Mathematical Modeling of the Process of Engineering Structure Curvature Determination for Remote Quality Control of Plaster Works

  • Nadezhda IvannikovaEmail author
  • Pavel Sadchikov
  • Alexandr Zholobov
Conference paper
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 199)


Nowadays the plaster works are very popular, especially in restoration of old buildings that have complex geometric configuration. The plaster works are labor intensive, and shall be controlled. The quality control of plaster works on curved surfaces assumes the use of individual templates of curved surfaces for control of compliance with the design statement. This is not an efficient technology. The analysis of methods of the surface curvature determination for large objects available in the allied fields of sciences showed that the existing methods that can be used for computer-aided monitoring are not applicable for measurement of the surface curvature of fixed 3D structures. To solve this problem the authors of this Article have developed a method for noncontact quality control of plaster works. This method is based on a math model of the process of determination of a geometrical form of a structure to be plastered. The curvature of the plastered surface is defined with use of formulae received by way of solution of equations of surface of complex geometric bodies. This Article describes the process of determination of a formula for the surface of the central part of the Cathedral of Vladimir Icon of the Mother of God, which has a shape of a rectangular parallelepiped limited in the upper part by a dome having a shape of elliptic paraboloid. The results of this study are used for the development of a method of noncontact determination of curvature of an engineering structure surface.


Mathematical modeling Curved surface Elliptic paraboloid Plastering Engineering structure Projected plane Remote inspection Construction quality control 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Astrakhan State University Architectural and Civil EngineeringAstrakhanRussia
  2. 2.Don State Technical UniversityRostov-on-DonRussia

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