The Perception of Surface Folding in Static and Animated Displays

Abstract

How do we interpret outline drawings of surfaces? Although pictorial depictions are projectively ambiguous, observers demonstrate definite preferences of interpretation. Additionally, they commit typical errors. A study is reported of one specific arrangement of surfaces as it is represented in outline drawings, namely the arrangement that results when two arbitrary surfaces are joined at a common edge to form an angle in 3-D (‘phenomenic folding’). With some of these arrangements, observers report that the angle formed by the two surfaces is zero (complete folding). With others, they report that the angles are greater than zero (incomplete folding). Both interpretations are actually valid. Several investigators have proposed that observer preferences such as these are due to a tendency to prefer a 3-D interpretation that will make the depicted 3-D shape regular. Three experiments were performed to test this regularisation hypothesis. In the first, observers were shown pairs of four-sided polygons joined at one equal side. Their task was to imagine how the smaller polygon could be folded completely towards the larger, and, subsequently, to report on its position after the folding (‘mental folding’). Reported positions were consistent with 3-D interpretations that caused figural regularisations. In the second and third experiments, observers were shown drawings of diamonds and parallelograms folded along a number of differently positioned and oriented segments (‘folding edge’). Their task was to estimate verbally the extent of the dihedral angle formed by the two surfaces. Results indicated that the perception of incomplete folding is determined by 3-D interpretation of the orientation of the drawing with respect to the picture plane. In a fourth experiment, observers were asked whether projective equivalences might be disambiguated by animating two kinds of displays that yield the ‘incomplete folding’ effect but that should be distinguishable on the basis of the trajectories of the vertexes of the folding parts. Results demonstrated that even in these conditions observers are unable to interpret the foldings correctly. These results might be taken to indicate that projective, static information leading to a simpler and more regular interpretation of the display can prevail over explicit motion information that should force the system to achieve a nonregular solution.