from 01.10.2008 until now
Russian Federation
UDC 514
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.
applied geometry, engineering geometry, descriptive geometry, distance between geometric shapes, distance
1. Bubennikov A.V. Nachertatel'naya geometriya [Tekst] / A.V. Bubennikov, M.Ya. Gromov. — M.: Vysshaya shkola, 1973. — 416 s.
2. Vazhon'i A. Nauchnoe programmirovanie v promyshlennosti i v torgovle [Tekst] / A. Vazhon'i. — M.: Izd-vo inostrannoy literatury, 1963. — 388 s.
3. Vinnickiy I.G. Nachertatel'naya geometriya [Tekst] / I.G. Vinnickiy. — M.: Vysshaya shkola, 1975. — 280 s.
4. Vinogradov V.N. Nachertatel'naya geometriya [Tekst] / V.N. Vinogradov. — Minsk: Vysh. shkola, 1977. — 268 s.
5. Vorob'ev B.M. Reshenie nekotoryh zadach lineynogo programmirovaniya sredstvami nachertatel'noy geometrii [Tekst] / B.M. Vorob'ev, P.A. Lyashkevich. — M.: Izd-vo MGI, 1972. — 76 s.
6. Vygodskiy M.Ya. Analiticheskaya geometriya [Tekst] / M.Ya. Vygodskiy. — M.: Fizmatizdat, 1963. — 526 s.
7. Vygodskiy M.Ya. Differencial'noe ischislenie [Tekst] / M.Ya. Vygodskiy. — M.: Fizmatgiz, 1965. — 592 s.
8. Glagolev N.A. Nachertatel'naya geometriya [Tekst] / N.A. Glagolev. — M.-L.: ONTI NKTP SSSR, Glavnaya redakciya obschetehnicheskoy literatury i nomografii, 1936. — 160 s.
9. Golovincov A.G. Issledovanie rabochih ciklov porshnevyh dvigateley vneshney generacii rabochego tela [Tekst]: dis. ... d-ra tehn. nauk: 05.00.00 / A.G. Golovincov. — V 2 t. — M., 1956. — 294 s.
10. Gordon V.O. Kurs nachertatel'noy geometrii [Tekst] / V.O. Gordon, M.A. Semencov-Ogievskiy. — M.: Nauka, 1977. — 268 s.
11. Grohot-pitatel'. — Sal'kov N.A. — Avtorskoe svidetel'stvo SU 1025461 A1, 30.06.1983. Zayavka № 3333233 ot 25.06.1981.
12. Dvuhchervyachnyy smesitel' dlya pastoobraznyh materialov. Sal'kov N.A. Avtorskoe svidetel'stvo SU 1199625 A1, 23.12.1985. Zayavka № 3773765 ot 23.07.1984.
13. Dobryakov A.I. Kurs nachertatel'noy geometrii [Tekst] / A.I. Dobryakov. — M.-L.: Gos. izd-vo literatury po stroitel'stvu i arhitekture, 1952. — 496 s.
14. Ivanov G.S. Nachertatel'naya geometriya [Tekst] / G.S. Ivanov. — M.: Izd-vo MGUL, 2012. — 340 s.
15. Klimuhin A.G. Nachertatel'naya geometriya [Tekst] / A.G. Klimuhin. — M.: Stroyizdat, 1978. — 334 s.
16. Kolotov S.M. Kurs nachertatel'noy geometrii [Tekst] / S.M. Kolotov, E.E. Dol'skiy, V.E. Mihaylenko i dr. Kiev: Gos. izd-vo literatury po stroitel'stvu i arhitekture USSR, 1961. — 316 s.
17. Koroev Yu.I. Nachertatel'naya geometriya [Tekst] / Yu.I. Koroev. — M.: KNORUS, 2011. — 432 s.
18. Korotkiy V.A. Nachertatel'naya geometriya: konspekt lekciy [Tekst] / V.A. Korotkiy, L.I. Hmarova, I.V. Butorina. — Chelyabinsk: Izd-vo YuUrGU, 2014. 191 s.
