# Contour line

isothermcontourscontour mapcontourcontour linesisobarisobarsisothermsisohyetcontour plot
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, so that the curve joins points of equal value.wikipedia
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### Cross section (geometry)

cross sectioncross-sectioncross sections
It is a plane section of the three-dimensional graph of the function f(x, y) parallel to the (x, y)-plane.
The boundary of a cross section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation.

### Map

Mapspolitical mapelectronic map
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.
In addition to location information, maps may also be used to portray contour lines indicating constant values of elevation, temperature, rainfall, etc.

### Level set

level curvelevel setssublevel set
A level set is a generalization of a contour line for functions of any number of variables.
When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline.

### Weather map

weather chart850 mb pressure surfacemap
Meteorological contour maps may present collected data such as actual air pressure at a given time, or generalized data such as average pressure over a period of time, or forecast data such as predicted air pressure at some point in the future
Maps using isotherms show temperature gradients, which can help locate weather fronts.

### Freezing level

freezing
An isotherm at 0 °C is called the freezing level.
The freezing level, or 0 °C (zero-degree) isotherm, represents the altitude in which the temperature is at 0 °C (the freezing point of water) in a free atmosphere (i.e. allowing reflection of the sun by snow, etc.).

### Wind

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The distribution of isobars is closely related to the magnitude and direction of the wind field, and can be used to predict future weather patterns.
It flows parallel to isobars and approximates the flow above the atmospheric boundary layer in the midlatitudes.

### Geostrophic wind

geostrophicgeostrophic balancegeostrophic flow
Isallobaric gradients are important components of the wind as they increase or decrease the geostrophic wind.
The geostrophic wind is directed parallel to isobars (lines of constant pressure at a given height).

### Topographic map

topographical maptopographic mapsland survey
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.
In modern mapping, a topographic map is a type of map characterized by large-scale detail and quantitative representation of relief, usually using contour lines, but historically using a variety of methods.

### Choropleth map

choroplethchoropleth mappingstatistical maps
The idea of an isopleth map can be compared with that of a choropleth map.
Choropleth maps are based on statistical data aggregated over previously defined regions (e.g., counties), in contrast to area-class and isarithmic maps, in which region boundaries are defined by data patterns.

### Cartography

cartographercartographicmapping
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. "Contour line" is the most common usage in cartography, but isobath for underwater depths on bathymetric maps and isohypse for elevations are also used.
A topographic map is primarily concerned with the topographic description of a place, including (especially in the 20th and 21st centuries) the use of contour lines showing elevation.

### Elevation

hightopographic elevationelevated
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 topographical map is the main type of map used to depict elevation, often through use of contour lines.

### Isopycnal

An isopycnal is a line of constant density.
Isopycnals are often displayed graphically to help visualize "layers" of water in the ocean or gases in the atmosphere in a similar manner to how contour lines are used in topographic maps to help visualize topography.

### Bathymetry

bathymetricisobathbathymetric survey
"Contour line" is the most common usage in cartography, but isobath for underwater depths on bathymetric maps and isohypse for elevations are also used.
Bathymetric (or hydrographic) charts are typically produced to support safety of surface or sub-surface navigation, and usually show seafloor relief or terrain as contour lines (called depth contours or isobaths) and selected depths (soundings), and typically also provide surface navigational information.

### Meteorology

meteorologicalmeteorologistmeteorologists
In meteorology, the barometric pressures shown are reduced to sea level, not the surface pressures at the map locations.
Late in the 19th century, the motion of air masses along isobars was understood to be the result of the large-scale interaction of the pressure gradient force and the deflecting force.

### Sea level

mean sea levelMSLAMSL
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. In meteorology, the barometric pressures shown are reduced to sea level, not the surface pressures at the map locations.
When referring to geographic features such as mountains on a topographic map, variations in elevation are shown by contour lines.

### Magnetic declination

magnetic variationvariationdeclination
In the study of the Earth's magnetic field, the term isogon or isogonic line refers to a line of constant magnetic declination, the variation of magnetic north from geographic north.
Isogonic lines are lines on the Earth's surface along which the declination has the same constant value, and lines along which the declination is zero are called agonic lines.

### Contour plowing

Contour ploughingcontour bundingcontour farming
By contour planting and contour ploughing, the rate of water runoff and thus soil erosion can be substantially reduced; this is especially important in riparian zones.
Contour bunding or contour farming or Contour ploughing is the farming practice of plowing and/or planting across a slope following its elevation contour lines.

### Graph of a function

graphgraphsgraphing
It is a plane section of the three-dimensional graph of the function f(x, y) parallel to the (x, y)-plane.

### Isoquant

cost and production
An isoquant (in the image at right) is a curve of equal production quantity for alternative combinations of input usages, and an isocost curve (also in the image at right) shows alternative usages having equal production costs.
An isoquant (derived from quantity and the Greek word iso, meaning equal) is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs.

### Isopach map

isopachIsochore mapisopachs
Isopach maps use isopachs (lines of equal thickness) to illustrate variations in thickness of geologic units.
Isopachs are contour lines of equal thickness over an area.

### Image segmentation

segmentationSegmentation (image processing)segment
The result of image segmentation is a set of segments that collectively cover the entire image, or a set of contours extracted from the image (see edge detection).

### Magnetic dip

magnetic inclinationmagnetic equatordip angle
An isoclinic line connects points of equal magnetic dip, and an aclinic line is the isoclinic line of magnetic dip zero.
Contour lines along which the dip measured at the Earth's surface is equal are referred to as isoclinic lines.

### Thermodynamic diagrams

thermodynamic diagramgraphically plottingthermodynamic
Thermodynamic diagrams use multiple overlapping contour sets (including isobars and isotherms) to present a picture of the major thermodynamic factors in a weather system.

### Schiehallion experiment

confirming Newton's theory of gravitation
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.
As an additional benefit, the concept of contour lines, devised to simplify the process of surveying the mountain, later became a standard technique in cartography.