Russian Federation
Astrakhan Tatishchev State University (Assistant Professor of the Department of Electrical Engineering, Electronics and Automation)
Russian Federation
The paper considers various ways to construct the intersection curves of surfaces, available in the scientific literature. The analysis shows that the exact build intersection surfaces finds extensive practical application when designing constructions from sheet material, which must be built. In this case, the accuracy of manufacturing elements construction depends largely on the accuracy of the projections of the intersection of surfaces on an integrated drawing. In this work the examples build the intersection of several complex surfaces 2nd order among themselves and with the curve line using 2D and 3D technologies. In this case, the accuracy of manufacturing elements construction depends largely on the accuracy of the projections of the intersection of surfaces on an integrated drawing. In this work the examples build the intersection of several complex surfaces 2nd order among themselves and with the curve line using 2D and 3D technologies. Provides an algorithm of building solid model of certain surfaces, which significantly reduces the time to solving problems at the intersection of the surfaces, making visibility into the solution, create a realistic model of the object. In General, this work demonstrates that one of the stages of further reform in teaching descriptive geometry is the evolutionary path of development, outlining the many issues (e.g., intersection of surfaces) using electronic kuhlmann. In this case, students will receive a decision not by pushing buttons, and applying the methods of descriptive geometry, simultaneously developing spatial imagination and computer skills are already in the first year. And the final stage of teaching descriptive geometry will transition to 3D modelling, when the above tasks will instantly and clearly resolved by simply pressing buttons.
descriptive geometry, the line crossing, surface of the 2nd order, COMPASS-Chart, 2D technology, 3D modeling, solid surface model.
Кривые поверхности широко применяются в науке и технике. Построение линии пересечения поверхностей рассмотрено в многочисленных научных статьях, диссертациях [2; 3; 13; 14; 17–19; 22; 24; 25; 30; 31].
В работе [3] рассматривается построение линии пересечения нелинейчатых поверхностей 2-го порядка при скрещивающихся осях методом подобия. Автор справедливо отмечает, что построение линии пересечения таких поверхностей представляет значительную сложность и обойтись без построения кривых 2-го порядка при использовании вспомогательных секущих плоскостей не всегда удается.
1. Aleksandrova E.P. Kochurova L.V. Nosov K.G. Stolbova N.D. Intensifikatsiya graficheskoy podgotovki studentov na osnove geometricheskogo modelirovaniya [The intensification of the graphic preparation of students on the basis of the geometric modeling]. V Mezhdunarodnaya internet-konferentsiya KGP-2015 [V international online conference, KGP-2015]. Available at: http://dgng.pstu.ru/conf2015/papers/41. (in Russian).
2. Vel´tishchev V.V. Polubinskaya L.G. Fedorenkov A.P. Zadacha na postroenie liniy peresecheniya poverkhnostey v kurse «Mashinnaya grafika» [The task of building the lines of intersection of surfaces in the course "computer graphics"]. Nachertatel´naya geometriya poverkhnostey: sb. nauchno-metodicheskikh statey po nachertatel´noy geometrii i inzhenernoy grafike [Descriptive geometry of surfaces: sat. scientifically-methodical articles on descriptive geometry and engineering graphics.]. I. 14. Moscow, Vyssh. Shkola Publ., 1987, pp. 88-92. (in Russian).
3. Veniaminova N. Ob odnom sposobe postroeniya linii perekhoda poverkhnostey 2-go poryadka [About one way of building a line of transition surfaces 2-th order]. Trudy Moskovskogo seminara po nachertatel´noy geometrii i inzhenernoy grafike [Proceedings of the Moscow Seminar on descriptive geometry and engineering graphics]. Moscow, 1958, pp. 22-34. (in Russian).
4. Volkov V.Ya., Kaygorodtseva N.V., Panchuk K.L. O vozmozhnom napravlenii razvitiya kafedr geometro-graficheskoy podgotovki [Possible direction of development of geometro-graphics training]. Problemy kachestva graficheskoy podgotovki studentov v tekhnicheskom vuze: traditsii i innovatsii. Materialy IV Mezhdunarodnoy nauchno-prakticheskoy internet-konferentsii (g. Perm´, fevral´ - mart 2014 g.) [Problems with the quality of the graphic preparation of students in technical high school: tradition and innovation. (IV) the materials of the international scientifically-practical conference online (Perm, February-March, 2014.)]. Izd-vo PGTU Publ., 2014, pp. 161-166. (in Russian).
