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. 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. The polyhedral terrain is a generalization of the two-dimensional geometric object, the monotone polygonal chain.
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