With few exceptions (Fantoni et al, 2008; Fulvio et al, 2009) the amodal completion of angles has been conceived as the production of a trajectory that interpolates veridically represented input segments. This is the case also for the Gerbino illusion, originally explained as the consequence of amodal additions based on good continuation (Gerbino, 1978). Alternatively, amodal completion might involve approximation. Curve fitting by polynomial functions makes the difference clear (Ullman, 1996). Interpolation generates a curve that connects all points and minimizes the changes of direction; approximation generates a curve that minimizes the distances from points, with a variable error intrinsic to noisy data. In the Gerbino illusion approximation generates of a smooth hexagon that cannot match the arrangement of input segments, given the coincidental occlusion of vertices. Fantoni et al (2008) provided evidence of approximation in amodal completion of 3D surfaces. With reference to such phenomena I will discuss the assumption that perceptual experience includes representations not only of the optic input but also of the degree of mismatch between the input and approximated shapes.
