Тең деңгей сызықтары

Curve along which a 3 D surface is at equal elevation
lines of equal value in maps and diagrams

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. 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. 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. The contour interval of a contour map is the difference in elevation between successive contour lines. 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.

The idea of lines that join points of equal value was rediscovered several times. The oldest known isobath (contour line of constant depth) is found on a map dated 1584 of the river Spaarne, near Haarlem, by Dutchman Pieter Bruinsz. In 1701, Edmond Halley used such lines (isogons) on a chart of magnetic variation. The Dutch engineer Nicholas Cruquius drew the bed of the river Merwede with lines of equal depth (isobaths) at intervals of 1 fathom in 1727, and Philippe Buache used them at 10 fathom intervals on a chart of the English Channel that was prepared in 1737 and published in 1752. Such lines were used to describe a land surface (contour lines) in a map of the Duchy of Modena and Reggio by Domenico Vandelli in 1746, and they were studied theoretically by Ducarla in 1771, and Charles Hutton used them in the Schiehallion experiment. In 1791, a map of France by J. L. Dupain Triel used contour lines at 20 metre intervals, hachures, spot heights and a vertical section. In 1801, the chief of the French Corps of Engineers, Haxo, used contour lines at the larger scale of 1:500 on a plan of his projects for Rocca d'Anfo, now in northern Italy, under Napoleon. By around 1843, when the Ordnance Survey started to regularly record contour lines in Great Britain and Ireland, they were already in general use in European countries. Isobaths were not routinely used on nautical charts until those of Russia from 1834, and those of Britain from 1838. As different uses of the technique were invented independently, cartographers began to recognize a common theme, and debated what to call these "lines of equal value" generally. The word isogram was proposed by Francis Galton in 1889 for lines indicating equality of some physical condition or quantity, though isogram can also refer to a word without a repeated letter. As late as 1944, John K. Wright still preferred isogram, but it never attained wide usage. During the early 20th century, isopleth (πλῆθος) was being used by 1911 in the United States, while isarithm (ἀριθμός) had become common in Europe. Additional alternatives, including the Greek English hybrid isoline and isometric line (μέτρον), also emerged. Despite attempts to select a single standard, all of these alternatives have survived to the present. When maps with contour lines became common, the idea spread to other applications. Perhaps the latest to develop are air quality and noise pollution contour maps, which first appeared in the United States in approximately 1970, largely as a result of national legislation requiring spatial delineation of these parameters.

Most commonly contour lines are drawn in plan view, or as an observer in space would view the Earth's surface: ordinary map form. However, some parameters can often be displayed in profile view showing a vertical profile of the parameter mapped. Some of the most common parameters mapped in profile are air pollutant concentrations and sound levels. In each of those cases it may be important to analyze (air pollutant concentrations or sound levels) at varying heights so as to determine the air quality or noise health effects on people at different elevations, for example, living on different floor levels of an urban apartment. In actuality, both plan and profile view contour maps are used in air pollution and noise pollution studies.

Labels are a critical component of elevation maps. A properly labeled contour map helps the reader to quickly interpret the shape of the terrain. If numbers are placed close to each other, it means that the terrain is steep. Labels should be placed along a slightly curved line "pointing" to the summit or nadir, from several directions if possible, making the visual identification of the summit or nadir easy. Contour labels can be oriented so a reader is facing uphill when reading the label. 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 conventions, called automatic label placement.