5. Volkov V.Ya., Kaygorodtseva N.V., Panchuk K.L. Sovremennye napravleniya i perspektivy razvitiya nauchnykh issledovaniy po geometrii i grafike: obzor dokladov na mezhdunarodnoy konferentsii ICGG 2014 [Trends and prospects of the research on geometry and graphics: overview of the reports on the International Conference 2014 ICGG / V International Online Conference, HACO-2015]. V Mezhdunarodnaya internet-konferentsiya KGP-2015 [V international online conference, HACO-2015]. Available at: http://dgng.pstu.ru/conf2015/papers/1. (in Russian).
6. Voloshinov D.V. Instrument dlya geometricheskogo eksperimenta. Kakim emu byt´? [Tool geometry for the experiment. What it be?]. V Mezhdunarodnaya internet-konferentsiya KGP-2015 [V international online conference, HACO-2015]. Available at: http://dgng.pstu.ru/conf2015/papers/47. (in Russian).
7. Voloshinov D.V. Nachertatel´naya geometriya. Est´ li u nee budushchee v vuze? [Descriptive geometry. Does it have a future in high school?] Problemy kachestva graficheskoy podgotovki studentov v tekhnicheskom vuze v usloviyakh FGOS VPO: Materialy II Mezhdunar. nauch.-prakt. internet-konf. (g.Perm´, fevral´ - mart 2011 g.). [Problems with the quality of the graphic preparation of students in technical universities in GEF VPO: proceedings of the II International. researcher Scient. Internet Config. (Perm, February-March, 2011, 2011)]. Perm´, Izd-vo Perm. gos. tekhn. un-ta Publ., 2011, pp. 103. (in Russian).
8. Voloshinov D.V., Solomonov K.N. Konstruktivnoe geometricheskoe modelirovanie kak perspektiva prepodavaniya graficheskikh distsiplin [Constructive geometric modeling as the prospect of teaching graphics disciplines]. Geometriya i grafika [Geometry and graphics]. 2013, V. 1, I. 2, pp. 10 - 13. DOI:https://doi.org/10.12737/778. (in Russian).
9. Voprosy soderzhaniya i realizatsii graficheskoy podgotovki v vuze pri perekhode na obrazovatel´nye standarty novogo pokoleniya [Questions of content and implementation of graphic preparation in the University during the transition to a new generation of educational standards]. E.P. Aleksandrova, M.N. Kraynova, I.D. Stolbova, E.V. Kornilkova Problemy kachestva graficheskoy podgotovki v usloviyakh FGOS VPO: materialy Mezhdunar. nauch.-prakt. internet- konf. [Problems with the quality of the graphic preparation of the GEF in HPE: proceedings Internat. researcher Scient. Internet Config]. Perm´, Izd-vo Perm. gos. tekhn. un-ta Publ., 2011. Available at: http:// dgng.pstu.ru/conf2011/members/59. (in Russian).
10. Vyshnepol´skiy V.I., Sal´kov N.A. Tseli i metody obucheniya graficheskim distsiplinam [Objectives and methods of teaching graphic disciplines]. Geometriya i grafika [Geometry and graphics]. 2013, V. 1, I. 2, pp. 8-9. DOI:https://doi.org/10.12737/777. (in Russian).
11. Vyshnepol´skiy V.I. Eshche raz k voprosu o postroenii tochek peresecheniya okruzhnosti i ellipticheskogo konusa [Once again the issue of construction of intersection of a circle and an elliptical cone]. V Mezhdunarodnaya internet-konferentsiya KGP-2015 [V international online conference, HACO-2015]. Available at: http://dgng.pstu.ru/conf2015/papers/110/. (in Russian).
12. Vyshnepol´skiy V.I. Zhurnal «Geometriya i grafika» v RINTs i SCOPUS [Journal for geometry and graphics in INDEX and SCOPUS]. V Mezhdunarodnaya internet-konferentsiya KGP-2015 [V international online conference, HACO-2015]. Available at: http://dgng.pstu.ru/conf2015/papers/9/. (in Russian).
13. Glazunov E.A. O proektsii linii peresecheniya dvukh poverkhnostey vtorogo poryadka, imeyushchikh obshchuyu ploskost´ simmetrii [The projection of the line of intersection of two quadrics, sharing a common plane of symmetry]. Trudy Moskovskogo seminara po nachertatel´noy geometrii i inzhenernoy grafike [Proceedings of the Moscow Seminar on descriptive geometry and engineering graphics]. Moscow, 1958, pp. 35-69. (in Russian).
