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Constant Affine Velocity Predicts the 1/3 Power Law of Drawing and Planar Motion Perception

Pollick, Frank E.; Sapiro, Guillermo



Abstract: Numerous studies have shown that the power of 1/3 is important in relating Euclidean velocity to radius of curvature (R) in the production and perception of planar movement. Although the relation between velocity and curvature is clear and very intuitive, no valid explanation for the specific 1/3 value was found yet. We show that if instead of computing the Euclidean velocity we compute the affine one, a velocity which is invariant to affine transformations, then we obtain that the unique function of R which will given an affine invariant velocity is precisely R to the 1/3 power. This means that the 1/3 power law, experimentally found in the studies of hand-drawing and planar motion perception, implies motion at constant affine velocity. Since drawing at constant affine velocity implies that curves of equal affine length will be drawn in equal time, we performed an experiment to further support this result. support this result. Results showed that drawing was performed at constant affine velocity. Possible reasons for the appearance of affine transformations in the production and perception of planar movement are discussed.

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