DGM-RDW: Redirected Walking with Dynamic Geometric Mapping Between Environments

Redirected walking (RDW) subtly adjusts the user's visual perspective on head-mounted displays during natural walking to reduce forced resets, thus enlarging the size of the virtual environment that can be explored beyond that of the physical environment. Alignment-based RDW controllers aim to minimize spatial discrepancies by optimizing the alignment between the user's physical and virtual environments. We introduce a novel alignment-based method that dynamically calculates mapping functions between physical and virtual geometries to enhance the algorithm's awareness of the RDW environments. To achieve this, we first construct an abstract model defining a mapping function between physical and virtual geometries and establish feasibility constraints in differential form. We then concretize this mapping, optimize it, and develop a practical implementation for dynamic geometric mapping in RDW. Our approach distinguishes itself by determining dense spatial mappings around the user, rather than aligning environments according to limited metrics. Through extensive testing, our algorithm has proven to markedly decrease reset incidents in natural walking, surpassing existing RDW controllers. The introduction of dynamic geometric mapping provides a fresh perspective, contributing significant insights and advancing the field.