14. Guznenkov V. N. Informacionnye tehnologii v graficheskih disciplinah tehnicheskogo universiteta [Information technologies in graphic disciplines Technical University]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 3-4, pp. 26-28. DOI:https://doi.org/10.12737/2128. (in Russian).
15. Zhilina N. D., Rotkov S. I. Podgotovka kadrov vysshey kvalifikatsii po spetsial´nosti 05.01.01 - Inzhenernaya geometriya i komp´yuternaya grafika [Training of highly qualified personnel in specialty 05.01.01 - engineering geometry and computer graphics]. V Mezhdunarodnaya internet-konferentsiya KGP-2015 [V international online conference, HACO-2015] Available at: http://dgng.pstu.ru/conf2015/papers/3/. (in Russian).
16. Konakbaev K.K., Matveeva E.N. O linii peresecheniya 2-kh kvadrik [On the intersection of 2-x quadrics]. Kremonovy preobrazovaniya i ikh prilozheniya: nauchnye trudy Mosk. lesotekhn. in-t [Kremonovy/quadrics transform and their applications: scientific papers Mock. lesotehn. Inst.]. I. 39. Moscow, 1971. (in Russian).
17. Korotkij V. A. Ob odnom osobom sluchae peresechenija kvadrik [One special case of intersection of quadrics]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 2, pp. 49-52. DOI:https://doi.org/10.12737/790. (in Russian).
18. Kutanova L.I., Beloguzhev V.A. Peresechenie kvadrikov, imeyushchikh odnu ploskost´ simmetrii pri proizvol´nom raspolozhenii v etoy ploskosti ikh osey s pomoshch´yu polnogo polyarnogo sootvetstviya. [Kvadrikov, intersection with a single plane of symmetry with arbitrary location in this plane of their axes by using the full arctic affinity]. Voprosy nachertatel´noy geometrii i inzhenernoy grafiki: nauchnye trudy Tashkentskogo in-ta inzhenerov zheleznodorozhnogo transporta. [Issues of descriptive geometry and engineering graphics: scientific papers Tashkent Instiute of railway transport engineers]. I. 59. Tashkent, 1970, pp. 26-33. (in Russian).
19. Loktev O.V. Primenenie odnogo kvadratichnogo preobrazovaniya k nekotorym voprosam peresecheniya poverkhnostey [Application of quadratic transformation to some issues crossing surfaces]. Trudy Moskovskogo seminara po nachertatel´noy geometrii i inzhenernoy grafike. [Proceedings of the Moscow Seminar on descriptive geometry and engineering graphics]. Moscow, 1958, pp. 70-96. (in Russian)
20. Ryzhkov V.V. Nachertatel´naya geometriya krivykh liniy i poverkhnostey [Descriptive geometry of curved lines and surfaces]. Voprosy sovremennoy nachertatel´noy geometrii: sb. statey / pod red. N.F. Chetverukhina [Questions of descriptive geometry: sat. articles edited. N.F. Chetverukhina]. Moscow, OGIZ Publ., 1947, pp. 244-285. (in Russian).
21. Sal´kov N.A. Ob amerikanizatsii rossiyskogo obrazovaniya [About the Americanization of Russian education]. V Mezhdunarodnaya internet-konferentsiya KGP-2015. [V international online conference, HACO-2015]. Available at: http://dgng.pstu.ru/conf2015/papers/22/ (in Russian).
22. Sobolev N.A. Tochnye sposoby resheniya zadachi na peresechenie poverkhnostey [Exact solutions to task at the intersection of surfaces]. Trudy Moskovskogo nauchno-metodicheskogo seminara po nachertatel´noy geometrii i inzhenernoy grafike [Proceedings of the Moscow scientific-methodical seminar on descriptive geometry and engineering graphics]. I. 2. Moscow, 1963, pp. 101-106. (in Russian).
23. Stolbova I.D. Obzor aktual´nykh problem graficheskoy podgotovki v vysshey shkole [Overview of current graphics problems training in high school] Sb. tr. 3-y Mezhdun. nauch.-metod. konf. po inzhenernoy geometrii i komp´yuternoy grafike / Mosk. gos. un-t tonkikh khim. tekhnologiy im. M.V. Lomonosova [Tr. 3-th Annu. researcher-method. CONF. Engineering geometry and computer graphics/Mosk. GOS. University of fine chemical. technologies to them. M.V. Lomonosov Moscow State University.]. Moscow, 2010, pp. 118-135. (in Russian).
