It is known that rotation of a furnished room around the roll axis of erect subjects produces an illusion of 360 degrees self-rotation in many subjects. Exposure of erect subjects to stationary tilted visual frames or rooms produces only up to 20 degrees of illusory tilt. But, in studies using static tilted rooms, subjects remained erect and the body axis was not aligned with the room. We have revealed a new class of disorientation illusions that occur in many subjects when placed in a 90 degrees or 180 degrees tilted room containing polarised objects (familiar objects with tops and bottoms). For example, supine subjects looking up at a wall of the room feel upright in an upright room and their arms feel weightless when held out from the body. We call this the levitation illusion. We measured the incidence of 90 degrees or 180 degrees reorientation illusions in erect, supine, recumbent, and inverted subjects in a room tilted 90 degrees or 180 degrees. We report that reorientation illusions depend on the displacement of the visual scene rather than of the body. However, illusions are most likely to occur when the visual and body axes are congruent. When the axes are congruent, illusions are least likely to occur when subjects are prone rather than supine, recumbent, or inverted.

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The modeling of Bézier curves and surfaces with their shape parameters is the most popular area of research in computer aided geometric design/computer aided manufacturing (CAGD/CAM) due to their geometric characteristics. In this paper, we propose an important idea to tackle the problem in construction of some engineering symmetric revolutionary curves and symmetric rotation surfaces by using the generalized hybrid trigonometric Bézier (or GHT-Bézier, for short) curve. The shape of the curves and surfaces can be modified by the alteration of shape parameters. The free-form complex curves using GHT-Bézier curves with constraints of parametric continuity are constructed. Finally, by using the GHT-Bézier curves with their continuity conditions and symmetric formulas, we construct different types of symmetric figures, symmetric revolutionary curves and symmetric rotation surfaces in R 2 and R 3 to show the efficiency of modeling. These symmetric examples show that the proposed method is time saving, effective and efficient in construction of complex engineering symmetric curves and surfaces.