Modeling Steering Times of Oblique 3D Paths Article

Koyo Motoe, Taiyu Homma, Nobuhito Kasahara, Shota Yamanaka, Wolfgang Stuerzlinger, Homei Miyashita

Abstract:

Understanding how users perform steering tasks on planar user interfaces (UIs) presented at oblique angles is important for designing effective interfaces in 3D workspaces such as VR, where the viewer's angle relative to the content can vary. However, existing steering models have mainly assumed frontal viewing and do not fully account for viewpoint-dependent changes in apparent path geometry. We conducted a VR experiment in which users performed raycasting-based steering on circular paths displayed on a UI plane. We varied the oblique angle φ from 0° to 60°. We found that movement time generally increased as φ increased, and error rate was significantly higher at 60° than in the 0°, 20°, and 40° conditions. To model this effect, we extended the steering law using apparent path length, apparent width, and projected local curvature computed from the user's viewpoint. A baseline steering model based only on geometric path length and width on the UI plane achieved an adjusted R² of 0.9024, whereas a viewpoint-dependent global steering model based on apparent path length and width achieved an adjusted R² of 0.9637. A local curvature-integrated steering model further improved the fit, achieving the highest adjusted R² of 0.9910 and the lowest AIC among the compared models. In leave-one-out cross-validation, this model showed the best predictive performance among the compared models. These results show that steering time under oblique interaction can be predicted more accurately by incorporating viewpoint-dependent apparent geometry, providing quantitative guidance for designing spatially fixed UIs in VR and large-display environments.

Date of publication: Nov - 2026
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