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ENGINEERING GEOMETRY AND COMPUTER GRAPHICS

Geometrical models of quadratic-rectangular sets with particular examples of composite solutions

Vestnik MGSU 9/2014
  • Polezhaev Yuriy Olegovich - Moscow State University of Civil Engineering (MGSU) Associate Professor, Department of Descriptive Geometry and Graphics, member of International Union of Russian Artists, Moscow State University of Civil Engineering (MGSU), 6 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-83; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Borisova Anzhelika Yur'evna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (MGSU), 6 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-83; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Borisova Viktoria Aleksandrovna - Moscow State University of Civil Engineering (MGSU) student, Institute of Environmental Engineering and Mechanization, Moscow State University of Civil Engineering (MGSU), 6 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-83; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 161-167

During the current decades the aspect of geometrography compositions formation on the basis of basic images has been actively developed. The basic images possess the qualities of harmonies, expressed by lines, squares, tone, color. The relations of square-rectangular forms belonging to plane geometry of parabolic, hyperbolic and elliptic fields has been already analyzed by scientists. This article introduces equiareals construction of square-rectangular shapes, as well as their rows - in classical composition of elementary figures of "squaring the circle". Variations of such constructions, in their turn, offer the possibility to seek and capture new geometrical graphical compositions, practical application of which can be wide enough in technology design and mechanical engineering, architecture and construction, decoration of household items, arts and crafts and costume fabrics, et cetera. The authors consider the topic of plane geometry "Field-M", which is based on a rectilinear grid of ortholines with circulations in its nodal points. The conclusions made by the authors is that the necessity of solutions for more and more various and complicated problems in the conditions of time limitation determines the development of geometrography methods as an effective operating system along with program methods of cognitive graphics.

DOI: 10.22227/1997-0935.2014.9.161-167

References
  1. Kapustina O.M., Martynenko Yu.G. Ispol'zovanie sistem simvol'nykh vychisleniy v prepodavanii teoreticheskoy mekhaniki [Application of Symbolic Calculation in Teaching Theoretical Mechanics]. MEI, MGU, Publ., 2012. Available at: http://vuz.exponenta.ru/PDF/book/KapMart2.pdf. Date of access: 21.04.2014.
  2. Kheyfets A.L. Uchebnyy kurs teoreticheskikh osnov 3D-komp'yuternogo geometricheskogo modelirovaniya i ego perspektivy [Study Course of Theoretical Foundations of 3D Computer Geometric Modeling and its Opportunities]. Informatizatsiya inzhenernogo obrazovaniya : trudy Mezhdunarodnoy nauchno-metodicheskoy konferentsii. INFORINO-2012 (Moskva, 10—11 aprelya 2012 g.) [Information of Engineering Education : Works of International Research and Methodology Conference. INFORINO-2012 (Moscow, April 10—11, 2012)]. Moscow, MEI Publ., 2012, pp. 119—122.
  3. Kondrat'eva T.M., Polezhaev Yu.O. Chastnye voprosy geometrografii primenitel'no k sisteme "Pole-metr" i kvadrature kruga [Special Questions of Geometrography Relating to the System "Pole-metr" and Quadrature of a Circle]. Inzhenernaya geometrografiya — issledovaniya i razrabotki : sbornik nauchnykh trudov. Moscow, MGSU Publ., 2006.
  4. Polezhaev Yu.O., Borisova A.Yu., Kondrat'eva T.M. Lineynye puchki v tsirkul'no-ellipticheskikh sootvetstviyakh [Linear Bundles within the Framework of Coincidence of Circle and Ellipse]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 6, pp. 62—67.
  5. Polezhaev Yu.O., Mitina T.V. Sootnosheniya geometricheskikh elementov kvadratury kruga v «Pole-M» [Correlation of Geometric Entities of the Quadrature of the Circle]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 5, pp. 250—254.
  6. Arkhimed, Gyugens, Lezhandr, Lambert. O kvadrature kruga [On Squaring the Circle]. Editorial USSR, 2003, 239 p.
  7. Khal Khellman. Velikie protivostoyaniya v nauke. Desyat' samykh zakhvatyvayushchikh disputov [Great Confrontations in Science. Ten of the Liveliest Disputes Ever]. Moscow, ID Vil'yams Publ., 2007, 320 p.
  8. Polya G. Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition. 1981, Wiley; Combined edition, 432 p.
  9. Fedorov E.S. Nachala ucheniya o figurakh [Foundamentals of the Theory of Figures]. Moscow, EE Media Publ., 2012, 418 p.
  10. Gil'bert D. Osnovaniya geometrii [Foundations of Geometry]. Moscow, Leningrad, OGIZ Publ., 1948, 491 p.
  11. Hilbert D., Cohn-Vossen S. Anschauliche Geometrie. 1996, Springer; Auflage: 2. Aufl., 365 p.
  12. Klein F. Neevklidova geometriya [Non-Euclidean Geometry]. Moscow, Leningrad, GTTI Publ., 1936, 355 p.
  13. Bashlykov A.A. Obraznoe predstavlenie sostoyaniya slozhnykh tekhnologicheskikh ob"ektov upravleniya [Figurative State Representation of Complex Engineering Systems]. Iskusstvennyy intellekt i prinyatie resheniy [Artificial Intellect and Decision-Making]. 2013, no. 3, pp. 9—18. Available at: http://www.aidt.ru/images/documents/2012-03/9_18.pdf. Date of access: 11.09.2013.
  14. Gornov A.O., Shatsillo L.A. Fraktal'nyy podkhod k strukturirovaniyu geometro-graficheskoy podgotovki [Fractal Approach to Structuring of Geometry-Graphical Education]. Innovatsionnye tekhnologii v inzhenernoy grafike. Problemy i perspektivy : Materialy Mezhdunarodnoy nauchno-prakticheskoy konferentsii (Brest 21 marta 2014 g.) [Innovation Technologies in Engineering Graphics. Problems and Opportuninties : Materials of International Scientific and Practical Conference (Brest, March, 21, 2014)]. Brest, BrGTU Publ., 2014, pp. 19—22. Available at: http://ng.sibstrin.ru/wolchin/img/Brest%202014.pdf. Date of access: 11.05.2014.
  15. Shcheglov G.A. O kompetentsiyakh CAD/CAE integratsii geometrograficheskikh modeley [On the Competences of CAD/CAE Integration of Geometrographical Models]. Informatsionnye sredstva i tekhnologii : trudy 20 Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii (20—22 noyabrya 2012 g. Moskva) : v 3 t. [Informational Media and Technologies : Works of the 20th International Science and Technical Conference (November 20—22, 2012, Moscow) : in 3 volumes]. Moscow, MEI Publ., 2012, vol. 2, pp. 81—84.

