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Maria Hadjigeorgieva, Bettina Friedrich, Frank E Pollick; Perception and action in drawing circles. Journal of Vision 2003;3(9):265. doi: https://doi.org/10.1167/3.9.265.
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A circle viewed from the side will appear more circular than the ellipse projected onto the retina. This phenomenal regression to the real object is a basic result in shape constancy. We examined what happens to shape constancy when people are asked to draw circular shapes from different viewing directions. We addressed two questions. The first was whether the width-to-height ratio of the drawing motion would change as the viewing direction changed from frontal to oblique. The second was what form the velocity profile of the drawing would take. Of interest here is the fact that the 1/3 power law of planar drawing predicts a relationship between local velocity and shape such that the hand slows down to draw more curved sections. Moreover, that this relation provides motion at constant affined velocity so that the apparent velocity-curvature relation is invariant upon viewing direction. Participants were asked to draw with their fingertip 5 circles of radius 3 inches, centred at eye level, on a board oriented in the vertical plane while position of the fingertip was recorded at a rate of 200 Hz. Viewing was binocular and oblique angles obtained by rotating about the centre of the circle in the horizontal plane. In one condition participants received visual feedback of the drawing motion, in the other there was no visual feedback. When feedback was available participants could see the global shape revealed by a visible trace on the board. Results of global shape indicated that the width-to-height ratio increased for the more oblique viewing directions. However this result was obtained for both feedback and no-feedback conditions, precluding a purely visual interpretation of the effect. Results of the velocity profile analysis showed that velocity was roughly constant with small variation. These results will be discussed within the context of models of visuo-motor processing which couple visual perception and visually-guided action.
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