24. Sufljaeva N.E. Sovremennye aspekty prepodavanija graficheskih disciplin v tehnicheskih vuzah [Modern aspects of teaching graphics disciplines in technical universities]. Geometrija i grafika [Geometry and graphics]. 2014, V. 2, I. 4, pp. 28-33. DOI:https://doi.org/10.12737/8294. (in Russian).
25. Sukhina I.A. K voprosu postroeniya linii peresecheniya poverkhnostey vtorogo poryadka s lineychatymi poverkhnostyami [The issue of constructing the intersection of quadrics with linejčatymi surfaces]. Trudy Moskovskogo nauchno-metodicheskogo seminara po nachertatel´noy geometrii i inzhenernoy grafike [Proceedings of the Moscow scientific-methodical seminar on descriptive geometry and engineering graphics]. I. 2. Moscow, 1963, pp. 107-110. (in Russian).
26. Kharakh M.M., Kozlova I.A. Nachertatel´naya geometriya na osnove informatsionnykh tekhnologiy: uchebnoe posobie. [Descriptive geometry based on information technology: a tutorial]. Astrakhan´, Izd-vo AGTU Publ., 2010. (in Russian).
27. Kheyfets A.L. Nachertatel´naya geometriya kak «beg v meshkakh» [Descriptive geometry as "running in sacks»] V Mezhdunarodnaya internet-konferentsiya KGP-2015 [V international online conference, HACO-2015]. Available at: http://dgng.pstu.ru/conf2015/papers/72/ (in Russian).
28. Kheyfets A.L. Teoreticheskie osnovy 3d-komp´yuternogo geometricheskogo modelirovaniya i Gaspar Monzh [Theoretical basis of computer 3d geometric modeling and Gaspard Monge]. III Mezhdunarodnaya Internet-konferentsiya KGP-2012 [V international online conference, HACO-2012]. Available at: http://dgng.pstu.ru/conf2012/papers/70/ (in Russian).
29. Kheyfets A.L., Butorina I.V., Vasil´eva V. N. Modeli detalej slozhnoj formy v pakete AutoCAD [Models of parts of complex shapes in AutoCAD package] Geometrija i grafika [Geometry and graphics]. 2013, V. 1. I. 1, pp. 70-72. DOI:https://doi.org/10.12737/481. (in Russian).
30. Khrushchev G.I. Ob odnom novom metode postroeniya proektsiy linii peresecheniya poverkhnostey vtorogo poryadka [One new method of constructing the projections of intersection of quadrics] Trudy Moskovskogo nauchno-metodicheskogo seminara po nachertatel´noy geometrii i inzhenernoy grafike [Proceedings of the Moscow scientific-methodical seminar on descriptive geometry and engineering graphics]. I. 2. Moscow, 1963, pp. 111-116. (in Russian).
31. Tsirinskiy N.A. Postroenie linii peresecheniya poverkhnostey 2-go poryadka s tremya ploskostyami simmetrii sposobom zameny poverkhnostey [Construction of the line of intersection of the surfaces of order 2 with three planes of symmetry means replace surfaces]. Prikladnaya geometriya i inzhenernaya grafika v mashinostroenii. Omskiy politekhnicheskiy in-t, Zapadno-sibirskoe knizhnoe izdatel´stvo [Applied geometry and engineering graphics in engineering. Omsk Polytechnic Institute, West-Siberian book publishing house], 1969, pp. 20-30. (in Russian).
32. Shheglova A.V. Primenenie komp´juternyh tehnologij v processe izuchenija graficheskih disciplin [Application of computer technology in the process of studying graphic disciplines]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 1, pp. 73-74. DOI:https://doi.org/10.12737/482. (in Russian).
33. Yakunin V.I., Sidoruk R.M., Raykin L.I., Sosnina O.A. Innovatsionnaya strategiya kompleksnoy informatizatsii geometricheskoy i graficheskoy podgotovki v vysshem tekhnicheskom professional´nom obrazovanii v GOSakh 3-go pokoleniya [Innovation strategy a comprehensive informatization of geometrical and graphical training in higher technical vocational education in GOSah 3-rd generation]. Nauchno-metodicheskie problemy geometricheskogo modelirovaniya, komp´yuternoy i inzhenernoy grafiki v vysshem professional´nom obrazovanii: Sbornik statey Mezhdunarodnoy nauchno-metodicheskoy konferentsii 9-11 iyunya 2009 g. [Scientific and methodical problems of geometric modeling, computer graphics and engineering in higher vocational education: a collection of articles of international scientific-methodical Conference 9-11 June, 2009], Penza. (in Russian).
