Placement of multiple virtual objects in physical space in augmented reality applications

Introduction. The challenges of placing virtual objects in a real-world environment limit the potential of augmented reality (AR) technology. This situation identifies a gap in scientific knowledge that requires additional research. Therefore, the main task of this study was to develop a method for optimal placement of virtual objects, in which the objective function of comfort was minimized. This approach is aimed at improving AR systems and developing the corresponding theory.Materials and Methods. The conducted research was based on the analysis of the placement of virtual objects in AR/VR applications with particular emphasis on optimization. The concept of comfort of placement was proposed, taking into account the size of the object and the distance to the boundaries of free space in X, Y, Z coordinates.Results. As part of the study, formulas were obtained for the optimal placement of objects with an arbitrary comfort function. The basic criterion was to minimize the difference between comfort levels from different sides of the object. It was found that a successful placement of objects required taking into account their size and comfort zones, as well as solving a system of n linear equations.Discussion and Conclusion. The results obtained make an important contribution to the study of the problem of placing virtual objects in AR/VR/MR. They open up new opportunities for improving user interaction and conducting further research in the field of spatial computing. Possible directions for further development are dynamic adjustments and integration of the results into various XR scenarios.