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
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between ...
that joins them does not intersect any obstacles. (In the
Earth's atmosphere 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
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 ar ...
and has applications in
computer graphics,
motion planning, and other areas.
Concepts and problems
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Point visibility
*
Edge visibility[E. 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
In computational geometry, the visibility polygon or visibility region for a point in the plane among obstacles is the possibly unbounded polygonal region of all points of the plane visible from . The visibility polygon can also be defined for v ...
*
Weak 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 ...
*
Art gallery problem or museum problem
*
Visibility graph
**
Visibility graph of vertical line segments
The visibility is the measure of the distance at which an object or light can be clearly discerned. In meteorology it depends on the transparency of the surrounding air and as such, it is unchanging no matter the ambient light level or time o ...
*
Watchman route problem
*Computer graphics applications:
**
Hidden surface determination
**
Hidden line removal
In 3D computer graphics, solid objects are usually modeled by polyhedra. A face of a polyhedron is a planar polygon bounded by straight line segments, called edges. Curved surfaces are usually approximated by a polygon mesh. Computer programs ...
**
z-buffering
**
portal engine
In computer-generated imagery and real-time 3D computer graphics, portal rendering is an algorithm for visibility determination. For example, consider a 3D computer game environment, which may contain many polygons, only a few of which may be vi ...
*
Star-shaped polygon
**Kernel of a polygon
*
Isovist
*
Viewshed
*
Zone of Visual Influence
A viewshed is the geographical area that is visible from a location. It includes all surrounding points that are in line-of-sight with that location and excludes points that are beyond the horizon or obstructed by terrain and other features (e.g. ...
*
Painter's algorithm
References
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*
* 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
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