Ekaterinburg, Russian Federation
employee from 01.01.1989 to 01.01.2020
Ekaterinburg, Russian Federation
Based on the published data, the essence of computational graphics has been laid down. Have been reported examples of new results obtained only through accurate computer constructions and measurements. The work content is a presentation of new ways to achieve the goal by solving non-traditional engineering problems. The author's method of projection with time-stamps, which, in fact, is a computer descriptive geometry, allows solve multi-parameter (not to be confused with multi-dimensional) problems with 9 variables [1–3; 13]. The author’s method of two-axis equal-sized evolvement [11; 12; 17] allows quantitatively measurements of solid angles. The addition of trigonometric functions (sinuses, sinusoids, etc.) can also be considered as a novelty [10; 11; 14]. At the junction of analytic (AG) and descriptive geometries have been calculated parameters of dodecahedron and has been given its mathematical description. In the traditional AG task, the required parameters have been calculated graphically, including a point’s speed of movement. Has been presented the author’s method for determining the instantaneous center in theoretical mechanics. For the first time, the equality of the angles of rotation for points and the link as a whole has been established, and a continuous centroid has been built. By decomposition of vectors a new way for summing up theirs vertical projections has been demonstrated. The developed method of projections with time-stamps allows simultaneously consider such parameters as spatial coordinates of moving objects (two or more) in time, their speeds and even sizes, including the variable ones. Has been shown the possibility for graphical programming while solving systems of equations, as well as for graphical solution of algebraic and stereometric problems. This publication aims to disseminate computer methods for engineering problems solving.
computer graphics, analytical and descriptive geometry, theoretical mechanics, algebra, stereometry, problem solving, KOMPAS-3D editor
1. Beglov I.A. Metod vrashcheniya geometricheskikh ob"yektov vokrug krivolineynoy osi [Mof rotation of geometrical objects around the curvilinear axis]. Geometrija i grafika [Geometry and graphics]. 2017, V. 5, I. 3, pp. 45–50. DOI: 10.12737/article_59bfa4eb0bf488.99866490. (in Russian)
2. Borovikov Ivan F., Ivanov Gennadiy Sergeevich, Surkova N., O primenenii preobrazovaniy pri reshenii zadach nachertatel'noy geometrii [On application of transformations at descriptive geometry’s problems solution]. Geometrija i grafika [Geometry and graphics]. 2018, V. 6, I. 2, pp. 78–84. DOI:10.12737/article_5b55a35d683a33.30813949. (in Russian)
3. Vasil'eva V.N. Zolotoye secheniye i zolotyye pryamougol'niki pri postroyenii ikosaedra, dodekaedra i tel arkhimeda, osnovannykh na nikh [Golden section and golden rectangles when building icosahedron, dodecahedron and archimedean solids based on them]. Geometrija i grafika [Geometry and graphics]. 2019, V. 7, I. 2, pp. 47–55. DOI: 10.12737/article_5d2c1ceb9f91b1.21353054. (in Russian)
4. Vygodsky M.Ya. Spravochnik po vysshey matematike [Handbook of Higher Mathematics]. Moscow: AST: Astrel Publ., 2010. 703 P. (in Russian)
5. Korotkiy V.A. Soprikosnoveniye konicheskikh secheniy [Contact of conic sections]. Geometrija i grafika [Geometry and graphics]. 2017, V. 4, I. 3, pp. 36–45. DOI: 10.12737/21532. (in Russian)
6. Kletenik D.V. Sbornik zadach po analiticheskoy geometrii [Collection of problems in analytic geometry]. Moscow: Science. Fizmatlit Publ., 1998. 224 p. (in Russian)
7. Monge G. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, Academy of Sciences of the USSR Publ., 1947. 291 p. (in Russian)
8. Panchuk K.L. Lyubchinov E.V. Tsiklograficheskaya interpretatsiya ikomp'yuternoye resheniye odnoy sistemy algebraicheskikh uravneniy [Cyclographic interpretation and computer solution of one system of algebraic equations] Geometrija i grafika [Geometry and graphics]. 2019, V. 7, I. 3, pp. 3–14. DOI: 10.12737/article_5dce5e528e4301.77886978. (in Russian)
9. Saveliev Yu.A. Grafika mnimykh chisel [Imaginary Graphics]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 1, pp. 22–23. DOI: 10.12737/465. (in Russian)
10. Saveliev Yu.A., Babich E.V. Graficheskaya trigonometriya v modernizatsii sushchestvuyushchikh i proyektirovanii novykh mashin i mekhanizmov [Graphical trigonometry in upgrading of existing and new machinery design]. Innovatsionnyy transport [Innovative transport]. 2017, I. 31 (23), pp. 55–62. (in Russian)
11. Saveliev Yu.A., Nevolin D.G., Babich E.V. Graficheskiye vychisleniya na osnove redaktora «Compas 3D» [Graphic calculations based on the Compass-3D editor]. Yekaterinburg, UrGUPS Publ., 2019. 196 p. (in Russian)
12. Saveliev Yu.A. Graficheskoye vektornoye ischisleniye [Graphic vector calculus]. Geometrija i grafika [Geometryand graphics]. 2013, V. 2, I. 4, pp. 3–6. – DOI: 10.12737/8291. (in Russian)
13. Saveliev Yu.A. Graficheskoye programmirovaniye [Graphical programming]. Sbornik nauchnykh trudov PGUAiS [Collection of scientific works of PSUAiS]. Penza, 2014, pp. 86–91. (in Russian)
14. Saveliev Yu.A. Graficheskoye ustroystvo dlya vypolneniya arifmeticheskikh operatsiy [Arithmetic graphics device]. Patent RF na izobretenie №2259590. Prioritet ot 02.09.2005 [RF patent for the invention No. 2259590. Priority from 02.09.2005].
