A technique for approximating a tubular helical surface with strips of toruses
DOI:
https://doi.org/10.15587/1729-4061.2025.343193Keywords:
line of curvature, tangent strip, geodesic curvature, sweeping surface, numerical integrationAbstract
This study’s object is the approximation of a non-swept helical tubular surface by strips of sweeping surfaces (toruses) and the construction of sweeps of these strips.
Approximating non-swept tubular surfaces by sections of sweep ones is a common practice in the design of various types of pipelines. A clear example of such an approximation is a sports ball whose outer shell consists of a certain number of separate elements. These elements must fit most tightly to the non-swept surface along its certain lines. Such lines are the lines of curvature. The task is to find these lines on the surface in order to subsequently analytically describe the torus strip, which is tangent to the non-swept surface along this line.
As is known, there are two families of mutually perpendicular lines of curvature on surfaces. This paper considers a family of curvature lines that has advantages over another one in terms of approximation. This explains the results reported here. Their special feature is that in order to find the desired family of curvature lines, it is necessary to solve a differential equation.
The solution to this equation was borrowed from a scientific article and used for further calculations. The results were visualized in the form of an approximated tubular surface with four and six strips.
The sweeps of these strips were constructed for a tubular surface, in which the center line is a helical line r = 1. All dimensions are given in linear units. Instead of a circle generatrix, it is given by the radius of the cylinder a = 2, which hosts it, and the helical parameter b = 1.5 (step H = 9.4). The radius of the circle generatrix of the tubular surface of the original tubular surface in the approximated surface in the given examples is a polygon (square or equilateral hexagon).
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Copyright (c) 2025 Andrii Nesvidomin, Serhii Pylypaka, Victor Nesvidomin, Vitaliy Babka, Olga Shoman, Oleksandr Savoiskyi, Taras Pylypaka, Mykola Lokhonia, Svetlana Semirnenko, Yana Borodai
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