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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 ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a ...
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the cap is equal to the radius of the sphere, the spherical ...
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 ...
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.
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 ...
The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non ...
In baseball, to lead off, or to take a lead, refers to the position a baserunner takes just prior to a pitch, a short distance away from the base the player occupies. [2] A "lead" can also refer to that distance. [2] A typical lead is six to ten feet (two to three meters) from the base. If the lead is too large, the runner risks being picked off.