Polyhedral terrain

Image:Piecewise linear function2D.svg

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.{{cite journal

| first1=Richard | last1=Cole

| first2=Micha | last2=Sharir | authorlink2=Micha Sharir

| title=Visibility problems for polyhedral terrains

| journal=Journal of Symbolic Computation

| volume=7

| issue=1

| pages=11–30

| year=1989

| doi=10.1016/S0747-7171(89)80003-3 | doi-access=free}} 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.{{cite book

| title=Handbook of Computational Geometry

| editor-first1=Jörg-Rüdiger | editor-last1=Sack | editor-link1=Jörg-Rüdiger Sack

| editor-first2=Jorge | editor-last2=Urrutia

| year=2000

| doi=10.1016/B978-0-444-82537-7.X5000-1| isbn=978-0-444-82537-7 }} [https://books.google.com/books?id=uZdAqAWB3BcC&pg=PA352 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.