To the Question of the Classification for Analytical Surfaces

Stanislav Strashnov; Marina Rynkovskaya

doi:10.12737/2308-4898-2022-10-1-36-43

UDC 51

TO THE QUESTION OF THE CLASSIFICATION FOR ANALYTICAL SURFACES To the Question of the Classification for Analytical Surfaces

АА Аа

Published in Geometry & Graphics · Volume 10, Issue 1 · Pages 36–43 · Rubric: Methodical questions of teaching

DOI: https://doi.org/10.12737/2308-4898-2022-10-1-36-43

Received: 20.06.2022 Accepted: 29.06.2022 Published: 29.06.2022

Authors

Stanislav Strashnov

ORCID Scopus SPIN

Marina Rynkovskaya

Stanislav Strashnov

Academic degree: candidate of technical sciences

RUDN University Associated professor · General education courses department · Russian Federation · Moscow

ORCID Scopus SPIN

Marina Rynkovskaya

Academic degree: candidate of technical sciences

Peoples’ Friendship University of Russia Associated professor · Department of Civil Engineering · Moscow

ABSTRACT

Until this day, in scientific and technical literature there are descriptions of around 600 analytical surfaces, divided into 38 classes. In turn, it is possible to divide almost each class of surfaces into sub-classes, groups, or types, that is, to compose a classification for surfaces. It will make it easier their further study. For some classes of surfaces there is no sense to set up classification schemes, since these classes consist of a small number of surfaces, or the classification will contain a bare listing of surfaces. These surfaces can include minimal and one-sided surfaces, spiral and helical ones, surfaces of Ciceika and Edlinger, as well as undulating, wavy and corrugated surfaces, and several others. The "others" category includes surfaces which, although highlighted in separate classes, are few, or they are in the process of studying. The study of scientific literature has shown that a classification for revolution surfaces, as well as for transfer and Peterson ones has not yet been set up. This paper is devoted to these classes of analytical surfaces. As the study has showed, it is possible to draw interesting conclusions based on presented classifications. In this paper it has been shown how the appearance of scientific publications devoted to classification for surfaces promote the emergence of numerous works on application of relevant surfaces in architecture, construction, engineering, shipbuilding, light industry products, topography and cartography. But devotion to analytic surfaces’ geometric forms should not be an end in itself in actual practice. So, today architects are passionate about parametric architecture, which is based on knowledge of analytical surfaces’ geometry. However, some leading architects believe that the parametric architecture oversaturated the human life’s space, resulting in a style crisis. Despite architects and engineers’ conflicting opinions, geometers must go ahead of society's immediate demands, creating new forms, classifications, and proposals.

KEYWORDS

analytical surfaces, surface classification, revolution surfaces, transfer surfaces, Peterson surfaces

1. Alaeva T.Yu. K voprosu o klassifikacii poverhnostey// V sbornike: Aktual'nye problemy nauki v agropromyshlennom komplekse. Sbornik statey 71-y mezhdunarodnoy nauchno-prakticheskoy konferencii. V 3-h tomah. Pod redakciey S.V. Cybakina, M.A. Ivanovoy, A.V. Rozhnova. 2020. S. 6-11.

2. Bazderova T.A. Voprosy klassifikacii lineychatyh poverhnostey i postroenie ih razvertok [Tekst] / T. A. Bazderova // Kuzbas. politehn. in - t. - Kemerovo, 1985. - 53 s. Rukopis' dep. v VINITI 19 iyunya 1985 g., № 4375-85 Dep.

3. Belyakova M.S. Povyshenie effektivnosti processov konstruktorsko - tehnologicheskogo proektirovaniya na osnove razrabotki informacionnoy sistemy modelirovaniya poverhnostey [Tekst]: avtoref. dis. …kand. tehn. nauk / M. S. Belyakova. - M., 2007. - 26 s.

4. Berestova S.A. Geometriya samonesuschih pokrytiy na pryamougol'nom plane [Tekst] / S.A. Berestova, N.E. Misyura, E.A. Mityushov // Stroitel'naya mehanika inzhenernyh konstrukciy i sooruzheniy. - 2017. - № 4. - S. 15 - 18. - DOI:https://doi.org/10.22363/1815-5235-2017-4-15-18.

5. Boykov A.A. Komp'yuternaya proverka resheniy zadach nachertatel'noy geometrii dlya inzhenerno-graficheskogo obrazovaniya/ Geometriya i grafika. - 2020. - T. 8. - № 2. - S. 66 - 81.

6. Burlov V.V. 3D-modelirovanie poverhnostey 2-go poryadka [Tekst] / V. V. Burlov, L.A. Nesterenko, L.V. Remontova, N.S. Orlov // Geometriya i grafika. - 2016. - T. 4. - № 4. - S. 48 - 59.

