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

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  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.
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ANALYSIS OF JOHNSON POLYHEDRA USING PROJECTIVE GEOMETRY TECHNIQUES

Вестник МГСУ 5/2013
  • 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 .
  • Kondrat’eva Tat’yana Mikhaylovna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Chair, Department of Descriptive Geometry and Graphics; +7 (499) 183-24-83., Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Страницы 226-229

The authors analyze the capabilities of projective geometry techniques based on the method of tracing for diagrams, as applied to problems of Johnson polyhedra and formation of convex polyhedral structures. Johnson polyhedra, known as Johnson solids, demonstrate a specific type of symmetry. Each polyhedron can serve as the core for varied shapes capable of preserving their properties. The authors believe that the research into clusters of Johnson solids have a stronger potential than any research into a single Johnson polyhedron. The paper shows how the change of parameters (rotation angles, axis of symmetry, and number of facets) can be preserved for a variety of shapes; this is a very lucrative property in terms of architecture and design. Specialized computer software is used for the practical implementation of the method.

DOI: 10.22227/1997-0935.2013.5.226-229

Библиографический список
  1. Zalgaller V.A. Vypuklye mnogogranniki s pravil’nymi granyami [Convex Polyhedra Having Regular Faces]. Moscow, Nauka Publ., 1967, vol. 2, pp. 5—221.
  2. Gurin A.M. K istorii izucheniya vypuklykh mnogogrannikov s pravil’nymi granyami [Background of Study of Convex Polyhedra with Regular Faces]. Sib. elektron. matem. izv. [Siberian Electronic News of Mathematics]. 2010, vol. 7, pp. 5—23.
  3. Vennidzher M. Modeli mnogogrannikov [Models of Polyhedra]. Moscow, Mir Publ.,1974.
  4. 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.
  5. Gamayunov V.N. Proektivografiya [Projective Geometry Means of Graphic Presentation]. Moscow, MGPI Publ., 1976.
  6. Gol’tseva R.I. Geometriya mnogogrannykh n-epyurnykh sistem [Geometry of Polyhedral n-faced Systems]. Formoobrazovanie v stroitel’stve i arkhitekture [Shape Formation in Construction and Architecture]. Moscow, MISI im. Kuybysheva Publ., 1986, pp. 175—222.
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  8. Dutch S. Polyhedra with Regular Polygon Faces. Available at: http://www.uwgb.edu/dutchs/symmetry/johnsonp.htm.

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FEATURES OF COMPUTER IMPLEMENTATION OF CONSTRUCTING PLANAR DESARGUES CONFIGURATION

Вестник МГСУ 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.

Страницы 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

Библиографический список
  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)
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  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)
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  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.
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  15. Skiena S. Algoritmy. The Algorithm Design Manual. Springer; 2nd ed. 2008 edition, 730 p.
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  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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SEQUENCE VARIANTS IN THE CONSTRUCTION OF THE CONFIGURATION OF DESARGUES

Вестник МГСУ 9/2016
  • 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 130-139

The article presents the results of the analysis to assess the multi-variant approaches to constructing the Desargues configuration which is the fundamental to projective geometry and projective graphics. From the practical point it is the basis for the theory of perspective and is widely used to solve various tasks, such as constructing shadows in perspective, a direct, incidentally out of the rich within the drawing of the vanishing point, etc. The authors present the algorithm of the possible variants of construction of the Desargues configuration using computer technologies. The computer implementation of theoretical provisions of separate aspects of projective geometry and graphics has previously been considered as applied to Johnson polyhedrons. As any other figure the configuration of Desargues may be constructed by different methods. The authors consider the choice of points and directs included into the configuration and different interpretations of the relations of the point. The considered algorithm of the possible variants of the Desargues configuration construction will allow widely using the configuration in design of complex architectural and design volumes, consisting of a series of simple overlapping forms, by means of modern computer technology.

DOI: 10.22227/1997-0935.2016.9.130-139

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