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Geometric models of junctions of quadrics in fragments of architectural pieces

Vestnik MGSU 9/2012
  • Polezhaev Yuriy Olegovich - Moscow State University of Civil Engineering (MGSU) Associate Professor, Department of Descriptive Geometry and Graphics 8 (499) 183-24-83, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Fatkullina Alina Alimovna - Moscow Institute of Architecture (MARHI) Candidate of Architecture, Associate Professor, Associate Professor of Department of Descriptive Geometry, Moscow Institute of Architecture (MARHI), 11 Rozhdestvenka St., Moscow, 107031, Russian Federation.
  • Borisova Anzhelika Yurevna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Associate Professor of Department of Descriptive Geometry and Graphics 8 (499) 183-24-83, Moscow State University of Civil Engineering (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 18 - 23

The subject matter of the article represents a summarized analysis of the geometrography of
a fragment of St. Isaac Cathedral, namely, the fragments that include surfaces of its domes. Their
detailed analysis has also required an overview of the properties of astroids and other elliptical multiplicities
limited by their relation to the spherical surface.
Further, the authors provide sample models of three types of domes, including circular, elliptical
and cone-shaped domes. The authors provide sketches and sample surface models of domes
and their descriptions. The authors also provide their explanation of the astroid origin and planimetric
properties of elliptical multiplicities under consideration, as well as interrelations between them,
if they are positioned on the spherical surface.
The information provided in the article and recommendations developed by the authors may
be used in the design of dome-shaped fragments of pieces of architecture.

DOI: 10.22227/1997-0935.2012.9.18 - 23

References
  1. Gil’berd D., Kon-Fossen S. Naglyadnaya geometriya [Visual Geometry]. Moscow, Nauka Publ., 1981, 343 p.
  2. Gil’bert D. Osnovaniya geometrii [Fundamentals of Geometry]. Moscow, OGIZ Publ., 1948.
  3. Korn G. Spravochnik po matematike [Handbook of Mathematics]. Moscow, Nauka Publ., 1974, 872 p.
  4. Polezhaev Yu.O. Ratsional’nye proportsii arkhitekturno-stroitel’nykh ob”ektov v proektsionnoy geometrii [Rationa l Proportions of Pieces of Architecture in Projective Geometry]. Moscow, ASV Publ., 2010, 200 p.
  5. Saprykina N.A. Osnovy dinamicheskogo formoobrazovaniya v arkhitekture [Fundamentals of Dynamic Shaping in Architecture]. Moscow, Arkhitektura-S Publ., 2005, 312 p.

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