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Polyhedral terrain
In computational geometry, 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) or the empty set.〔Richard Cole, Micha Sharir, "Visibility problems for polyhedral terrains" 1989, 〕 Without loss of generality, 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.〔''Handbook in Computational Geometry'' (p. 352 )〕
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 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.〔
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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