Planning and drawing complex shapes

Abstract

Arm and hand movements are generally controlled using a combination of sensory-based and memory-based guidance mechanisms. This study examined similarities and differences in visually-guided and memory-guided arm movements, and sought to determine to what extent certain control principles apply to each type of movement. In particular, the 2/3 power law is a principle that appears to govern the formation o f complex, curved hand trajectories; it specifies that the tangential velocity should be proportional to the radius of curvature raised to an exponent o f 1/3. A virtual reality system was used to project complex target paths in three-dimensional (3D) space.Human subjects first tracked (with the tip of a hand-held pen) a single target moving along an unseen path. The entire target path then became visible and the subject traced the shape. Finally, the target shape disappeared and the subject was to draw it, in the same 3D space, from memory. Most aspects of the movements (speed, path size and shape, arm postures) were very similar across the three conditions. However, subjects adhered to the 2/3 power law most closely in the tracing condition, when the entire target path was visible. Also, only within the tracing condition, there were significant differences in the value of the exponent depending on the size and the spatial orientation of the trajectory. In the tracking and drawing conditions, the exponent was greater than 1/3, indicating that subjects spent more time in areas of tight curvature. This may represent a strategy for learning and remembering the complex shape.2

Movement Timing and Invariance Arise from Several Geometries

“…Several other recent studies have also reported strong departures from the two-thirds power law [58],[59]; for locomotion, see also [16],[17]. These studies either employed different experimental paradigms from those used here or offered alternative explanations for the observed violations of the power law.…”

“…Examining the generation of different patterns of complex figural forms in various tasks and conditions (tracking, drawing from memory, tracing) Flanders et al [59] also showed significant differences in the values of the exponent of the power law depending on the size and orientation of the trajectory. In particular the authors suggested that strategic or cognitive factors affect the relation between hand velocity and curvature.…”

“…Future work should deal with 3D Motion, as well as with movements performed in different orientations, as in [58],[59], and at different depths with respect to the body. This will certainly require considering additional geometries and may reveal certain failures of invariance due to the influence of biomechanical factors.…”

Differentiation between external and internal cuing: An fMRI study comparing tracing with drawing

“…Having emphasised this dissociation, it should be mentioned that there remains a degree of overlap in the neural circuitry controlling externally and internally cued movements. The cerebellum can function during internally cued movements (Mushiake and Strick, 1993) and the basal ganglia and SMA in externally cued movements (Jueptner et al ., 1997a/b; Vaillancourt, Mayka and Corcos, 2006; Vaillancourt, Thulburn and Corcos, 2003). These findings can be explained by the presence of specific sub circuits within the cerebellar and basal ganglia systems that are specific for each movement type and which are superimposed on a background of overlapping functions (Van Donkelaar et al ., 1999;2000).…”

“…Previous behavioural work has demonstrated differences between tracing and drawing eye-hand coordination with and without visual cues, suggesting that the two forms of movement recruit different brain areas. Flanders, Mrotek and Gielen, (2006) compared the kinematics of tracing a seen shape with subsequent drawing from memory of that shape. They observed highly similar patterns between the two tasks but compared to the tracing task, subjects spent more time in areas of tight curvature during drawing and proposed that this represented a strategy for learning and remembering the shape.…”