Setting a Pair of Nearest Points on Intersecting Lines by Graphical and Computational Methods
T. P. Malyutina, Ya. R. Limanovskiy
Donbas National Academy of Civil Engineering and Architecture
Abstract: The article proposes a solution to the positional problem for crossing lines – the operation of the nearest points on these lines. Two algorithms are considered: graphical, solved by the method of descriptive geometry, and computational, based on the analytical method of point calculus. With the help of the mathematical apparatus of Balyuba-Naidysh (BN) – calculation, the current positions of the bases of perpendiculars drawn from the corresponding points on the crossing lines were set. A system of then-Chechen equations is obtained, which determines the definition of the nearest points located on the common perpendicular of two crossing lines. If the points coincide, the intersection point of the lines will be found. The detailed description of the computational algorithm for finding the distance between intersecting straight lines is an example of the introduction of point geometry elements within the discipline «Engineering and Computer Graphics» in the preparation of bachelors of engineering specialties.
Keywords: BN-calculus, point equation, computational algorithm, base of the perpendicular, metric operator of three points.
Pages: 48-52.
Link for citation: Malyutina, T. P.; Limanovskiy, Ya. R. Setting a Pair of Nearest Points on Intersecting Lines by Graphical and Computational Methods. – Text : electronic. – In: Proceeding of the Donbas National Academy of Civil Engineering and Architecture. – 2022. – Issue 2022-4(156) Scientific and technical achievements of students of the construction and architectural industry. – Р. 48-52. – URL: https://donnasa.ru/publish_house/journals/vestnik/2022/2022-4(156)/st_09_malyutina_limanovskyi.pdf (date of access: 15.10.2024). (in Russian)
Issue 2022-4 (156)Journal: Proceeding of the Donbas National Academy of Civil Engineering and Architecture
Publish house: Donbas National Academy of Civil Engineering and Architecture