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ENGINEERING GEOMETRY AND COMPUTER GRAPHICS

Configuration of Desargue in architectural and design engineering

Vestnik MGSU 9/2014
  • Ivashchenko Andrey Viktorovich - Union of Moscow Architects 90/17 Shosseynaya str., Moscow, 109383, Russian Federation; ivashchenkoa@inbox.ru, Union of Moscow Architects, 7 Granatnyy per., Moscow, 123001, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Znamenskaya Elena Pavlovna - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 154-160

The Desargue configuration plays an essential role not only in projective geometry, being the main configuration in projective and perspective correspondence of rows of points and lines, but is also rich in applications in architectural and design engineering. The article describes the main aspects of planar and spatial configuration of Desargue, and fundamental principles having particular importance in the shaping theory based on projectography. The described configuration properties indicate the possibility of wide application in architectural design and engineering and allow predicting the effects of perception of rather complex architectural forms. Examples of a number of buildings are given, where in modern design solutions of architects spatial configuration motives are visible. Planar configuration option is often used as decoration and fencing. The authors conclude that researching the configuration of Desargue in different variants and modifications not only contributes to better understanding of the theory of perspective and shadows, but also provides opportunity to detect relations of the problems, which are different at the first sight. However it is necessary to take into account, that many postulates of the theory are quite complicated and significant amount of time is needed for learning it.

DOI: 10.22227/1997-0935.2014.9.154-160

References
  1. Berzhe M. Geometriya [Geometry]. Moscow, Mir Publ., 1984, vol. 1, 297 p.
  2. Vinogradov I.M., editor. Matematicheskaya entsiklopediya [Mathematical Encyclopedia]. Moscow, Sovetskaya entsiklopediya Publ., 1979, vol. 2, 1104 p.
  3. Gamayunov V.N. Proektivografiya. Geometricheskie osnovy khudozhestvennogo konstruirovaniya. [Projectography. Geometric Foundations of Artistic Design]. Moscow, MGPI Publ., 1976, 25 p.
  4. Prokhorov Yu.V., editor. Matematicheskiy entsiklopedicheskiy slovar' [Encyclopedic Dictionary of Mathematics]. Moscow, Sovetskaya entsiklopediya Publ., 1988, 848 p.
  5. Wieleitner H. Istoriya matematiki ot Dekarta do serediny 19 stoletiya [History of Mathematics from Descartes to the mid-19th century]. Moscow, Fizmatlit Publ., 1960, 468 p.
  6. Ivashchenko A.V., Kondrat'eva T.M. Proektivograficheskiy analiz mnogogrannikov Dzhonsona [Analysis of Johnson’s Polyhedra Using Projective Geometry Techniques]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 5, pp. 226—229.
  7. Hilbert D., Cohn-Vossen S. Anshauliche Geometrie. Berlin, Springer, 1996, 365 s.
  8. Chetverukhin N.F. Proektivnaya geometriya [Projective Geometry]. 7th edition. Moscow, Gosudarstvennoe uchebno-pedagogicheskoe izdatel'stvo Publ., 1961, 360 p.
  9. Coxeter H.S.M. Projective Geometry. New York, Blaisdell Publ., 1964, pp. 26—27.
  10. Lelong-Ferrand J. Les Fondements de La Geometrie. Presses universitaires de France; 1re ed edition, 1985, 287 p.
  11. Semple J., Kneebone G. Algebraic Projective Geometry. Oxford, 1952, 405 p.
  12. Ivashchenko A.V., Kondrat'eva T.M. Proektivograficheskie chertezhi mnogokomponentnykh sistem mnogogrannikov [Shape Generation by Means of a New Method of Orthographic Representation ("Proektivografiya"): Drawings of Multi-Component Polyhedra]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 6, pp. 155—160.
  13. Efimov N.V. Vysshaya geometriya [Higher Geometry]. 5th edition. Moscow, Nauka Publ.,1971.
  14. Voloshinov A.V. Matematika i iskusstvo [Mathematics and Art]. Moscow, Prosveshchenie Publ., 2000, 400 p.
  15. Sobolev N.A. Obshchaya teoriya izobrazheniy [The General Theory of Images]. Moscow, Arkhitektura-S Publ., 2004, 672 p.
  16. Runge V.F., Sen'kovskiy V.V. Osnovy teorii i metodologii dizayna [Fondamentals of Design Theory and Methodology]. Moscow, MZ-Press, 2003, 252 p.

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FEATURES OF COMPUTER IMPLEMENTATION OF CONSTRUCTING PLANAR DESARGUES CONFIGURATION

Vestnik MGSU 9/2015
  • Ivashchenko Andrey Viktorovich - Union of Designers of Moscow Candidate of Technical Sciences, designer, Union of Designers of Moscow, 90/17 Shosseynaya str., SFGA, room 206, 109383, Moscow, Russian Federation.
  • Znamenskaya Elena Pavlovna - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Technical Sciences, Associate Professor , Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 168-177

The authors present the main properties of the planar configuration of Desargues, which open the possibility of its widespread use in architectural design and the design of complex volumes, consisting of a series of simple overlapping forms. However, the computer implementation of Desargues configuration construction is associated with certain difficulties caused by the fact that the monitor can only discretely represent the graphical information. In this article we identified and analyzed the properties of Desargues configuration, the use of which allows overcoming these difficulties and solving the problem of the limited capacity of monitors in the development of complex architectural forms with the help of computer graphics. Along with this, the use of the allocated properties allows predicting complex effects of the perception of architectural forms, for example, the difference of perception of architectural objects near and afar with account for perspective distortion, and they are also the basis for the development of the algorithm of construction sequence during design.

