Level Lines and Surfaces

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Level Lines and Surfaces

 

(also contour lines and surfaces), sets of points at which the function u(P) of point P of a plane or three-dimensional space assumes constant values. The equation u(P) = const in a two-dimensional domain defines a level line; in a three-dimensional domain it defines a level surface. Level lines and surfaces are used extensively to represent functions in meteorology, such as isotherms and isobars, and in geodesy and topography. Level lines and surfaces degenerate into points at the extrema of the function u(p). The gradient of the function u(P) is perpendicular to the level line or surface at the corresponding point.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.