A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines.
More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. The gradient of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A level set is a generalization of a contour line for functions of any number of variables.
Contour lines are curved or straight lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer relative gradient of a parameter and estimate that parameter at specific places. Contour lines may be either traced on a visible three-dimensional model of the surface, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from estimated surface elevations, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks.
Other articles related to "contour line, contour, line":
... A properly labeled contour map helps the reader to quickly interpret the shape of the terrain ... Labels should be placed along a slightly curved line "pointing" to the summit or nadir, from several directions if possible, making the visual identification ... Manual labeling of contour maps is a time-consuming process, however, there are a few software systems that can do the job automatically and in accordance with cartographic ...
... Isobath - a contour line linking regions of the same depth ... Isopleth - contour line joining points corresponding to similar values ... isotherm - contour line connecting points with the same temperature ...
Famous quotes containing the words line and/or contour:
“Writing fiction has developed in me an abiding respect for the unknown in a human lifetime and a sense of where to look for the threads, how to follow, how to connect, find in the thick of the tangle what clear line persists. The strands are all there: to the memory nothing is ever really lost.”
—Eudora Welty (b. 1909)
“The living language is like a cowpath: it is the creation of the cows themselves, who, having created it, follow it or depart from it according to their whims or their needs. From daily use, the path undergoes change. A cow is under no obligation to stay in the narrow path she helped make, following the contour of the land, but she often profits by staying with it and she would be handicapped if she didnt know where it was or where it led to.”
—E.B. (Elwyn Brooks)