An Algorithmic Complex for Dynamic Adaptation of Educational Environment Interfaces in Virtual Reality Based on Geometric Modeling

This paper presents an algorithmic complex for geometric modeling and dynamic adaptation of user interfaces in virtual reality (VR) environments, based on methods of engineering geometry and computer graphics. The primary problem addressed is the fundamental inefficiency of traditional 2D design methods, which fail to account for complex spatial relationships and the biomechanical limitations of natural hand movements, often leading to increased cognitive load, physical fatigue, and the risk of cybersickness. The proposed complex is a unified framework that integrates engineering-geometric and computer graphics methods for optimal 3D layout generation and visualization of VR menus, a predictive user behavior model for analysis and forecasting, and reinforcement learning algorithms for dynamic, real-time interface tuning. The core of the methodology is an intelligent system based on Q-learning, which manages interface parameters such as the size, placement, and shape of elements, thus establishing a closed loop of continuous adaptation where each user interaction refines and improves the interface design for future tasks. The feedback for the agent is derived from a multi-objective reward function that carefully balances performance metrics (speed, accuracy) with ergonomic characteristics of user movements, including path efficiency and smoothness (jerk metric). To enhance learning efficiency and guide the exploration of the parameter space, a predictive model based on Gaussian Processes (GPR) is used to forecast user performance and quantify prediction uncertainty, thereby effectively managing the exploration-exploitation trade-off. Experimental validation with 17 students confirmed the approach’s effectiveness, showing a significant reduction in task completion time and high user satisfaction (94.1%). Key metrics, including average task completion time, jerk metric, and path efficiency, showed sustained improvement over the course of the experiment. The results demonstrate that the developed complex provides a robust framework for creating ergonomic and efficient VR interfaces, which is particularly valuable for educational and training applications where long-term, comfortable use is critical for successful learning and minimizing health risks.