ENGINEERING GEOMETRY AND COMPUTER GRAPHICS

Configuration of Desargue in architectural and design engineering

Вестник МГСУ 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; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • 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; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 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

Библиографический список
  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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