Coordination of gaze and hand movements for tracking and drawing in 3D

In this study we have investigated movements in three-dimensional space. Since most studies have investigated planar movements (like ellipses, cloverleaf shapes and ‘‘figure eights’’) we have compared two generalizations of the two-thirds power law to three dimensions. In particular we have tested whether the two-thirds power law could be best described by tangential velocity and curvature in a plane (compatible with the idea of planar segmentation) or whether tangential velocity and curvature should be calculated in three dimensions. We defined total curvature in three dimensions as the square root of the sum of curvature squared and torsion squared. The results demonstrate that most of the variance is explained by tangential velocity and total curvature. This indicates that all three orthogonal components of movements in 3D are equally important and that movements are truly 3D and do not reflect a concatenation of 2D planar movement segments. In addition, we have studied the coordination of eye and hand movements in 3D by measuring binocular eye movements while subjects move the finger along a curved path. The results show that the directional component and finger position almost superimpose when subjects track a target moving in 3D. However, the vergence component of gaze leads finger position by about 250 msec. For drawing (tracing) the path of a visible 3D shape, the directional component of gaze leads finger position by about 225 msec, and the vergence component leads finger position by about 400 msec. These results are compatible with the idea that gaze leads hand position during drawing movement to assist prediction and planning of hand position in 3D space