Quantitative Analysis of User Navigation in Virtual Reality Environments: A Trajectory-Based Approach to Motion Smoothness

This study presents a trajectory-based analytical framework for evaluating spatial accessibility and wayfinding performance in immersive virtual environments. The method was applied to the proposed Emergency Department (ED) of Nasr City Hospital, Cairo, involving six medical professionals. Participants performed scenario-based tasks in Virtual Reality (VR), during which motion data—comprising spatial coordinates, yaw rotation, and timestamps—were collected. A custom Python workflow processed the data to compute key mobility metrics: total distance, average speed, speed variability, and rotational variability. A composite metric, the Normalized Weighted Smoothness Index (NWSI), was introduced to reflect temporal consistency and directional coherence. Results revealed differences in navigation fluency across participants. High smoothness and low variability suggested efficient spatial understanding and minimal cognitive load. In contrast, abrupt changes in speed and direction indicated wayfinding difficulties, often linked to reduced visibility or unclear spatial cues. Mapping these behaviors identified zones with potential design inefficiencies. The proposed method offers a quantitative, evidence-based approach for assessing environmental legibility and supports iterative improvements in VR-based healthcare design.