Using motor tasks to quantitatively judge 3-D surface curvatures.

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects' sensitivity to the curvature of a curve lying on a surface and changes in the curvature as defined by Euler's formula, which relates maximum and minimum principal curvatures and their directions. Regardless of direction and surface shape (elliptic and hyperbolic), subjects could report the curvature of a curve lying on a surface through a drawing task. In addition, multiple curves drawn by subjects were used to reconstruct the surface. These reconstructed surfaces could be better accounted for by analysis that treated the drawing data as a set of curvatures rather than as a set of depths. A pointing task was utilized in Experiment 2, and subjects could report principal curvature directions of a surface rather precisely and consistently when the difference between principal curvatures was sufficiently large, but performance was poor for the direction of zero curvature (asymptotic direction) on a hyperbolic surface. In Experiment 3, it was discovered that sensitivity to the sign of curvature was different for perceptual judgments and motor responses, and there was also a difference for that of a curve itself and the same curve embedded in a surface. These findings suggest that humans are sensitive to relative changes in curvature and are able to comprehend quantitative surface curvature for some motor tasks.