Visibility is a mathematical abstraction of the real-life notion of visibility

Visibility

In meteorology, visibility is a measure of the distance at which an object or light can be clearly discerned. It is reported within surface weather observations and METAR code either in meters or statute miles, depending upon the country. Visibility affects all forms of traffic: roads, sailing...

.

Given a set of obstacles in the Euclidean space

Euclidean space

In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions...

, 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.

Computation of visibility is among the basic problems in computational geometry

Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...

 and finds applications in computer graphics

Computer graphics

Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....

, motion planning

Motion planning

Motion planning is a term used in robotics for the process of detailing a task into discrete motions....

, and other areas.

Notions and problems

• Point visibility
• Edge visibility
• Visibility polygon
  Visibility polygon
  The visibility polygon or visibility region for a point p in the plane among non-transparent obstacles is the possibly unbounded polygonal region of all points of the plane visible from p....
  
  
• Weak visibility
• Art gallery problem
  Art gallery problem
  The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from a real-world problem of guarding an art gallery with the minimum number of guards which together can observe the whole gallery...
  
   (The museum problem)
• Visibility graph
  Visibility graph
  In computational geometry and robot motion planning, a visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane. Each node in the graph represents a point location, and each edge represents a visible connection between them...
  
  
  • Visibility graph of vertical line segments
• Watchman route problem
  Watchman route problem
  The Watchman Problem is an optimization problem in computational geometry where the objective is to compute the shortest route a watchman should take to guard an entire area with obstacles given only a map of the area. The challenge is to make sure the watchman peeks behind every corner and to...
  
  
• Computer graphics applications:
  • Hidden surface determination
    Hidden surface determination
    In 3D computer graphics, hidden surface determination is the process used to determine which surfaces and parts of surfaces are not visible from a certain viewpoint...
    
    
  • Hidden line removal
    Hidden line removal
    Hidden line removal is an extension of wireframe model rendering where lines covered by surfaces are not drawn.This is not the same as hidden face removal since this involves depth and occlusion while the other involves normals....
    
    
  • z-buffering
    Z-buffering
    In computer graphics, z-buffering is the management of image depth coordinates in three-dimensional graphics, usually done in hardware, sometimes in software. It is one solution to the visibility problem, which is the problem of deciding which elements of a rendered scene are visible, and which...
    
    
  • portal engine
• Star-shaped polygon
  Star-shaped polygon
  A star-shaped polygon is a polygonal region in the plane which is a star domain, i.e., a polygon P is star-shaped, if there exists a point z such that for each point p of P the segment zp lies entirely within P.The set of all points z with the described property is called the kernel of...
  
  
  • Kernel of a polygon
• Isovist
  Isovist
  A single isovist is the volume of space visible from a given point in space, together with a specification of the location of that point. Isovists are naturally three-dimensional, but they may also be studied in two dimensions: either in horizontal section or in other vertical sections through...
  
  
• Viewshed
  Viewshed
  A viewshed is an area of land, water, or other environmental element that is visible to the human eye from a fixed vantage point. The term is used widely in such areas as urban planning, archaeology, and military science...
  
  
• Zone of Visual Influence
  Zone of Visual Influence
  A Zone of Visual Influence is the area from which a development is theoretically visible. It is usually represented as a map using color to indicate visibility....
  
  

Software

• VisiLibity: A free open source C++ library of floating-point visibility algorithms and supporting data types