geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, visibility is a mathematical

abstraction Abstraction is a process where general rules and concepts are derived from the use and classifying of specific examples, literal (reality, real or Abstract and concrete, concrete) signifiers, first principles, or other methods. "An abstraction" ...

of the real-life notion of visibility. Given a set of obstacles in the

Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces ...

, two points in the space are said to be visible to each other, if the

line segment In geometry, a line segment is a part of a line (mathematics), straight line that is bounded by two distinct endpoints (its extreme points), and contains every Point (geometry), point on the line that is between its endpoints. It is a special c ...

that joins them does not intersect any obstacles. (In the

Earth's atmosphere The atmosphere of Earth is composed of a layer of gas mixture that surrounds the Earth's planetary surface (both lands and oceans), known collectively as air, with variable quantities of suspended aerosols and particulates (which create weathe ...

light follows a slightly curved path that is not perfectly predictable, complicating the calculation of actual visibility.) Computation of visibility is among the basic problems in computational geometry and has applications in

computer graphics Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...

motion planning Motion planning, also path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of valid configurations that moves the object from the source to destination. The term is used ...

, and other areas.

Concepts and problems

*Point visibility *Edge visibilityE. Roth, G. Panin and A. Knoll,
Sampling feature points for contour tracking with graphics hardware
, "In International Workshop on Vision, Modeling and Visualization (VMV)", Konstanz, Germany, October 2008. * Visibility polygon *Weak visibility *

Art gallery problem The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from the following real-world problem: "In an art gallery, what is the minimum number of guards who together can observe the ...

or museum problem *

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 re ...

** Visibility graph of vertical line segments * Watchman route problem *Computer graphics applications: **

Hidden surface determination In 3D computer graphics, hidden-surface determination (also known as shown-surface determination, hidden-surface removal (HSR), occlusion culling (OC) or visible-surface determination (VSD)) is the process of identifying what surfaces and parts o ...

** Hidden line removal **

z-buffering A z-buffer, also known as a depth buffer, is a type of data buffer used in computer graphics to store the depth information of fragments. The values stored represent the distance to the camera, with 0 being the closest. The encoding scheme may ...

** portal engine * Star-shaped polygon **Kernel of a polygon * Isovist * Viewshed * Zone of Visual Influence *

Painter's algorithm The painter's algorithm (also depth-sort algorithm and priority fill) is an algorithm for Hidden-surface determination#Visible surface determination, visible surface determination in 3D computer graphics that works on a polygon, polygon-by-polyg ...

References

* * * Chapter 15: "Visibility graphs"

External links

Software

VisiLibity: A free open source C++ library of floating-point visibility algorithms and supporting data types
Geometry Geometric algorithms {{geometry-stub