3D SIMULATION OF SECOND-ORDER SURFACES
Abstract and keywords
Abstract (English):
This paper’s material is destined for high educational institutions’ graduate students and teachers whose professional activity is connected with problems of descriptive geometry and engineering graphics teaching improving on the basis of modern computer technology. The paper will be useful to students of technical universities in their further understanding the course of descriptive geometry and inoculation them an interest in their personal geometric and graphic training, without which a quality engineering creativity is impossible. The paper focuses on use of KOMPAS-3D software possibilities which enables solution of nearly all educational, as well as professional engineering and graphics problems. At the same time, the promotion of domestic IT-product in educational area is an urgent task, arising from the problem of technical education at the present stage of public education’s system development. A number of examples related to solution of spatial problems connected with second-order surfaces simulation have been considered. On the basis of descriptive geometry’s laws applicable to surface problems, a feature of their solution and display on computer screen has been illustrated. For example, in the graphic editor KOMPAS-3D there is the Ellipse command, but there are no Hyperbola or Parabola commands. But without these curves it is impossible to create a 3D model of hyperboloid (one- or two-sheet), paraboloid, or hyperbolic paraboloid. To create these curves it has been proposed to use conics of circular cone, canonical or parametric equations of hyperbolas and parabolas. For each of these options the examples of second-order surfaces 3D models creation have been considered.

Keywords:
cone, cylinder, section, library, canonical and parametric equations, hyperbola, parabola, associative drawing, paraboloid, one- and two-sheet hyperboloid, hyperbolic paraboloid, plot of functional dependence
Text

На современном этапе преподавания начертательной геометрии в технических вузах страны актуальной задачей является сохранение ее как важнейшей дисциплины, формирующей у обучающихся пространственно-плоскостное мышление, без которого немыслимо никакое инженерное творчество. С  этой целью необходимо, во-первых, сохранить преемственность различных классических научных школ [7; 8; 19; 21], во-вторых, обеспечить сочетание классических знаний с современными представлениями о месте и роли начертательной геометрии в учебном процессе как технической дисциплины [1; 3; 4; 17; 20].

Из ряда публикаций [6; 10; 12–16] следует, что активное использование в учебных целях компьютерного сопровождения занятий по начертательной геометрии позволяет значительно облегчить процесс обучения в условиях дефицита времени, а также развить наглядное представление о связи пространства и плоскости у обучаемых.

References

1. Artsikhovskaya-Kuznetsova L.V. O golovolomnosti v nachertatel´noy geometrii [About puzzling in descriptive geometry]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 3, pp. 31–35. DOI: 10.12737/6523.

2. Boykov A.A. O krugovykh orbitakh planet [On the circular orbits of the planets]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 66–67. DOI: 10.12737/795.

3. Boykov A.A. Komp´yuternye sredstva podderzhki uchebnykh kursov graficheskikh distsiplin [Computer training courses graphical tools support disciplines]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 29–30. DOI: 10.12737/784.

4. Voloshinov D.V. Konstruktivnoe geometricheskoe modelirovanie kak perspektiva prepodavaniya graficheski distsiplin [Design geometric modeling as the prospect of teaching graphic disciplines]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 10–13. DOI: 10.12737/778.

5. Vygodskiy M.Ya. Spravochnik po vysshey matematike [Handbook of higher mathematics]. Moscow, «Astrel´» Publ., 2002.992 p.

6. Girsh A.G. Mnimosti v geometrii [Imaginaries in Geometry]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 2, pp. 3–8. DOI: 10.12737/5583.

7. Ivanov G.S. Nachertatel´naya geometriya [Descriptive geometry]. Moscow, Mashinostroenie Publ., 1995. 224 p.

8. Ivanov G.S. Teoreticheskie osnovy nachertatel´noy geometrii [Theoretical foundations of descriptive geometry]. Moscow, Mashinostroenie Publ., 1998. 160 p.

9. KOMPAS-3D V13: rukovodstvo pol´zovatelya [KOMPAS-3D V13: user manual]. Moscow, ITAR-TASS Publ., 2012, V. 3, 424 p.

10. Komp´yuternaya grafika v nachertatel´noy geometrii [Computer Graphics in descriptive geometry]. Penza, Penzenskii gos. tekhnolog. un-t Publ., 2013. 151 p.

11. Kozlova I.A. Postroenie liniy peresecheniya nekotorykh slozhnykh poverkhnostey [Construction of crossing lines of some composite surfaces]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 2, pp. 38–45. DOI: 10.12737/12167.

12. Korotkiy V.A. Nachertatel´naya geometriya na ekrane komp´yutera [Descriptive geometry on the computer screen]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I 1, pp. 32–34. DOI: 10.12737/2083.

13. Sal´kov N.A. Parametricheskaya geometriya v geometricheskom modelirovanii [Parametric geometry in the geometric modeling]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 3, pp. 7–13. DOI: 10.12737/6519.

14. Sal´kov N.A. Svoystva tsiklid Dyupena i ikh primenenie [Properties Dupin Dupin and their application]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 1, pp. 16–25. DOI: 10.12737/10454

15. Sal´kov N.A. Svoystva tsiklid Dyupena i ikh primenenie [Properties Dupin Dupin and their application]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 2, pp. 9–22. DOI: 10.12737/12164.

16. Seregin V.I. Geometricheskie preobrazovaniya v nachertatel´noy geometrii i inzhenernoy grafike [Geometric transformation in descriptive geometry and engineering graphics]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 2, pp. 23–28. DOI: 10.12737/12165.

17. Suflyaeva N.E. Sovremennye aspekty prepodavaniya graficheskikh distsiplin v tekhnicheskikh vuzakh [Modern aspects of teaching graphic disciplines in technical colleges]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 4, pp. 28–33. DOI: 10.12737/8294.

18. Taktarov N.G. Spravochnik po vysshey matematike [Handbook of higher mathematics]. Moscow, LIBROKOM Publ., 2014. 880 p.

19. Frolov S.A. Nachertatel´naya geometriya [Descriptive geometry]. Moscow, Mashinostroenie Publ., 2008. 240 p.

20. Kheyfets A.L. Reorganizatsiya kursa nachertatel´noy geometrii kak aktual´naya zadacha razvitiya kafedr grafiki [The reorganization of the course of descriptive geometry as an urgent task of the graphics departments]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 21–23. DOI: 10.12737/781.

21. Chetverukhin N.F. Proektivnaya geometriya [Projective geometry]. Moscow, «Prosveshchenie» Publ., 1969. 368 p.

Login or Create
* Forgot password?