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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.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
In three (and higher) dimensions the problem is NP-hard in the general case, [1] but there exist efficient approximation algorithms that run in polynomial time based on the idea of finding a suitable sample of points on the obstacle edges and performing a visibility graph calculation using these sample points.
In a transmissometer the extinction coefficient is determined by measuring direct light transmissivity, and the extinction coefficient is then used to calculate visibility range. [ 2 ] Atmospheric extinction is a wavelength dependent phenomenon, but the most common wavelength in use for transmissometers is 550 nm , which is in the middle of the ...
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 ...
Searching for points that are on the line and on the sphere means combining the equations and solving for , involving the dot product of vectors: Equations combined ‖ o + d u − c ‖ 2 = r 2 ⇔ ( o + d u − c ) ⋅ ( o + d u − c ) = r 2 {\displaystyle \left\Vert \mathbf {o} +d\mathbf {u} -\mathbf {c} \right\Vert ^{2}=r^{2 ...
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The international definition of fog is a visibility of less than 1 km (3,300 ft); mist is a visibility of between 1 km (0.62 mi) and 2 km (1.2 mi) and haze from 2 km (1.2 mi) to 5 km (3.1 mi). Fog and mist are generally assumed to be composed principally of water droplets, haze and smoke can be of smaller particle size.