DESCRIPTIVE GEOMETRY — THE BASE OF COMPUTER GRAPHICS
Abstract (English):
Everyone knows that descriptive geometry is a science, but there is no definition of the computer graphics. If computer graphics is announced as a science, you can continue to call descriptive geometry outdated and to demand of its abolition. But if the computer graphics has nothing to do with the science, and if it is only a tool to perform the procedures of descriptive geometry and other branches of geometry, everyone who tried to discredit descriptive geometry, will be in a difficult position: they will have nothing more to say, because in it is unwise to replace science on tool. It is known that engineering graphics so far does not have the status of science. It is a discipline that fully applies the laws of other geometrical sciences. There are many questions such as: why are there claims that descriptive geometry is 2D? Why do some specialists claim that descriptive geometry is a projection on a single plane? They forgot that descriptive geometry uses the method of two images or method of two traces. But this method of two images is used everywhere! On the first lecture we tell students: the projection is carried out on two planes of projection, a point in space can be fixed only by means of three coordinates and the point must have at least two projections. It means, that descriptive geometry works with three coordinates, in other words — in 3D. The image produced on the display screen in the so-called 3D, is neither more nor less than axonometric projection on the plane — appropriate section of descriptive geometry. In conclusion, the author offers to classify the computer graphics as a tool for the experience of all branches of geometrical science, but not as a free-standing science.

Keywords:
pedagogy, descriptive geometry, computer graphics, engineering graphics, the quality of education.

## 1. О соотношении начертательной

геометрии и компьютерной графики Общеизвестно, что начертательная геометрия – это наука. Наука об изображениях и база для геометрического моделирования. Это бесспорно и не подлежит сомнению. При этом начертательная геометрия имеет в своем арсенале следующие разделы: проекции в ортогональных проекциях, развертки, аксонометрические проекции, перспективные проекции, проекции с числовыми отметками, теория теней (которая включает построение теней и в ортогональных проекциях, и в аксонометрии, и в перспективе, и в числовых отметках), многомерная начертательная геометрия, мнимая начертательная геометрия, номография. Как видим, проекции в ортогональных проекциях занимают довольно-таки скромное место в общем объеме интересов, попадающих в поле внимания начертательной геометрии. Чтобы узнать, какое – для этого достаточно полистать любой учебник для архитекторов. Скромное. Поэтому вызывает удивление тот факт, что, уцепившись за ортогональные проекции, некоторые наши партнеры изо всех сил пытаются доказать какую-то нелепость, ссылаясь на компьютерную графику.

А что же такое компьютерная графика? Какое место среди учебных дисциплин занимает она? И какое место – среди научных дисциплин? Попробуем разобраться.

1. Voloshinov D.V. About Prospects of Development of Geometry and Its Tools. Geometrija i grafika [Geometry and graphics]. 2014, V. 1, I. 2, p. 15–21. (in Russian). DOI: 10.12737/3844.

2. Vol´berg O.A. Lekcii po nachertatel´noj geometrii [Lectures on descriptive geometry]. Leningrad, Gospedizdat Publ., 1947. (in Russian).

3. Vyshnepolsky V.I., Salkov N.A. Tseli i metody obucheniya graficheskim distsiplinam [The aims and methods of teaching drawing]. Geomerija i grafika [Geometry and graphics]. 2013, V. 1, I. 2, p. 8–9. DOI: 10.12737/777.

4. Glazunov E.A., Chetveruhin N.F. Aksonometrija [Axonometric view]. Moscow, Gosudarstvennoe izdatel´stvo tehniko-teoreticheskoj literatury, 1953. 292 p. (in Russian).

5. Ivanov G.S., Dmitrieva I.M. O zadachah nachertatel´noj geometrii s mnimymi reshenijami [Descriptive geometry problems with imaginary solutions]. Geometrija i grafika [Geometry and graphics]. 2015, V. 3, I. 2, p. 3–9. (in Russian). DOI: 10.12737/777.

