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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]
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. [1] The terms path integral, curve integral, and curvilinear integral are also used; contour integral is used as well, although that is typically reserved for line integrals in the complex plane.
Then, we use the so-called keyhole contour, which consists of a small circle about the origin of radius ε say, extending to a line segment parallel and close to the positive real axis but not touching it, to an almost full circle, returning to a line segment parallel, close, and below the positive real axis in the negative sense, returning to ...
Typical applications include the contour lines on topographic maps or the generation of isobars for weather maps. Marching squares takes a similar approach to the 3D marching cubes algorithm: Process each cell in the grid independently. Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners.
Then, the residue at the point c is calculated as: (,) = = = = using the results from contour integral of a monomial for counter clockwise contour integral around a point c. Hence, if a Laurent series representation of a function exists around c, then its residue around c is known by the coefficient of the ( z − c ) − 1 {\displaystyle ...
When the number of independent variables is two, a level set is called a level curve, also known as contour line or isoline; so a level curve is the set of all real-valued solutions of an equation in two variables x 1 and x 2.
The contour line of an isoquant represents every combination of two inputs which fully maximise a firm's use of resources (such as budget, or time). Full maximisation of resources is usually considered 'efficient'. Efficient allocation of factors of production occur only when two isoquants are tangent to one another.
A topographic profile or topographic cut or elevation profile is a representation of the relief of the terrain that is obtained by cutting transversely the lines of a topographic map. Each contour line can be defined as a closed line joining relief points at equal height above sea level. [1]