Abstract: This article is devoted to the creation of a national virtual university platform, geometric modeling of the design of exteriors, interiors and characters in the field of information technology based on 3D technologies. We know that visualization uses geometric splines and polygonal mesh construction methods. In virtual reality systems, each object is represented by a three-dimensional model. The real challenge now is to create custom models that control them. A three-dimensional model of a character is represented by a depth map, dots, a polygonal model, a parametric model describing anthropometric, ansaphic and profile features of a human face. The research process includes the study of the rules of visualization of virtual three-dimensional objects through internal and external models, the theory of geometric modeling, algorithms, methods and algorithms of computer modeling, the use of virtual reality algorithms in education. Today, when engineering and technology are rapidly developing in our country, traveling to the virtual world is of great interest to many. As a result, three-dimensional content and landscape design expand the human imagination and serve to capture our knowledge about the subject and object in our memory. It would be more effective to transfer practical classes in computer halls of educational institutions to the virtual world and organize them in this virtual environment using virtual objects. In addition, all aspects of the subject can be explained and taught, and students will be able to use it virtually. Creating a toolbar that includes all virtual objects becomes a priority. Object-oriented programming technologies and testing methods were used. This article proposes new methods of geometric modeling of three-dimensional objects mentioned above, that is, the constructive logical-algebraic method of R-functions (RFM). This method allows you to depict 3D objects of high complexity.

Keywords: Virtual environment, virtual universities, Polygonal model, Geometric spline functions, Constructive solid geometry, Function Rissi, Function Rvachev, three dimensional model, polygons, avatars

References:
Nikitenko M. S., & Karvovsky D. A. (2018). Implementation and optimization of the method of voxel global illumination of three-dimensional scenes. BC/NW, 1(32), 10.6.
Abdul Majeed, Muhammad Abbas, Faiza Qayyum, Kenjiro, T., Miura, Md Yushalify Misro, & Tahir Nazir. (2020). Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter, Modern Geometric Modeling: Theory and Applications, Mathematics, 8(12), 2102. Retrieved from https://doi.org/10.3390/math8122102
Chempinsky, L.A. (2017). Fundamentals of geometric modeling in mechanical engineering: lecture notes. Samara: Samara University Publishing House.
Lisnyak A.A., Choporov S.V., & Gomenyuk S.I. (2010). Methods of visualization of geometric objects described using r-functions. Bulletin of Zaporozhye National University, 1, 88-96.
Zaitsev, S. A., & Subbotin, S. A. (2011). The diagnostic model building on the basis of negative selection par

Abstract: The subject of the study is the features of the organization of virtual reality interfaces.
The author examines in detail such aspects of the topic as user involvement in the virtual environment,
various ways and scenarios of user interaction with virtual reality, user security in the virtual environment, as well as such a phenomenon as cyberbullying and ways to prevent it. The study also considers the use of voice control as an alternative to manual.
Particular attention in this study is paid to the classification of virtual reality interfaces, among which sensory interfaces, interfaces based on user motor skills, sensorimotor interfaces, interfaces for modeling and developing virtual reality are distinguished and considered in detail.    The main conclusion of the study is that the virtual reality interface should be designed taking into account the ergonomics of users to prevent muscle fatigue and cyber-pain.
In addition, it is very important to ensure the user's safety when designing virtual environment interfaces: using the virtual reality interface should not lead to injury to the user.
To create an ergonomic and secure virtual reality interface, a combination of different types of interfaces is often required, through which the user can access an alternative control method or improved navigation.
A special contribution of the author to the study of the topic is the description of the classification of virtual reality interfaces.

Keywords: Interface design, User motor skills, Muscle fatigue, Graphical interfaces, User engagement, Cyberbullying, Sensorimotor interfaces, Touch interfaces, Voice control, Virtual reality

References:
Berg, L.P., & Vance, J.M. (2017). Industry use of virtual reality in product design and manufacturing: a survey. Virtual Reality 21, 1–17. doi:10.1007/s10055-016-0293-9
Furht, B. (2008). Immersive Virtual Reality. Encyclopedia of Multimedia. Springer, Boston, MA. doi:10.1007/978-0-387-78414-4_85
Yan, F., Dorine, C., Duives, S.P.H. (2022). Wayfinding behaviour in a multi-level building: A comparative study of HMD VR and Desktop VR. Advanced Engineering Informatics. doi:10.1016/j.aei.2021.101475
Tao, G., Garrett, B., Taverner, T. et al. (2021). Immersive virtual reality health games: a narrative review of game design. J NeuroEngineering Rehabil 18, 31. doi:10.1186/s12984-020-00801-3
Valentine, A., Van Der Veen, T., Kenworthy, P., Hassan, G. M., Guzzomi, A. L., Khan, R. N., & Male, S. A. (2021). Using head mounted display virtual reality simulations in large engineering classes: Operating vs observing. Australasian Journal of Educational Technology, 37(3), 119–136. doi:10.14742/ajet.5487
Cru

