Improving Steering Law Throughput Calculation by Defining Effective Parameters in 3D Virtual Environments Inproceedings

Mohammadreza Amini, Wolfgang Stuerzlinger, Shota Yamanaka, Hai-Ning Liang Liang, Anil Ufuk Batmaz

Abstract:

Throughput is a widely used performance metric that combines speed and accuracy into a single measure and reduces the effect of subjective speed–accuracy trade-offs. While it has been extensively applied to 2D steering tasks, its direct extension to 3D mid-air interaction presents unique challenges since trajectories in 3D exhibit higher variability, and perceptual–motor factors challenge existing formulations. As a result, throughput has not been systematically adopted for evaluating 3D steering in Virtual Reality (VR). In this paper, we propose and validate a novel formulation of throughput for 3D mid-air steering tasks. Using a controlled user study in VR with a ring-and-wire task, we introduce an effective width calculation based on the bivariate standard deviation of the trajectory. Our results show that this formulation manages to provide smoother throughput values across subjective speed–accuracy differences and improves model fit compared with traditional approaches. This work advances our theoretical understanding of the Steering law in 3D contexts, provides researchers and practitioners with a robust evaluation method, and establishes a foundation for future studies of complex 3D trajectory interactions.

Date of publication: Apr - 2026
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