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For a polyhedron, the defect at a vertex equals 2π minus the sum of all the angles at the vertex (all the faces at the vertex are included). If a polyhedron is convex, then the defect of each vertex is always positive. If the sum of the angles exceeds a full turn, as occurs in some vertices of many non-convex polyhedra, then the defect is ...
The larger the angle an object subtends, the larger the apparent size of the object. The subtended angle increases as the object moves closer to the lens. Two objects with different actual size have the same apparent size when they subtend the same angle. Similarly, two objects of the same actual size can have drastically varying apparent size ...
A catoptric cistula is a box with insides made of mirrors so as to distort images of objects put into the box. Checker shadow illusion: The checker shadow illusion shows that when a shadow is cast onto a checked board, the colours of squares A and B in the photos appear to be different, when in fact they are the same. Chubb illusion
This idea that one does not see the different directions in which objects lie from oneself is a basis of the so-called "size–distance invariance hypothesis" (SDIH). That old SDIH logic (geometry) is typically illustrated using a diagram that resembles Figure 2, but has the physical visual angle θ substituted for the perceived visual angle θ ...
Of this point O in an object plane I, at right angles to the axis, and two other coordinates (x, y), the point in which the ray intersects the entrance pupil, i.e. the plane II. Similarly the corresponding image ray may be defined by the points (ξ', η'), and (x', y'), in the planes I' and II'.
The widely accepted interpretation of, e.g. the Poggendorff and Hering illusions as manifestation of expansion of acute angles at line intersections, is an example of successful implementation of a "bottom-up," physiological explanation of a geometrical–optical illusion. Ponzo illusion in a purely schematic form and, below, with perspective clues
The blue object lies nearer to the observer. Therefore, it has a "near" disparity d n. Objects lying more far away (green) correspondingly have a "far" disparity d f. Binocular disparity is the angle between two lines of projection . One of which is the real projection from the object to the actual point of projection.
In everyday life aberration is a well-known phenomenon. Consider a person standing in the rain on a day when there is no wind. If the person is standing still, then the rain drops will follow a path that is straight down to the ground. However, if the person is moving, for example in a car, the rain will appear to be approaching at an angle.