Determining the Distances between Geometric Shapes Using the Interactive Method

N. Sal&#039;kov

doi:10.12737/2308-4898-2024-12-4-3-14

UDC 378 UDC 514

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DETERMINING THE DISTANCES BETWEEN GEOMETRIC SHAPES USING THE INTERACTIVE METHOD Determining the Distances between Geometric Shapes Using the Interactive Method

АА Аа

Published in Geometry & Graphics · Volume 12, Issue 4 · Pages 3–14 · Rubric: Scientific problems of geometry

DOI: https://doi.org/10.12737/2308-4898-2024-12-4-3-14

Received: 12.05.2025 Accepted: 12.05.2025 Published: 12.05.2025

Authors

N. Sal'kov

Academic degree: candidate of technical sciences

Science rang: professor

MIREA – Russian technological university Russian Federation

ABSTRACT

Distance-related tasks are constantly encountered in various ways in industry, in transportation, in mathematical programming, and even in space. Basically, these tasks occur where there is a movement of geometric shapes. In this case, we are not talking about the distance between the centers of mass, as we find in physics, we are talking about the distance from the surface of one geometric shape to the surface of another. These tasks are especially pronounced in computer games, where, as shown in a couple of screenshots in the text of the article, secondary "inhabitants", the so-called Non-Player Character (NPC), are very effectively glued into the textures of the environment surrounding the player. The paper shows the general geometric position of the problem, geometric and mathematical solutions to the problem: the distance between two lines, between a line and a surface, between two surfaces, as well as the use of equidistant surfaces as intermediaries – all this using analytical and differential research tools. Then computer solutions are considered: linear search, linear sequential search, pendulum search, one-way search for a solution to the problem. Then the constraints that can be imposed on geometric shapes are considered. In the end, it talks about the simplicity of calculation in computer games: it is rather strange that, having in the arsenal of games such as those that occupy many gigabytes of memory on a hard drive, developers still have not been able to cope with such a small incongruity for the available computing speed in processors. This article will help them to overcome this disadvantage in the shortest possible time.

KEYWORDS

applied geometry, engineering geometry, descriptive geometry, distance between geometric shapes, distance

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JATS XML

Zamestitel' glavnogo redaktora, chlen redsoveta

Vladimir Vyshnyepolskiy

Glavnyy redaktor

A. A. Ishchenko

Vypuskayuschiy redaktor

Dar'ya Sklyankina

501@infra-m.ru

Deputy editor-in-chief, member of the editorial Board

N. Sal'kov

nikolaysalkov@mail.ru

GOST

Sal'kov N. A. Determining the Distances between Geometric Shapes Using the Interactive Method // Geometry & Graphics. 2025. no. 4. pp. 3-14. DOI: https://doi.org/10.12737/2308-4898-2024-12-4-3-14. (Date of access 24.09.2026).

MLA

N. Sal'kov. "Determining the Distances between Geometric Shapes Using the Interactive Method." Geometry & Graphics 12.4 (2025): 3-14. DOI: https://doi.org/10.12737/2308-4898-2024-12-4-3-14.

APA

Sal'kov N. A. (2025). Determining the Distances between Geometric Shapes Using the Interactive Method. Geometry & Graphics, 12(4), 3-14. https://doi.org/10.12737/2308-4898-2024-12-4-3-14

Chicago

N. Sal'kov. "Determining the Distances between Geometric Shapes Using the Interactive Method." Geometry & Graphics 12, no. 4 (2025): 3-14. https://doi.org/10.12737/2308-4898-2024-12-4-3-14.

WIKI

{{cite journal | author = Sal'kov N. A. | title = Determining the Distances between Geometric Shapes Using the Interactive Method | journal = Geometry & Graphics | year = 2025 | volume = 12 | issue = 4 | pages = 3-14 | doi = 10.12737/2308-4898-2024-12-4-3-14 }}

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DETERMINING THE DISTANCES BETWEEN GEOMETRIC SHAPES USING THE INTERACTIVE METHOD Determining the Distances between Geometric Shapes Using the Interactive Method

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