Modeling of quasisymmetric ring elements of the church using data of ground laser scanning

Lviv Polytechnic National University


The aim of this work is to develop an algorithm for mathematical three-dimensional modeling of a typical roof of a Ukrainian church based on ground-based laser scanning and to find ways to optimize the model depending on the input data set. Method. The accuracy of the simulation depends on the laser scan data. The number of points obtained and their accuracy will affect the final result - 3D model of the roof. Given the typical design of the church roof in the shape of a cone, you can apply the standard mathematical algorithm for modeling part of the buildings of a typical church. Result The proposed algorithm was developed in the MathCad software environment. 3D scanning materials of the Ukrainian typical church were used to develop the mathematical algorithm. The algorithm analyzes the location of the scanning points of the church roof and performs its averaging. As a result of the algorithm, erroneous measurements were rejected and a model of the part of the roof was obtained, which forms the optimal geometry of the structure. Scientific novelty and practical significance. The proposed mathematical algorithm allows to automate some modeling processes of a typical Ukrainian church for design decisions. This method of modeling can be used for similar structures of other buildings.

  1. Pang, G., Qiu, R., Huang, J., You, S., & Neumann, U. (2015, May). Automatic 3d industrial point cloud modeling and recognition. In 2015 14th IAPR international conference on machine vision applications (MVA) (pp. 22-25). IEEE.
  2. Patil, A. K., Holi, P., Lee, S. K., & Chai, Y. H. (2017). An adaptive approach for the reconstruction and modeling of as-built 3D pipelines from point clouds. Automation in construction, 75, 65-78.
  3. Budroni, A., & Boehm, J. (2010). Automated 3D reconstruction of interiors from point clouds. International Journal of Architectural Computing, 8(1), 55-73.
  4. Ochmann, S., Vock, R., & Klein, R. (2019). Automatic reconstruction of fully volumetric 3D building models from oriented point clouds. ISPRS journal of photogrammetry and remote sensing, 151, 251-262.
  5. Scopigno, R., Callieri, M., Cignoni, P., Corsini, M., Dellepiane, M., Ponchio, F., & Ranzuglia, G. (2011). 3D models for cultural heritage: Beyond plain visualization. Computer, 44(7), 48-55.
  6. Rocha, G., Mateus, L., Fernández, J., & Ferreira, V. (2020). A scan-to-BIM methodology applied to heritage buildings. Heritage, 3(1), 47-67.
  7. Poux, F., Neuville, R., Nys, G. A., & Billen, R. (2018). 3D point cloud semantic modelling: Integrated framework for indoor spaces and furniture. Remote Sensing, 10(9), 1412.
  8. Talapov, V. (2015). On some principles and characteristics of information modeling of architectural monuments.  Architecture and Modern Information Technologies, 2 (31). (in Russian).
  9. Krisko, O. A. (2014). Data processing obtained by NLS to create a geometric model of the actual surface of thin-walled shells of technical forms. Modern problems of modeling, (2), 51-56. (in Ukrainian).
  10. Pepe, M., Costantino, D., & Restuccia Garofalo, A. (2020). An efficient pipeline to obtain 3D model for HBIM and structural analysis purposes from 3D point clouds. Applied Sciences, 10(4), 1235.
  11. Katushkov, V. O., Schultz, R. V., & Sossa, B. R. (2012). The relationship between the expected accuracy of ground-based laser scanning and the requirements for the accuracy of engineering and geodetic works. Urban Planning and Spatial Planning, (44), 238-248. (in Ukrainian).
  12. Schultz, R. W., Belous, B., & Goncheryuk, O. M. (2016). Monitoring of architectural monuments with the help of ground laser scanning data. Contemporary problems of architecture and urban planning, (46), 202-207. (in Ukrainian).
  13. Vus A. Ya., & Maevsky, V. O. (2015). Mathematical Simulation of Log Cross Sections Based on the Results of their Scanning. Scientific Bulletin of NLTU of Ukraine, 25 (4), 337-345.
  14. Маліцький А.Ю. Контроль відхилень фізичної поверхні від базової за даними наземного лазерного сканування. Міжнародна науково-технічна конференція молодих вчених «Geoterrace-2017», 14-16 грудня 2017, Львів. (in Ukrainian).