A broad collection of illusions belonging to the Zollner and the Poggendorff families, including new variants - in particular, tilted and tilting squares - ate examined in the light of two possible formal principles : a principle of regression to right angles {RRA} and a principle of "orthogonal expansion", which is a perceptual expansion of the extent perpendicularly to the inducing lines. The domains of validity of the two principles arc compared. We propose that RRA is more pertinent when the target line is explicitely present and makes real intersections with the inducing Lines. Orthogonal expansion can produce RRA as a side-effect. It would be more pertinent when there are several parallel or nearly parallel inducing lines, and it does not require the presence of a real target. Both principles may be grounded on neurophysiological mechanisms. Orientation detectors would influence each other in the orientation domain, generating RRA and accounting for the illusions of the Poggendorff family. They would also influence each other in the extent domain, generating orthogonal expansion, and accounting for the illusions of the Zollner family.

Key wards: tilt illusions, tilting squares, Zollner illusion, Poggendorff illusion, orthogonal expansion