DOI: 10.22227/1997-0935.2015.9.168-177

References
  1. Isaeva M.A., Martynyuk A.N., Matveev O.A., Ptitsyna I.V. Vvedenie v deystvitel’nuyu proektivnuyu geometriyu [Introduction to the Real Projective Geometry]. Moscow, MGOU Publ., 2010, 138 p. (In Russian)
  2. Vol’berg O.A. Osnovnye idei proektivnoy geometrii [Basic Ideas of Projective Geometry]. 4th edition. Moscow, URSS Publ., 2009, 192 p. (Nauku vsem! — Shedevry nauchno-populyarnoy literatury [Science to Everyone! — Masterpieces of Popular Scientific Literature]) (In Russian)
  3. Martynyuk A.N., Matveev O.A., Ptitsyna I.V. Elementy proektivnoy geometrii [Elements of projective geometry]. Moscow, MGOU Publ., 2010, 134 p. (In Russian)
  4. Zacharias M. Vvedenie v proektivnuyu geometriyu [Introduction into Projective Geometry]. Transl. from German. Moscow, URSS Publ., 2010, 90 p. (Fiziko-matematicheskoe nasledie: matematika (geometriya) [Physical and Mathematical Heritage: Mathematics (Geometry)]) (In Russian)
  5. Smirnov S.A. Proektivnaya geometriya [Projective Geometry]. Moscow, Nedra Publ., 1976, 176 p. (In Russian)
  6. Chetverukhin N.F. Proektivnaya geometriya [Projective Geometry]. 8th edition. Moscow, Prosveshchenie Publ., 1969, 368 p. (In Russian)
  7. Glagolev N.A. Proektivnaya geometriya [Projective Geometry]. 2nd edition, revised. Moscow, Vysshaya shkola Publ., 1963, 343 p. (In Russian)
  8. Gorshkova L.S., Pan’zhenskiy V.N., Marina E.V. Proektivnaya geometriya [Projective Geometry]. Moscow, URSS Publ., 2007, 168 p. (In Russian)
  9. Hartshorne R. Foundations of Projective Geometry. Ishi Press, 2009, 190 p.
  10. Busemann H., Kelly P.J. Projective Geometry and Projective Metrics. 2005, Dover Publications, 352 p.
  11. Baer R. Linear Algebra and Projective Geometry. 2005, Dover Publications, 336 p.
  12. Berger M. Geometriya : v 2-kh tomakh [Geometry : in 2 Volumes]. Transl. from French. Moscow, Mir Publ., 1984, vol. 1, 560 s. ; T. 2. 368 s. (In Russian)
  13. Hilbert D., Cohn-Vossen S. Anschauliche Geometrie. Springer; Auflage: 2. Aufl. 1996, 364 p.
  14. Young. J.W., Oswald V. Projective geometry. Boston Ginn, 1918, 370 p.
  15. Skiena S. Algoritmy. The Algorithm Design Manual. Springer; 2nd ed. 2008 edition, 730 p.
  16. Faux I.D., Pratt M.J. Computational Geometry for Design and Manufacture. Chichester, West Sussex, John Willey & sons, 1979, 331 p.
  17. Preparata F.P., Shamos M. Computational Geometry. An Introduction. 1985, Springer-Verlag New York, 398 p. DOI: http://dx.doi.org/ 10.1007/978-1-4612-1098-6.
  18. Ivashchenko A.V., Znamenskaya E.P. Konfiguratsiya Dezarga v arkhitekturnom i dizayn-proektirovanii [Configuration of Desargue in Architectural and Design Engineering]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 9, pp. 154—160. (In Russian)
  19. Gamayunov V.N. Proektivografiya. Geometricheskie osnovy khudozhestvennogo konstruirovaniya dlya aspirantov slushateley FPK i studentov khuzhozhestvenno-graficheskogo fakul’teta [Projectography. Geometric Foundations of Artistic Design for Postgraduate Students of FPK and Students of Artistic-Graphical Department]. Moscow, MGPI im. V.I. Lenina, 1976, 25 p. (In Russian)
  20. Ivashchenko A.V., Kondrat’eva T.M. Proektivograficheskiy analiz mnogogrannikov Dzhonsona [Analysis of Johnson’s Polyhedra Using Projective Geometry Techniques]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 5, pp. 226—229. (In Russian)
  21. Ivashchenko A.V., Kondrat’eva T.M. Avtomatizatsiya polucheniya proektivograficheskikh chertezhey tel Dzhonsona [Automatic Receipt of Projective Geometry Drawings of Johnson Bodies]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 6, pp. 179—183. (In Russian)

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