule, the constructed curve is set by a set of pre-calculated or experimentally obtained conditions (points, tangents, values of curvature and torsion at these points). The horizontal and frontal projections (plan and profile) are calculated independently. As a result, the outline will consist of arcs of spatial curves no lower than the fourth order with unpredictable differential properties. The arcs of circular norm-curved spaces are devoid of this drawback. The article discusses some theoretical questions of curve theory for a rational choice of smooth contour components. It is proposed to use arcs of cubic circles as components of a spatial smooth one-dimensional contour. A cubic circle, being a special case of a cubic ellipse, intersects an improper plane at a real point and at two cyclic points. Such curves have better differential properties from the standpoint of the monotonicity of changes in the values of the angles of inclination of the tangents, curvature, and torsion, which significantly affects the dynamic qualities of the contour being constructed.