Role of a circle’s center in visual interpolation

Basic geometric patterns like straight lines and circles seem fundamental to human perception and mental imagery. In this study we examined subjects’ ability to interpolate circular curves—to derive the whole circle from an arc of 180° or less. Specifically, we tested how the center point is utilized during such visual interpolation. Naturally, a mechanism that interpolates by extending the curvature of the visible arc will be unaffected by the presence or absence of the center point. On the other hand, a mechanism that achieves the same end by completing the circle from estimates of the center and radius will be significantly aided by the presence of the center. We found that when the visible arc was long (180°), presenting the circle’s center did not affect the precision with which subjects localized the invisible section. However, when the visible arc was relatively short (90° or 45°), displaying the center point significantly increased spatial precision. Thus, both computational mechanisms appear to exist.