# 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 $f(x,y)$ parallel to the $(x,y)$-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]}

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]}