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ARCHITECTURE AND URBAN DEVELOPMENT. RESTRUCTURING AND RESTORATION

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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