Planning and drawing complex shapes

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 as 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 of complex, curved hand trajectories; it specifies that the tangential velocity should be proportional to the radius of curvature raised to an exponent of 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 handheld 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, shape and 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.