19. Krylov N.N. Nachertatel'naya geometriya [Tekst] / N.N. Krylov, P.I. Lobandievskiy, S.A. Men, V.L. Nikolaev, G.S. Ikonnikova. — M.: Vysshaya shkola, 1977. 231 s.
20. Krylov N.N. Nachertatel'naya geometriya [Tekst] / N.N. Krylov, G.S. Ikonnikova, V.L. Nikolaev, N.M. Lavruhina. — M.: Vysshaya shkola, 1990. — 240 s.
21. Kuznecov N.S. Nachertatel'naya geometriya [Tekst] / N.S. Kuznecov. — M.: Vysshaya shkola, 1981. — 262 s.
22. Kuznecov Yu.N. Matematicheskoe programmirovanie [Tekst] / Yu.N. Kuznecov, V.I. Kuzubov, A.V. Voloschenko. — M.: Vysshaya shkola, 1980. — 304 s.
23. Peklich V.A. Nachertatel'naya geometriya [Tekst] / V.A. Peklich. — M.: Izd-vo associacii stroitel'nyh vuzov, 2007. — 272 s.
24. Privalov I.I. Analiticheskaya geometriya [Tekst] / I.I. Privalov. — M.: Izd-vo tehnichesko-teoreticheskoy literatury, 1957. — 300 s.
25. Russkevich N.L. Nachertatel'naya geometriya [Tekst] / N.L. Russkevich. — Kiev: Vischa shkola, 1978. — 312 s.
26. Sal'kov N.A. Nachertatel'naya geometriya — baza dlya geometrii analiticheskoy [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2016. — T. 4. — № 1. — S. 44–54. DOI:https://doi.org/10.12737/18057
27. Sal'kov N.A. Nachertatel'naya geometriya — baza dlya komp'yuternoy grafiki [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2016. — T. 4. — № 2. — S. 37–47. — DOI:https://doi.org/10.12737/19832
28. Sal'kov N.A. Nachertatel'naya geometriya: bazovyy kurs [Tekst]: ucheb. posobie / N.A. Sal'kov. — M.: INFRA-M, 2013. — 184 s.
29. Sal'kov N.A. Nachertatel'naya geometriya: Konstruirovanie poverhnostey [Tekst] / N.A. Sal'kov. — M.: INFRA-M, 2022. — 220 s.
30. Sal'kov N.A. Ciklida Dyupena i krivye vtorogo poryadka. Chast' 1 [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2016. — T. 4. — № 2. — S. 19–28. — DOI:https://doi.org/10.12737/19829
31. Sal'kov N.A. Ciklida Dyupena i krivye vtorogo poryadka. Chast' 2 [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2016. — T. 4. — № 4. — S. 17–28. — DOI:https://doi.org/10.12737/21530
32. Sal'kov N.A. Ellips: kasatel'naya i normal' [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2013. — T. 1. № 2. — S. 52–53. — DOI:https://doi.org/10.12737/2084
33. Timrot E.S. Nachertatel'naya geometriya [Tekst] / E.S. Timrot. — M.: Gos. izd-vo literatury po stroitel'stvu, arhitekture i stroitel'nym materialam, 1962. — 280 s.
34. Filippov P.V. Nachertatel'naya geometriya mnogomernogo prostranstva i ee prilozhenie. — L.: Izd-vo Leningradskogo gos. un-ta, 1979. — 280 s.
35. Frolov S.A. Nachertatel'naya geometriya [Tekst] / S.A. Frolov. — M.: Mashinostroenie, 1983. — 240 s.
36. Chetveruhin N.F. Kurs nachertatel'noy geometrii [Tekst] / N.F. Chetveruhin [i dr.]. — M.: Gos. izd-vo tehniko-teoreticheskoy literatury, 1956. — 436 s.
