Informatics and Applications
2025, Volume 19, Issue 2, pp 45-54
ABOUT AN ALGORITHM FOR GEOMETRIC MODELING OF STRUCTURES BASED ON THE RESULTS OF LASER SCANNING
- Yu. I. Bityukov
- P. Yu. Bityukov
Abstract
Laser scanner technology makes it possible to obtain point images of surfaces with a high degree of detail; so, the task of reconstructing a surface (area) from a point cloud has recently attracted a lot of attention. This is a problem faced in reverse engineering, archaeology, etc. The main difficulty that arises when solving general surface restoration problems is that the surface to be restored is usually not a graph of some scalar function. One of the methods used to solve the reconstruction problem is a method based on wavelets and the Bregman algorithm, which is used to find the coefficients of decomposition of the desired function defining the area by scaling functions.
At the same time, the work does not pay attention to biorthogonal wavelets, in particular, spline wavelets, which are the main tool in geometric modeling problems (NURBS curves and surfaces), since real-world design tasks often require local surface modification and knowledge of the analytical expression for scaling functions, which is ensured by the use of spline wavelets. In this article, an algorithm has been developed for constructing a smooth approximation of a characteristic function of a bounded region of space, the boundary of which contains a given point cloud obtained in some way, for example, by laser scanning. For the algorithm to work, it is only necessary to specify two sequences defining a family of biorthogonal wavelets. The desired approximation is in the form of a decomposition according to one of the families of scaling functions (smooth) and it is not necessary to compile a matrix of values of these functions at points in the cloud to determine the decomposition coefficients. The coefficients themselves are found using the Bregman algorithm and the discrete Fourier transform.
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[+] About this article
Title
ABOUT AN ALGORITHM FOR GEOMETRIC MODELING OF STRUCTURES BASED ON THE RESULTS OF LASER SCANNING
Journal
Informatics and Applications
2025, Volume 19, Issue 2, pp 45-54
Cover Date
2025-07-10
DOI
10.14357/19922264250206
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelet; wavelet frame; wavelet transform; discrete Fourier transform; geometric modeling; Bregman algorithm
Authors
Yu. I. Bityukov  and P. Yu. Bityukov 
Author Affiliations
Moscow Aviation Institute (National Research University), 4 Volokolamskoe Sh., Moscow 125933, Russian Federation
National Research University "Moscow Power Engineering Institute," 1 bld. 14 Krasnokazarmennaya Str., Moscow, 111250, Russian Federation
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