6. Klimuhin A.G. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Stojizdat Publ., 1978. 334 p. (in Russian).

7. Koroev Ju.I. Nachertatel´naja geometrija [Descriptive geometry] Moscow, KNORUS Publ., 2011. 432 p. (in Russian).

8. Korotkij V.A., Hmarova V.A., Butorina I.V. Nachertatel´naja geometrija [Descriptive geometry]. Cheljabinsk, JuUrGU Publ., 2014. 191 p.

9. Krylov N.N., Ikonnikova G.S., Nikolaev V.L., Lavruhina N.M. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Vysshaya shkola Publ., 1990. 240 p. (in Russian).

10. Kuznecov N.S. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Vysshaja shkola Publ., 1981. 262 p. (in Russian).

11. Peklich V.A. Mnimaja nachertatel´naja geometrija [Imaginary descriptive geometry]. Moscow, Izdatel´stvo Associacii stroitel´nyh vuzov, 2007. 104 p. (in Russian).

12. P´jankova Zh.A. Formirovanie gotovnosti studentov operirovat´ prostranstvennymi ob#ektami v processe izuchenija geometrograficheskih discipline. Kand. Diss. [Formation of readiness of students to operate features in the process of studying the geometric-graphic disciplines. Cand. Diss]. Ekaterinburg, 2015. 31 p. (in Russian).

13. Russkevich N.L. Nachertatel´naja geometrija [Descriptive geometry]. Kiev, Vishha shkola Publ., 1978. 312 p. (in Russian).

14. Salkov N.A. Zadachnik po nachertatel´noj geometrii [Book of problems in descriptive geometry]. Moscow, INFRA-M Publ., 2013. 127 p. (in Russian).

15. Salkov N.A. Kinematic compliance of rotating spaces. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 1, p. 4–10. (in Russian). DOI: 10.12737/2074.

16. Salkov N.A. Modelirovanie avtomobil´nyh dorog [Modeling of highways]. Moscow, INFRA-M Publ., 2012. 120 p. (in Russian).

17. Salkov N.A. Nachertatel´naja geometrija: bazovyj kurs [Descriptive geometry: Basic course]. Moscow, INFRA-M Publ., 2013. 184 p. (in Russian).

18. Salkov N.A. Nachertatel´naja geometrija: Konstruirovanie i zadanie geometricheskih figur na chertezhe [Descriptive geometry: Constructing and specifying the geometric shapes on the drawing]. Moscow, MIKHiS Publ., 2008. 96 p. (in Russian).

19. Salkov N.A. Nachertatel´naja geometrija. Osnovnoj kurs [Descriptive geometry. The main course]. Moscow, INFRA-M, 2014. 235 p. (in Russian).

20. Sal´kov N.A. Problemy sovremennogo geometricheskogo obrazovanija [Modern geometric problems of education]. Problemy kachestva graficheskoj podgotovki studentov v tehnicheskom vuze: tradicii i innovacii [Problems of quality of graphic training of students in technical College: traditions and innovations]. 2014, V. 1, pp. 38–46. (in Russian).

21. Sal´kov N.A. Cherchenie dlja slushatelej podgotovitel´nyh kursov [Drawing for students of preparatory courses in: proc. the allowance]. Moscow, INFRA-M, 2016. 128 p. (in Russian).

22. Sal´kov N.A. Ciklida Djupena i ee prilozhenie [Cyclide of Dupin and its application]. Moscow, INFRA-M, 2016. 145 p. (in Russian).

23. Salkov N.A. Ellipse: tangent and normal. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 1, p. 28–31. (in Russian). DOI: 10.12737/2084.

24. Sysoeva E.V., Sa´kov N.A. Arhitekturnye konstrukcii i konstruirovanie malojetazhnogo zhilogo doma [Architectural design and construction of low-rise residential building: a Training manual]. Moscow, MGAHI im. V.I. Surikova Publ., 2014. 101 p. (in Russian).

25. Filippov P.V. Nachertatel´naja geom. mnogomernogo prostranstva i ee prilozhenija [Descriptive geom. the multidimensional space and its applications]. Leningrad, 1979. 280 p. (in Russian).

26. Hejfec A.L. Reorganization of the course in descriptive geometry as an urgent task development departments graphics. Geometrija i grafika. [Geometry and graphics]. 2013, V. 1, I. 2, p. 21–23. (in Russian). DOI: 10.12737/781.