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Application of Real and Functional Analysis Methods to the Study of Orthodontic Anomalies via Orthogonal Projections of Three-Dimensional Models
Yu.Zh. Pchelkina1, A.V. Kupriyanov1

1 Samara National Research University, Moskovskoye Shosse 34, Samara, 443086, Russia

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DOI: 10.18287/COJ2004

Article ID: 2004

Language: English

Abstract:
This paper presents an innovative approach to the automated detection of dentoalveolar anomalies based on the analysis of three-dimensional STL models of the oral cavity obtained by intraoral scanning. Using methods of real and functional analysis, an algorithm for orthogonal projection of models onto anatomical planes (frontal, sagittal, transversal) was developed, taking into account their geometric characteristics. The key element of the method is the computation of the center of mass and the inertia tensor, enabling automatic alignment of models and assessment of structural symmetry. It is shown that the application of matrix transformations and compensation of projection distortions ensures visualization accuracy of up to 0.1 mm. The practical significance of the work lies in reducing the subjectivity of diagnosis, decreasing analysis time, and minimizing X-ray exposure of patients.

Keywords:
three-dimensional STL models, intraoral scanning, triangulation surface, orthogonal projection onto a plane, inertia tensor.

Acknowledgements:
This work was performed within the State assignment for scientific research to Samara University (project FSSS-2024-0014).

Citation:
Pchelkina YZ, Kupriyanov AV. Application of Real and Functional Analysis Methods to the Study of Orthodontic Anomalies via Orthogonal Projections of Three-Dimensional Models. Computer Optics 2026; 50(3): 2004. doi: 10.18287/COJ2004.

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