Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#265056] of Guillermo Sapiro

Papers Published

  1. Pollick, FE; Maoz, U; Handzel, AA; Giblin, PJ; Sapiro, G; Flash, T, Three-dimensional arm movements at constant equi-affine speed., Cortex; a Journal Devoted to the Study of the Nervous System and Behavior, vol. 45 no. 3 (March, 2009), pp. 325-339, ISSN 0010-9452 [18678364], [doi]
    (last updated on 2019/06/19)

    It has long been acknowledged that planar hand drawing movements conform to a relationship between movement speed and shape, such that movement speed is inversely proportional to the curvature to the power of one-third. Previous literature has detailed potential explanations for the power law's existence as well as systematic deviations from it. However, the case of speed-shape relations for three-dimensional (3D) drawing movements has remained largely unstudied. In this paper we first derive a generalization of the planar power law to 3D movements, which is based on the principle that this power law implies motion at constant equi-affine speed. This generalization results in a 3D power law where speed is inversely related to the one-third power of the curvature multiplied by the one-sixth power of the torsion. Next, we present data from human 3D scribbling movements, and compare the obtained speed-shape relation to that predicted by the 3D power law. Our results indicate that the introduction of the torsion term into the 3D power law accounts for significantly more of the variance in speed-shape relations of the movement data and that the obtained exponents are very close to the predicted values.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320