| DOI | https://doi.org/10.15407/pmach2017.01.045 |
| Journal | Journal of Mechanical Engineering – Problemy Mashynobuduvannia |
| Publisher | A. Podgorny Institute for Mechanical Engineering Problems National Academy of Science of Ukraine |
| ISSN | 0131-2928 (Print), 2411-0779 (Online) |
| Issue | Vol. 20, no. 1, 2017 (March) |
| Pages | 45-51 |
| Cited by | J. of Mech. Eng., 2017, vol. 20, no. 1, pp. 45-51 |
Authors
Yu. S. Litvinova, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: litjuli56@gmail.com
K. V. Maksymenko-Sheiko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: m-sh@ipmach.kharkov.ua, ORCID: 0000-0002-7064-2442
T. I. Sheyko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: sheyko@ipmach.kharkov.ua, ORCID: 0000-0003-3295-5998
Abstract
This paper investigates the possibilities and proposes techniques for the functional representation of a geometric object in 3D using information about the equations of the boundaries of the sections of the object being restored. Geometrical objects are constructed using the apparatus of the R-functions theory and a software product supporting it. This method of constructing geometric objects is a universal tool for modeling and visualization. The use of letter parameters significantly expands the design possibilities for the implementation of the modeling of geometric objects. The model stored in the computer’s memory allows a researcher to manipulate the resulting spatial images using the software of interactive three-dimensional computer graphics, varying the values of the literal parameters. The constructed mathematical models of geometric objects are their analytical identification, as evidenced by the visualization of the obtained equations.
Keywords: R-functions, spline, modeling, visualization, three-dimensional objects
References
- Rvachev, V. L. (1982). Teoriya R-funktsiy i nekotoryye yeye prilozheniya [The R-functions theory and some of its applications]. Kiyev: Naukova Dumka, 552 p. (in Russian).
- Maksimenko-Sheyko, K. V. (2009). R-funktsii v matematicheskom modelirovanii geometricheskikh obektov i fizicheskikh poley [R-functions in mathematical modeling of geometric objects and physical fields]. Kharkov: A. Podgorny Institute of Mechanical Engineering Problems of NASU, 306 p. (in Russian).
- Lytvyn, O. M. (2002). Interlinatsiia funktsii ta deiaki yii zastosuvannia [Interlination of functions and some of its applications]. Kharkiv: Osnova, 544 p. (in Ukrainian).
- Maksimenko-Sheyko, K. V., Matsevity, A. M., Tolok, A. V., & Sheyko, T. I. (2007). R-funktsii i obratnaya zadacha analiticheskoy geometrii v trekhmernom prostranstve [R-functions and inverse problem of analytic geometry in three-dimensional space]. Informatsionnyye tekhnologii – Information technologies, no. 10, pp. 23–32 (in Russian).
- Rvachev, V. L., Tolok, A. V., Uvarov, R. A., & Sheyko, T. I. (2000). Novyye podkhody k postroyeniyu uravneniy trekhmernykh lokusov s pomoshch’yu R-funktsiy [New approaches to the construction of three-dimensional equations of the loci using the R-functions]. Visnyk Zaporiz’koho derzhavnoho universytetu – ZNU Herald, no. 2, pp. 119–130 (in Russian).
- Maksimenko-Sheyko, K. V. & Sheyko, T. I. (2010). R-funktsii v matematicheskom modelirovanii geometricheskikh ob”yektov v 3D po informatsii v 2D [R-functions in mathematical modeling of geometrical objects in 3D under the information in 2D]. Visnyk Zaporizkoho natsionalnoho universytetu – Visnyk of Zaporizhzhya National University, no. 1, pp. 98–104 (in Russian).
Received 26 December 2016
Published 30 March 2017