![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Courbe_niveau.svg/640px-Courbe_niveau.svg.png&w=640&q=50)
Contour line
Curve along which a 3-D surface is at equal elevation / From Wikipedia, the free encyclopedia
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A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.[1][2] It is a plane section of the three-dimensional graph of the function parallel to the
-plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value.[2]
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Courbe_niveau.svg/320px-Courbe_niveau.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Contour3D.jpg/640px-Contour3D.jpg)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Contour2D.svg/640px-Contour2D.svg.png)
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.[3] A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes.[4] The contour interval of a contour map is the difference in elevation between successive contour lines.[5]
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, straight or a mixture of both 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 the 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 the 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.[6]