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Chen, Jennie Jia Yi

University of British Columbia

The Steering Law has long been a fundamental model in predicting movement time for tasks involving navigating through constrained paths such as menu selections and virtual environments. The base model and past research on its extensions primarily focused on simple geometries such as straight lines and simple or compound circular arcs. While useful in simple user interfaces, they do not capture the complexities of real-world tasks where curvatures can vary arbitrarily. This limits the generalizability of the model to envi- ronments where users interact with more irregular paths. This thesis revisits and extends the Steering Law by introducing the total curvature pa- rameter K into the equation to account for the overall curviness characteristic of a path. Drawing on an information-theoretic interpretation of human motor behavior, we propose an extension to the Steering Law where K contributes as logarithmic noise in the movement time prediction equation: MT= a + b L + c·log2(K + 1) + d L·K To validate this extension, we conducted a mouse-steering experiment (N= 20) on fixed- width paths characterized by 3 levels of length and 3 levels of curviness. Width was held constant to isolate curvature effects. Results demonstrate that the introduction of K significantly improves model fitness for movement time prediction over traditional models. We further identify a significant in- teraction between length and curviness, which led to improved performance when incor- porated into the model. We also show that previous models developed for circular arc trajectories, when reformulated using the K parameter, generalize well to our experimental data. These findings support the hypothesis that curvature introduces a form of perceptual or motor noise that increases task difficulty in human steering behavior. Beyond empirical validation, this thesis presents a detailed account of the theoretical framing and experimental reasoning through a series of pilot studies and design explo- ration that informed the final model design. By integrating curvature in complex curved paths, this work advances our understanding of movement in curved paths and supports potential applications in fields like speech motor control and virtual navigation.

Text

2025-04-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/90833

Electrical and Computer Engineering

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/