Discrete modeling of building structures geometric images

  • Authors

    • Oleg Vorontsov
    • Larissa Tulupova
    • Iryna Vorontsova
    2018-06-20
    https://doi.org/10.14419/ijet.v7i3.2.15467
  • Discrete Modeling, Geometric Images, Finite Difference Method, Static-Geometric Method, Geometric Apparatus Of Superpositions.
  • For discrete modeling of geometric images, it is possible to use the numerical method of finite differences, the static-geometric method, the mathematical apparatus of numerical sequences. Each of them has certain advantages and disadvantages, which depend on the solution of specific practical problems.

    This article proposes to use the geometric apparatus of superpositions together with the above-mentioned methods. It allows significantly to improve the efficiency and expanding capacities of the process of geometric images discrete modeling. In particular, it makes it possible to investigate an opportunity of interpolating as parabolic functions as well as other elementary functional dependencies.

    The purpose of this article is to expand capacities of the classical finite difference method and static-geometric method by using the geometric apparatus of superpositions. It allows using hyperbolic functions as interpolators for the geometric images discrete modeling.

    The result of this study is the obtained interpolating and extrapolating templates, which allow modeling geometric images of architectural and building constructions in a form of chain lines discrete frames.

  • References

    1. [1] Guoliang Xu, Oing Pan, Chandrajit L. Bajaj. Discrete surface modelling using partial differential equations. Computer Aided Geometric Design. Volume 23, Issue 2, February 2006, pp. 125-145, https://doi.org/10.1016/j.cagd.2005.05.004

      [2] Lienhardt P. (1997) Aspects in topology-based geometric modeling Possible tools for discrete geometry?. In: Ahronovitz E., Fiorio C. (eds) Discrete Geometry for Computer Imagery. DGCI 1997. Lecture Notes in Computer Science, vol 1347. Springer, Berlin, Heidelberg pp 33-48. https://doi.org/10.1007/BFb0024828

      [3] Vorontsov O.V. Dyskretnykh modelyuvannya heometrychnist obraziv ob'yektiv proektuvannya superpozitsiyami odnovimirnikh chyslovykh poslidovnostey z urakhuvannyam funktsional noho navantazhennya / O.V. Vorontsov // Zbirnyk naukovykh prats (Haluzevyy mashynobuduvannya, budivnytstvo) / Poltav. nats. tekhn. un-t im. Yuriya Kondratyuka. - Poltava: PoltNTU, 2015. - Vyp. 3 (45). - S. 28 - 39. ISSN 2409-9074

      [4] Kovalev S.N. Formirovaniye diskretnykh modeley poverkhnostey prostranstvennykh arkhitekturnykh konstruktsiy: dis. ... doktora tekhn. nauk: 05.01.01 / S.N. Kovalev - M .: MAI, 1986. - 348 s

      [5] Savelov A.A. Ploskiye krivyye. Sistematika, svoystva, primeneniya. (Spravochnoye rukovodstvo). Pod redaktsiyey A.P. Nordena. Gosudarstvennoye izdatel'stvo fiziko-matematicheskoy literatury. Moskva 1960 g. - 293 s.

      [6] Vorontsov O. Recurrence formulae of a catenary in creation of geometric images. / O. Vorontsov., L. Tulupova // Oxford Journal of Scientific research No. 1. (9), January-June, 2015, Volume IV. P. 134 – 140. ISSN 0305-4882.

      [7] Vygodskiy M.YA. Differentsial'naya geometriya. Gosudarstvennoye izdatel'stvo tekhnicheskoy literatury. Moskva 1949 Leningrad. - 511 s.

      [8] Vorontsov O.V. Vyznachennya dyskretnoho analohu polinoma n-ho stepenya superpozitsiyami tochok chislovoyi poslidovnosti n-ho poryadku / O.V. Vorontsov // Prykladna heometriya ta inzhenerna hrafika: zb. nauk. pratsʹ - K .: KNUBA, 2012. - Vyp. 90. - S. 63 - 67. ISSN 0131-579X

      [9] Vorontsov O.V. Dyskretna interpolyatsiya superpozitsiyami tochok chyslovykh poslidovnostey drobovi-liniynikh funktsiy / O.V. Vorontsov, N.O. Makhinʹko // Prykladna heometriya ta inzhenerna hrafika: pratsi TDATU. - Melitopolʹ: TDATU, 2013. Vyp. 4. - T. 57. - S. 62 - 67.

      [10] Vorontsov O.V. Vlastyvosti superpozitsiy tochkovykh mnozhyny / O.V. Vorontsov // Prykladna heometriya ta inzhenerna hrafika: zb. nauk. pratsʹ - K .: KNUBA, 2010. - Vyp. 86. - S. 345 - 349. ISSN 0131-579X

      [11] Vorontsov O.V. Opredeleniye diskretnykh analogov klassov elementarnykh funktsiy superpozitsiyami odnomernykh tochechnykh mnozhestv [Elektronnyy resurs] / O.V. Vorontsov, L.O. Tulupova // Universsum. Ser.: Tekhnicheskiye nauki: elektron. nauchn. zhurn. − 2014. − № 3(4). – ISSN 2311-5122.

      [12] Vorontsov O.V. Dyskretna interpolyatsiya superpozytsiyamy odnovymirnykh tochkovykh mnozhyn transtsendentnykh funktsionalʹnykh zalezhnostey na prykladi hiperbolichnykh funktsiy. / O.V. Vorontsov // Visnyk Khersonsʹkoho natsionalʹnoho tekhnichnoho universytethu / Vyp. 3(54). – Kherson: KHNTU, 2015. – S. 551-554 ISSN 2078-4481

      [13] Vorontsov O.V. Dyskretna interpolyatsiya heometrychnykh obraziv superpozytsiyamy dvovymirnykh tochkovykh mnozhyn funktsionalʹnykh zalezhnostey / O.V. Vorontsov, L.O. Tulupova, I.V. Vorontsova // Visnyk Khersonsʹkoho natsionalʹnoho tekhnichnoho universytethu / Vyp. 3(62). T.2. – Kherson: KHNTU, 2017. – S. 66-70 ISSN 2078-4481

      [14] Kovalev S.N. O superpozytsyi / S.N. Kovalev // Prykladna heometriya ta inzhenerna hrafika: zb. nauk. pratsʹ. – K.: KNUBA, 2010. − Vyp. 84. – S. 38 – 42. ISSN 0131-579X

      [15] Vorontsov O.V. Diskretnoye modelirovaniye krivykh poverkhnostey superpozitsiyami dvumernykh tochechnykh mnozhestv / O.V. Vorontsov, L.O. Tulupova // Sbornik statey po materialam XL mezhdunarodnoy nauchno-prakticheskoy konferentsii «Tekhnicheskiye nauki – ot teorii k praktike». – Novosibirsk, 2014. – №11 (36). – S. 7 – 16. –ISSN 2308-5991.

      [16] Kochkarev D. Calculation methodology of reinforced concrete elements based on estimated resistance of reinforced concrete / D. Kochkarev, T. Galinska // Matec Web of Conferences 116, 02020 (2017), Materials science, engineering and chemistry, Transbud–2017, Kharkiv, Ukraine, April 19–21, 2017. https://doi.org/10.1051/matecconf/201711602020

  • Downloads

  • How to Cite

    Vorontsov, O., Tulupova, L., & Vorontsova, I. (2018). Discrete modeling of building structures geometric images. International Journal of Engineering & Technology, 7(3.2), 727-731. https://doi.org/10.14419/ijet.v7i3.2.15467