Abstract: The object of study is the volumetric rendering method based on three-dimensional textures and functionally defined surfaces in an interactive mode using graphic accelerators. A hierarchical approach to the representation of textures in memory and a method for managing large arrays of voxels are proposed. The hierarchical structure has a compact texture description using data homogeneity and the importance of information to reduce the required memory and computation speed. The method is based on effective texture management, in which texture memory is assigned according to the degree of significance of the region and the content of voxel data. The combination of data, interpolation, and data importance determine the selected set of tree nodes. These nodes determine how the volume should be laid out and represented in the texture memory. The research method is based on analytical geometry in space, differential geometry and vector algebra, theory of interpolation and matrix theory, based on mathematical modeling and theory of computing systems. The main conclusions of the study are: the ability to visualize a large number of volumes, functionally defined objects, complex translucent volumes, including volume intersections in constructive solid-state modeling. Rendering different volumes at the same time is a more complex problem than rendering one volume, because it requires intersection and blending operations. Functionally defined surfaces are well suited for embedding external objects in volumes. Models of medical instruments and the combination of surfaces with volumetric data are necessary for virtual computer surgery.

Keywords: texels, tile technology of visualization, voxels, graphics processing units, constructive solid geometry, ray casting, volume rendering, perturbation functions, function-based surfaces, three dimensional textures

References:
A. Mammen. Transparency and Antialiasing Algorithms Implemented with the Virtual Pixel Maps Technique. IEEE Computer Graphics Applications, Vol. 9. ¹ 4. July 1989. IEEE Computer Society Press Los Alamitos, CA, USA. doi>10.1109/38.31463. P. 43–55.
T. Porter and T. Duff. Compositing Digital Images. Computer Graphics, Vol. 18, ¹ 3 July, 1984, ACM New York, NY, USA, doi>10.1145/964965.808606. P. 253-259.
Vyatkin S. I. Preobrazovaniya funktsional'no zadannykh form // Programmnye sistemy i vychislitel'nye metody.-2014.-¹ 4.-S. 484 – 499.
C. Everitt. Interactive Order-Independent Transparency. Technical report NVIDIA OpenGL applications engineering, 2001.
Vyatkin S. I. Modelirovanie slozhnykh poverkhnostey s primeneniem funktsiy vozmushcheniya // Avtometriya, 2007, t. 43, ¹ 3. C. 40–47.
Vyatkin S.I., Dolgovesov B.S. A 3D Texture-Based Recursive Multi-Level Ray Casting Algorithm // Proceedings of the Second IASTED International Multi-Conference on Automation, Control, and Information Technology-ACIT`2005. "Software E

Abstract: the article reviews techniques and architecture of a system for transferring “live” lectures into virtual world vAcademia. The system records lector’s voice and uses Microsoft Kinect for capturing teacher’s gestures transforming this data into lector’s avatar animation. With the performance capabilities of streaming processors the content of the projector’s screen used by teacher is transferred directly to the virtual world and displayed in shared graphical workspace, and the additional analysis of the image from Kinect video camera is performed to more accurately determine the position of the body of the teacher. The stream processors allowed eff ectively implement the projector’s screen transfer to the virtual world shared workspace and also capture and recognize colored makers on the teacher’s body with little or no loss of performance. Using Kinect for lecture capture together with capturing image from the projector or interactive board and displaying it in the virtual world could allow teachers to use virtual worlds as a powerful learning tool while remaining in the familiar learning environment. That is the purpose of this research.

Keywords: vAcademia, Microsoft Kinect, stream processors, image analysis, virtual world, lecture capture, presentation, slide lectures, motion capture, discrete wavelet transform

