Comparison of cube rotations around axes inclined relative to the environment or to the cube.

Abstract

Observers judged whether 2 successive computer-displayed rotations of a cube were the same or different. With respect to the observers, each rotation was about a vertical axis (Y), a horizontal (line-of-sight) axis (Z), an axis tilted just 10 ° from vertical or horizontal, or a maximally oblique axis. Independently, with respect to the cube, each rotation was about a symmetry axis through opposite faces (F) or through opposite corners (C), an axis tilted 10 ° from one of these symmetry axes, or an axis of extreme nonsymmetry. Speed and accuracy of comparison decreased as the axes of the successive rotations departed from the canonical axes of the environment (Z, or especially, Y), or even more sharply, from the symmetry axes of the cube (C, or especially, F). The internalized principles that guide the perceptual representation of rigid motions evidently are ones of kinematic geometry more than of physics.Evidence from many sources has indicated that space is not psychologically isotropic. We and other animals are quickest and most accurate in detecting objects (e.g., Ogilvie & Taylor, 1958) and in discriminating objects or their orientations (e.g.,

Imagining physically impossible self-rotations: geometry is more important than gravity

“…He found that this task was dif®cult to perform overall, but speci®cally, the geometric relationships between the object, axes of rotation, and the environment predicted the level of performance. As in Shiffrar and Shepard (1991), performance was superior when the axes of the object, rotation, and gravitational vertical were aligned. Pani and Dupree (1994) investigated the in¯uence of axis of rotation in imagined rotation using a stimulus of a square attached to a rod.…”

“…In addition, some studies suggest that principles of geometric relations, rather than physics, truly guide representations of real and imagined transformations (Shepard, 1984;Shiffrar & Shepard, 1991). Shiffrar and Shepard (1991) asked observers to judge whether two actual rotations of a cube were the same or different. They found that response latencies were faster and more accurate when the rotational axis was aligned with a natural axis of the object, the environment, or both.…”

Fitting objects into holes: On the development of spatial cognition skills.

“…Researchers have long been of the opinion that mental rotation develops quite late, and that even adults have limitations in understanding mental rotation (Roberts and Aman 1993;Tversky, Kim et al 1999;Uttal, Gregg et al 2001). When two objects appear in the same orientation this task is easy, but it is surprisingly difficult and time-consuming when the orientations of the two objects differ, and one must imagine rotations of the 3D object to make it fit the aperture (Massironi and Luccio 1989;Shiffrar and Shepard 1991;Pani 1993). A classical study of object perception and mental rotation says that the greater the angular difference is, the longer time is required to decide whether two objects are identical (Shepard and Metzler 1971;Shepard and Feng 1972).…”

“…The more spatially complicated a task is, that is to say the more steps you must imagine, the more you have to realize and plan. When adults judge direction, they perform worse when the rotation angle is oblique than when it is vertical or horizontal (Shiffrar and Shepard 1991;Pani 1993;Pani, William et al 1995;Pani, Jeffres et al 1996), probably because humans discern the vertical and horizontal in the environment more easily (Howard 1982).…”

Mobility Matters: Identifying Cognitive Demands That Are Sensitive to Orientation

“…Because of the invariance of gravity, the up/down axis is a primary reference frame for defining the tops and bottoms of objects and whether one object is above (or below) another [cf. 27].…”