Angular induction is the perceptual process by which one line can bias the perceived orientation of another line or its projection. These effects are generally evaluated using long, straight lines, but the use of waveforms provides a way to vary the orientation of adjacent segments systematically. This may provide information about the nature of local and global interactions.The biological and perceptual mechanisms for judging the straightness and alignment of lines and points over long distances are not well understood. However, it is known that these attributes are affected by the relative position of the elements, as seen in classic illusions of angle and direction. For example, an oblique line segment will be misprojected across the space that lies between two horizontal or vertical parallels; this is one of the standard variants of the Poggendorff illusion. The direction of the misprojection is similar to the bending of light as it passes from air into water, but the degree of misprojection is a function of the angle of the oblique relative to each of the induction lines (Greene, 1987(Greene, , 1988. Essentially, horizontal and vertical lines have opposite effects on projection of the oblique, thus the influence of one line virtually cancels the effect of the other, even though they lie at different distances along the path of the projection.A long horizontal or vertical line segment has a greater influence on the projection than does a short segment. The present research examines the question of whether long lines derive their influence by the simple linear combination of effects from component segments. In this study, several patterns of line elements were constructed in a way that provided differential "loading" of components (e.g., a square waveform composed of successive short vertical and horizontal segments). Our goal was to evaluate the overall influence of the combined elements for inducing misprojection.
MEmODVisual stimulus materials were created using an Apple Macintosh computer and a laser printer (Adobe lliustrator software). Sinusoid, square, and triangular waveforms were presented on the page as parallel bands, This work was supported in part by the Neuropsychology Foundation.Sabah Al-Quaddoomi was on a sabbatical leave at the University of Southern California from Kuwait University for the 1987-88 academic year. Correspondence may be addressed to Ernest Greene, Department of Psychology, University ofSouthem California, Los Angeles, CA 90089.as illustrated in Figure 1. Each page also contained an oblique-line segment in one of the quadrants, positioned at 30 0 to the horizontal. The general configuration was the same as for one diagonal of a Poggendorff illusion.Each of the parallel waveforms consisted of a repeating cycle of a particular amplitude and wavelength of sine, square, left-facing, and rightfacing triangular (sawtooth) waves. The amplitude and wavelength of a I-unit wave was sized to be seen as 20 min of visual angle when viewed at 46 cm. The sizing was designed to allow compariso...