15. Savelyev Yu. A., Cherkasova E.Yu. Kolichestvennoye izmereniye telesnykh uglov [Quantitative measurements of solid angles]. Vestnik UrGUPS [Bulletin of UrGUPS]. 2015, I. 4 (28), pp. 32–42. (in Russian)
16. Saveliev Yu.A. Komp'yuternaya grafika [Computer graphics]. Yekaterinburg, UrGUPS Publ., 2004. 58 p. (in Russian)
17. Saveliev Yu.A., Babich E.V. Komp'yuternaya metodika izucheniya nachertatel'noy geometrii. Tekhnicheskoye zadaniye [Computer method for learning of descriptive geometry. Technical task]. Geometrija i grafika [Geometry and graphics]. 2018, V. 6, I. 1, pp. 67–74. DOI: 10.12737/article_5ad09d62e8a792.47611365. (in Russian)
18. Saveliev Yu.A. K opredeleniyu chisla korney [To determine the number of roots]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 1, pp. 24–25. DOI: 10.12737/466. (in Russian)
19. Saveliev Yu.A., Babich E.V. Trekhmernaya grafika sredstvami sistemy «Compas 3D» [Three-dimensional graphics by means of the Compass-3D system] Yekaterinburg, UrGUPS Publ., 2016. 143 p. (in Russian)
20. Saveliev Yu.A. Chetyrekhmernyy kontinuum prostranstvo-vremya [Four-dimensional space-time continuum]. Vestnik UrGUPS [Bulletin of UrGUPS]. 2013, I. 1 (17), pp. 14–23. (in Russian)
21. Sal'kov Nikolay. Geometricheskaya sostavlyayushchaya tekhnicheskikh innovatsiy [The geometric component of technical innovation]. Geometrija i grafika [Geometry and graphics]. 2018, V. 6, I. 2, pp. 85–93. DOI: 10.12737/article_5b559a548fa209.41386317. (in Russian)
22. Sal'kov Nikolay. Formirovaniye tsiklicheskikh poverkhnostey v kineticheskoy geometrii [The formation of cyclic surfaces in kinetic geometry]. Geometrija i grafika [Geometry and graphics]. 2017, V. 5, I. 4, pp. 24–36. DOI: 10.12737/article_5a17fbe3680f52.30844454. (in Russian)
23. Trautman N. F. Sbornik zadach po nachertatel'noy geometrii v primenenii k razlichnym oblastyam nauki i tekhniki [Collection of problems in descriptive geometry as applied to various fields of science and technology]. Moscow, Mashgiz Publ., 1953. 279 p. (in Russian)
24. Cherkasova E.Yu. Innovatsionnyy metod resheniya geometricheskikh zadach dlya samostoyatel'nogo uglublennogo izucheniya studentami nachertatel'noy geometrii [An innovative method for solving geometric problems for independent in-depth study of descriptive geometry by students]. Pedagogicheskiye nauki [Pedagogical sciences]. «Sputnik+» Publ., 2017, I. 6(87), pp. 72–79. (in Russian)
25. Cherkasova E.Yu. Novyy podkhod v reshenii zadach po nachertatel'noy geometrii dlya razvitiya prostranstvennogo voobrazheniya u studentov [A new approach to solving problems in descriptive geometry for the development of spatial imagination in students]. Pedagogicheskiye nauki [Pedagogical sciences]. «Sputnik+» Publ., 2018, I. 6(93), pp. 56–61. (in Russian)
26. Cherkasova E.Yu. Obosnovanie novogo metoda kosougol'nogo proecirovaniya v nachertatel'noj geometrii [Justification of the new oblique projection method in descriptive geometry]. Informatika, vychislitel'naya tekhnika i inzhenernoye obrazovaniye. YUFU [Computer science, computer engineering and engineering education. SFU]. 2019, I. 2 (35). Available at: http://www/ ivtio.sfedu.ru. (in Russian)
27. Frolov S.A. Metody preobrazovaniya ortogonal'nykh proyektsiy [Orthogonal projection conversion methods]. Moscow: Mechanical Engineering Publ., 1970. 152 p. (in Russian)
28. Frolov S.A. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, Mechanical Engineering Publ., 1983. 240 p. (in Russian)
