Journal for Geometry and Graphics 27 (2023), No. 2, 151--157
Copyright Heldermann Verlag 2023
Bending of the Torses by Changing the Regularity of the Reverse Edge Angle of Ascent
Serhiy Pylypaka
University of Life and Environmental Sciences, Kyiv, Ukraine
ps55@ukr.net
Tetiana Volina
University of Life and Environmental Sciences, Kyiv, Ukraine
t.n.zaharova@ukr.net
Iryna Hryshenko
University of Life and Environmental Sciences, Kyiv, Ukraine
hryshchenko@nubip.edu.ua
Oleksandra Trokhaniak
University of Life and Environmental Sciences, Kyiv, Ukraine
klendii_o@ukr.net
Iryna Taras
National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine
iryna.taras@nung.edu.ua
A spatial curve can be described by two natural equations: the curvature and the torsion dependencies of its arc length. If such a curve is taken to be a torse reverse edge, its bending can be controlled by changing the curve's torsion, since the curvature does not change. However, in practice, such bending is difficult to perform, since there is no simple transition from the natural equations of the spatial curve to the parametric ones. This transition requires numerical methods for solving a system of differential equations. Another way to solve this question is to replace the dependency of the torsion of the arc length of the curve with the dependency of the angle of ascent and also of the arc length of the curve. In this case, the formulas for the transition from natural to parametric equations become much simpler and, in some cases, do not require numerical integration. This approach is used in the article for the construction of torses. The parametric equations of the torse in the general form are presented, for which the reverse edge is a spatial curve defined by the dependencies of the curvature and the angle of ascent of the length of its arc. It is shown that by changing the regularity of the angle of ascent, the process of the torse bending can be controlled. Examples are given, and the results are visualized.
Keywords: Spatial curve, natural and parametric equations, torse, reverse edge, bending.
MSC: 53A04.
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