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 ...
, a polyhedral terrain in three-dimensional
Euclidean space is a
polyhedral surface that intersects every line parallel to some particular line in a connected set (i.e., a point or a
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 ...
) or the empty set.
, we may assume that the line in question is the ''z''-axis of the Cartesian coordinate system. Then a polyhedral terrain is the image of a
piecewise-linear function in ''x'' and ''y'' variables.
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The polyhedral terrain is a generalization of the two-dimensional geometric object, the monotone polygonal chain.
As the name may suggest, a major application area of polyhedral terrains include geographic information systems
A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a br ...
to model real-world terrains.[
]
Representation
A polyhedral model may be represented in terms of the partition of the plane into polygonal regions, each region being associated with a plane patch which is the image of points of the region under the piecewise-linear function in question.[
]
Problems
There are a number of problems in computational geometry which involve polyhedral terrains.
References
{{reflist
Computational geometry
Surfaces
Polyhedra