7. Grin'ko E.A. Klassifikaciya analiticheskih poverhnostey primenitel'no k parametricheskoy arhitekture i mashinostroeniyu [Tekst] / E. A. Grin'ko // Vestnik Rossiyskogo universiteta druzhby narodov. Seriya: Inzhenernye issledovaniya. - 2018. - T. 19. - № 4. - S. 438 - 456.

8. Zhiharev L.A. Fraktaly v trehmernom prostranstve. I-fraktaly [Tekst] / L. A. Zhiharev // Geometriya i grafika. - 2017. - T. 5. - № 3. - S. 51 - 66.

9. Zolotuhin V.F. Klassifikaciya poverhnostey [Tekst] / V. F. Zolotuhin // Volgograd. politehn. in-t. - Volgograd, 1979. - 11 s. Rukopis' dep. v VINITI 17 marta 1980 g., № 1007-80 Dep.

10. Ivanov V.N. Osnovy razrabotki i vizualizacii ob'ektov analiticheskih poverhnostey i perspektivy ih ispol'zovaniya v arhitekture i stroitel'stve [Tekst] / V. N. Ivanov, S. N. Krivoshapko, V. A. Romanova // Geometriya i grafika. - 2017. - T. 5. - № 4. - S. 3 - 14.

11. Ignat'ev S.A., Folomkin A.I., Muratbakeev E.H. Funkcional'nye vozmozhnosti sredy Wolfram Mathematica dlya vizualizacii krivyh liniy i poverhnostey// Geometriya i grafika. - 2021. - T. 9. - № 1. - S. 29 - 38.

12. Ignat'ev S.A., Folomkin A.I., Tret'yakova Z.O., Glazunov K.O. Elektronnaya obuchayuschaya sreda moodle kak effektivnoe sredstvo organizacii obucheniya nachertatel'noy geometrii v usloviyah pandemii covid-19 // Geometriya i grafika. - 2020. - T. 8. - № 3. - S. 52 - 66.

13. Krivoshapko S.N. Analiticheskie lineychatye poverhnosti i ih polnaya klassifikaciya [Tekst] / S. N. Krivoshapko // Stroitel'naya mehanika inzhenernyh konstrukciy i sooruzheniy. - 2020 - T. 16. - № 2. - S. 131 - 138. - DOI:https://doi.org/10.22363/1815-5235-2020-16-2-131-138.

14. Krivoshapko S.N. Analiticheskie poverhnosti v arhitekture zdaniy, konstrukciy i izdeliy [Tekst] / S. N. Krivoshapko, I. A. Mamieva. - M.: Knizhnyy dom «LIBROKOM», 2012, 2018. - 328 s..

15. Krivoshapko S.N. K voprosu ob oshibkah v terminologii po teorii poverhnostey i geometricheskogo modelirovaniya// Geometriya i grafika. - 2017. - Tom 5. - № 2. - S. 32-38.

16. Krivoshapko S.N. Klassifikaciya ciklicheskih poverhnostey [Tekst] / S. N. Krivoshapko, V. N. Ivanov // Stroitel'naya mehanika inzhenernyh konstrukciy i sooruzheniy. - 2006. - № 2. - S. 25 - 34.

17. Krivoshapko S.N. Obolochki vrascheniya nekanonicheskih form [Tekst] / S. N. Krivoshapko // Izvestiya vysshih uchebnyh zavedeniy. Stroitel'stvo. - 2018. - № 7 (715). - S. 66 - 79.

18. Mamieva I.A. Analiticheskie poverhnosti dlya parametricheskoy arhitektury v sovremennyh zdaniyah i sooruzheniyah [Tekst] / I. A. Mamieva // Academia. Arhitektura i stroitel'stvo. - 2020. - № 1. - S. 150 - 165.

19. Miftahutdinov I.H. Naglyadnaya geometriya obolochek minimal'noy poverhnosti [Tekst] / I. H. Miftahutdinov. - Kazan': ZAO «Novoe znanie», 2009. - 40 s.

20. Parametricheskie poverhnosti i tela [Parametrische Flächen und Körper] Available at: http://www.3d-meier.de/tut3/Seite0.html (accessed 29 October 2021)

21. Peterson K.M. Ob otnosheniyah i srodstvah mezhdu krivymi poverhnostyami [Tekst] / K. M. Peterson // Matematicheskiy sbornik. - 1866. - T. 1. - S. 391 - 438.

22. Pischulina I.Ya. Poverhnosti vtorogo poryadka [Tekst] / I. Ya. Pischulina, E. V. Kukushkina. - Ekaterinburg: UrFU, 2012. - 166 s.

