In today's fast-paced world of technology, where innovation plays a crucial role in our daily lives, the importance of search engines for identical models cannot be overstated. Every day, technological progress is becoming an integral part of our existence, penetrating various aspects of our lives. In this context, the search and identification of identical or similar 3D models become particularly relevant and become an integral part of innovative technologies. This article is an in-depth study in the field of creating and describing a mathematical model to search for similar 3D models. Developed using advanced comparison algorithms, this model has enormous potential and can be used in a variety of fields. It is important to emphasize that it is not limited to just one area of application, but finds its application in many areas of human activity. The application of such algorithms is important in various fields, including automated manufacturing, where accuracy and speed of component identification and classification are critical. They also find use in archaeology, where they help in the analysis and study of artifacts and structures. Architecture is also seeing great benefit from these innovations, allowing for more complex and detailed 3D models to be created for design and visualization. The new approach presented in the paper is based on an optimized matching algorithm that enables accurate recognition of geometric structures associated with 3D models without complex data preprocessing or image enhancement. This is a significant step forward in improving the efficiency and accuracy of identifying similar 3D models, even in low-resolution images. However, the application of this model is not limited to these areas. Its integration into real-time systems allows for the identification and classification of both individual 3D objects and complex 3D scenes created from image or video sequences. This is of great importance for the development of virtual and augmented reality technologies, where a high degree of detail and identification is necessary to create captivating and realistic visual effects. Thus, the presented mathematical model and the corresponding software open up enormous prospects for us in various fields. This is an important step forward in the development of technologies related to computer vision and image processing, as well as in the field of virtual and augmented reality, promoting progress and innovation
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