![]() ![]() Unlike inflectional deviations, however, the origin and properties of noninflectional deviations, as well as the conditions that cause fragmentation, are poorly understood.Īlthough the curvature profile in principle carries the full directional information of a movement, it fails to uniquely define the path shape when represented as a function of time,, depends on the speed profile. These observations led to the segmented control hypothesis that complex movements could be generated by concatenating smaller and simpler movement segments, each of which separately obeys the one-third power law ( 2, 3). ![]() log curvature plot into multiple line segments ( Fig. These noninflectional deviations occur in complex movements and are characterized by fragmentation of the log speed vs. Deviations have also been observed for movements without inflection points ( 1– 4). One class of deviation occurs when the curvature changes sign: The power law predicts the speed should diverge to infinity as the curvature approaches zero, which is physically implausible, whereas actual movements exhibit smooth, finite speed profiles at such inflection points. 1 have been observed for some movement trajectories. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and −2/3 for simple movements that can be characterized by a single angular frequency. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the −1/3 power for ellipses. In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 power of the local curvature, which is widely thought to hold for general curved shapes. ![]()
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