References:
Smorkalov, A.Yu. Realizatsiya obrazovatel'nykh instrumentov v virtual'nykh 3D-sredakh s ispol'zovaniem potokovykh protsessorov / A.Yu. Smorkalov // Obrazovatel'nye tekhnologii i obshchestvo.-T. 14. ¹ 3, 2011.-S. 409-425.
Smorkalov, A.Yu. Matematicheskaya i programmnaya modeli generatsii tekstur na graficheskikh potokovykh protsessorakh / A.Yu. Smorkalov // Programmnye sistemy i vychislitel'nye metody.-¹ 1, 2013.-S. 116-128. DOI: 10.7256/2305-6061.2013.01.10
L. Jingtang, Z. Gang, T. Dunming, and X. Junjie “Research of skeletal-based virtual human animation using Cal3D,” in 3rd International Conference on System Science, Engineering Design and Manufacturing Informatization (ICSEM) Chengdu, China, 2012, p. 269–273.
Mikhail Morozov, Alexey Gerasimov, Mikhail Fominykh, Andrey Smorkalov. Asynchronous Immersive Classes in a 3D Virtual World: Extended Description of vAcademia // Trans. on Comput. Sci. XVIII, LNCS 7848, p. 81-100.
Microsoft, Kinect. Web: http://www.microsoft.com/en-us/kinectfo

Abstract: The authors suggest method of teaching the tactical actions by simulating game situations in virtual reality. A database of players is filled on the server, the coach forms the attacking and defending teams, their initial placement and the location of implement at the field, that will be sent to the players’ computers. The players of attacking ream try to bring the virtual game object to the affected area or to hit the gate of the defending team. Players of the defending team tries to possess the virtual game object and to prevent the actions of the attacking team. The proposed method allows to simulate and unlimited number of game situations, analyze different scenarios and improve the game thinking and interaction of players. It can be used for tactical teaching in teams of varying level of training specializing in football, hockey, handball, rugby, basketball and other team sports.

Keywords: sports games, tactical training, computer technologies, virtual reality, individual actions, group actions, team actions, game thinking, young athletes, skilled athletes

References:
Kovalev V.D., Golomazov V.A., Keraminas S.A. Sportivnye igry: Uchebnik dlya studentov pedagogicheskikh institutov. M.: Prosveshchenie, 1988. 304 s.
Portnykh Yu.I., Fetisova S.L. Ispol'zovanie metoda igrovogo proektirovaniya v protsesse obucheniya igrovoi sorevnovatel'noi deyatel'nosti // Uchenye zapiski universiteta im. P.F. Lesgafta. 2010. ¹ 1. S. 85-88.
Drandrov G.L., Krasnov Yu.I., Fattakhov R.V. Takticheskaya podgotovka yunykh futbolistov na osnove realizatsii printsipa obobshcheniya v obuchenii // Vestnik Chuvashskogo gosudarstvennogo pedagogicheskogo universiteta im. I.Ya. Yakovleva. 2011. ¹ 2-2. S. 86-91.
Kozina Zh.L. Metody primeneniya sovremennykh informatsionnykh tekhnologii dlya aktivizatsii obraznogo vospriyatiya zanimayushchimisya elementov tekhniki i taktiki v v sportivnykh igrakh // Pedagogika, psikhologiya i mediko-biologicheskie problemy fizicheskogo vospitaniya i sporta. 2007. ¹ 1. S. 58-64.
Pomeshchikova I.P., Pomeshchikov S.S., Chucha N.I. Issledovanie effektivnosti obuchen

Abstract: 3D-record of a lesson is a powerful tool for education in virtual worlds. However, as with the video records, the 3D-record needs to be edited by the teacher to turn into a high-quality educational content. As opposed to a video stream a 3D-record is a complex sequence of changes of synchronized properties bound to the timeline that starts from the beginning of the lesson. 3D-record editing capabilities require solving number of technical problems related to the size of the original data, removing unnecessary resources, speed of the record replay and the size of the network packages. The article is devoted to these issues.

Keywords: Software, 3d-content, editing, virtual worlds, 3d-record, education, synchronization, multimedia, resources, collection

References:
Smorkalov A.Yu. Realizatsiya obrazovatel'nykh instrumentov v virtual'nykh 3D-sredakh s ispol'zovaniem potokovykh protsessorov. //Obrazovatel'nye tekhnologii i obshche-stvo.– 2011.– T. 14.– N 3.– S. 409-425.
Ryzhenkov M.E., Morozov M.N., Gerasimov A.V. Generatsiya i redaktirovanie 3D-kontenta v virtual'nykh obrazovatel'nykh sredakh. //Obrazovatel'nye tekhnologii i obshchestvo.– 2011.– T. 14.– N
– S. 425-439. 3. URL: www.vacademia.com
Smorkalov, A.Yu. Podderzhka operatsiy risovaniya v sisteme obrabotki rastrovykh izobrazheniy na potokovykh protsessorakh. Sbornik materialov Vserossiyskoy nauch-no-prakticheskoy konferentsii «Informatsionnye tekhnologii v professional'noy deyatel'nosti i nauchnoy rabote». – Yoshkar-Ola: MarGTU, 2011.– S. 201-206