23. Savel'ev Yu.A., Cherkasova E.Yu. Vychislitel'naya grafika v reshenii netradicionnyh inzhenernyh zadach// Geometriya i grafika. - 2020. - T. 8. - № 1. - S. 33 - 44.

24. Sal'kov N.A. Obschie principy zadaniya lineychatyh poverhnostey. Chast' 2 [Tekst] / N. A. Sal'kov // Geometriya i grafika. - 2019. - T. 7. - № 1. - S. 14 - 27.

25. Sal'kov N.A. Formirovanie ciklicheskih poverhnostey v kineticheskoy geometrii [Tekst] / N. A. Sal'kov // Geometriya i grafika. - 2017. - T. 5. - № 4. - S. 24 - 36.

26. Tevlin A.M. Kvazivintovye poverhnosti i voprosy ih konstruirovaniya i otobrazheniya [Tekst] / A. M. Tevlin // Kinematicheskie metody konstruirovaniya tehnicheskih poverhnostey. - M.: MAI, 1970. - Vyp. 213. - S. 112 - 114.

27. Tupikova E.M. Vybor optimal'noy obolochki pokrytiya na kvadratnom plane v vide poverhnosti perenosa [Tekst] / E. M. Tupikova // Stroitel'naya mehanika inzhenernyh konstrukciy i sooruzheniy. - 2019. - T. 15. - № 5. - S. 367 - 373.

28. Usataya T.V., Deryabina L.V., Reshetnikova E.S. Sovremennye podhody k proektirovaniyu izdeliy v processe obucheniya studentov komp'yuternoy grafike/ Geometriya i grafika. - 2019. - T. 7. - № 1. - S. 74 - 82.

29. Corato A. Classification of Complex Algebraic Surfaces. Master Thesis. 2018. 70 p.

30. Gil-oulbé M. Geometry and classification of carved Monge surfaces / Gil-oulbé M., Ndomilep A. J. I. // Journal of Physics: Conference Series. 2020. V. 1687, International Conference on Engineering Systems 2020, 14 - 16 October 2020, Moscow, Russia.

31. Krivoshapko S.N. Classification of cyclic surfaces and geometrical research of canal surfaces / Krivoshapko S.N., Hyeng C. A. B. // International Journal of Research and Reviews in Applied Sciences. 2012. V. 12. I. 3. pp. 360 - 374.

32. Krivoshapko S.N., Ivanov V.N. Encyclopedia of Analytical Surfaces. Cham, Heidelberg, New York, Dordrecht, London, Springer International Publishing Switzerland, 2015. 752 p. DOI:https://doi.org/10.1007/978-3-319-11773-7.

33. Mamieva I.A. Influence of the geometrical researches of rare type surfaces on design of new and unique structures / Mamieva I.A., Gbaguidi-Aisse G.L. // Stroitel'stvo i rekonstrukciya. 2019. № 5 (85). S. 23-34.

34. Murre J.P. Classification of algebraic varieties / Murre J.P. // Nieuw. Arch. Wisk. 1977. 25. No. 3. pp. 308 - 338.

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

Strashnov S. V., Rynkovskaya M. I. To the Question of the Classification for Analytical Surfaces // Geometry & Graphics. 2022. no. 1. pp. 36-43. DOI: https://doi.org/10.12737/2308-4898-2022-10-1-36-43. (Date of access 08.10.2026).

MLA

Stanislav Strashnov, Rynkovskaya M. I.. "To the Question of the Classification for Analytical Surfaces." Geometry & Graphics 10.1 (2022): 36-43. DOI: https://doi.org/10.12737/2308-4898-2022-10-1-36-43.

APA

Strashnov S. V., Rynkovskaya M. I. (2022). To the Question of the Classification for Analytical Surfaces. Geometry & Graphics, 10(1), 36-43. https://doi.org/10.12737/2308-4898-2022-10-1-36-43

Chicago

Stanislav Strashnov, Rynkovskaya M. I.. "To the Question of the Classification for Analytical Surfaces." Geometry & Graphics 10, no. 1 (2022): 36-43. https://doi.org/10.12737/2308-4898-2022-10-1-36-43.

WIKI

{{cite journal | author = Strashnov S. V., Rynkovskaya M. I. | title = To the Question of the Classification for Analytical Surfaces | journal = Geometry & Graphics | year = 2022 | volume = 10 | issue = 1 | pages = 36-43 | doi = 10.12737/2308-4898-2022-10-1-36-43 }}

Copy

Export: BibTeX EndNote RefMan RusMARC

TO THE QUESTION OF THE CLASSIFICATION FOR ANALYTICAL SURFACES To the Question of the Classification for Analytical Surfaces

Confirmation