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Visibility affects all forms of traffic: roads, railways, sailing and aviation. The geometric range of vision is limited by the curvature of the Earth and depends on the eye level and the height of the object being viewed. In geodesy, the atmospheric refraction must be taken into account when calculating geodetic visibility.
In geometry, visibility is a mathematical abstraction of the real-life notion of visibility. Given a set of obstacles in the Euclidean space , two points in the space are said to be visible to each other, if the line segment that joins them does not intersect any obstacles.
To determine the visibility of a target cell, each cell between the viewpoint cell and target cell is examined for line of sight. Where cells of higher value are between the viewpoint and target cells the line of sight is blocked. If the line of sight is blocked then the target cell is determined to not be part of the viewshed.
Visibility graphs may be used to find Euclidean shortest paths among a set of polygonal obstacles in the plane: the shortest path between two obstacles follows straight line segments except at the vertices of the obstacles, where it may turn, so the Euclidean shortest path is the shortest path in a visibility graph that has as its nodes the start and destination points and the vertices of the ...
If one looks at a one-centimeter object at a distance of one meter and a two-centimeter object at a distance of two meters, both subtend the same visual angle of about 0.01 rad or 0.57°.
The pointwise definition may be expanded to a visibility function varying over time or space. For example, the phase difference varies as a function of space in a two-slit experiment . Alternately, the phase difference may be manually controlled by the operator, for example by adjusting a vernier knob in an interferometer .
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Vis(x,x' ) is a visibility function, defined to be 1 if the two points x and x' are visible from each other, and 0 if they are not. The geometrical form factor (or "projected solid angle") F ij . F ij can be obtained by projecting the element A j onto the surface of a unit hemisphere, and then projecting that in turn onto a unit circle around ...