Contour line
Isolines ( from Ancient Greek ἴσος, equal to ' ), also known as Isarithmen, lines on which occurs at each point are the same value. The best known example are contour lines ( " contour lines " ) on maps. Going along an isoline, the value (for example, height ) is neither greater nor less, but always remains the same. Isolines are a special case of the level set.
Properties
In order to distinguish the lines, a variation of the line form is applied by normal, count and intermediate lines are inserted. At the scale on a map ( as a benchmark about 1:1 million) pushes this method to its limits. Isodistanzen ( lines that connect points of equal distance ), however, can occur at all scales. The lines are always closed in themselves or walk to the edge of the map from out with the exception of the intermediate lines that are inserted only where they are needed.
The oldest method for Isoliniengewinnung is the interpolation. Each isoline indicates a form. From the geometry of the Isolinienschar can therefore be the object shape reconstruction. For reduction of the scale of the representation in reality continuous surfaces ( continua ) in fixed steps done. For this purpose, the relief is broken down into characteristic stages, interval space - the area between two contour lines - are used.
The representation of isolines and the intervening interval surfaces by means of objectively tested color signatures. A representation by means of grids is now only seldom used, is and was, however, used in black-and- white illustrations frequently. The low values are often associated with dark, saturated colors and low gray values . The display of multiple surfaces is not difficult or impossible due to the resulting overlay.
If with the iso the change of a certain size for a parameter considered, providing the latter with the prefix Isallo. If you want to bring the constancy of an averaged value expressed as one uses the shortened prefix Is Iso instead.
Contour diagram
A contour lines or contour diagram is a two dimensional representation of a bivariate function with the variables and. The function value at the point is illustrated by a contour line or a coloration.
The drawing on the right illustrates the process in one-dimensional. Above, the function is plotted as a function of. Below the x-axis is simply drawn. The function value is given by the amount of points with figures, the points have been extended for better representation for vertical lines. In addition, the value of the gray value was coded. The steeper the function is, the closer are the contour lines.
2D examples:
Undistorted contour plot
Contour plot with color -coded to indicate the isolines
Pseudoisolinien
As Pseudoisolinien refers to the application of the isolines procedure to data that do not describe continua, but Diskreta. Diskreta are " getreppte " areas that represent a value that transitions between the values do not exist.
The Isolinienmethode is in principle reserved continua, as in the construction interpolations occur that are not actually present, although in nature, but are in the range of possible values of the spectrum, such as the 800 -meter contour line, which is not real visible, but in nature still occur.
Pseudoisolinien use this method, and apply it to statistical values ( surfaces) that do not continua but Diskreta but are (eg: population density, the value is a fixed - area relation, ie the mean applies to the entire surface ) and thus, strictly speaking, no interpolation may be subjected.
1855 was the first card with Pseudoisolinien (the term " Isopleten " was formerly used only for the population density), it has been heavily criticized and the method came after a brief period of euphoria into oblivion. With the advent of modern software packages they moved again to the fore and is now the subject of research.
Isolines in the room
If you're dealing with data in three-dimensional space, so are the isolines of iso-surfaces, ie surfaces which connect adjacent points of the same characteristics or values. In dimensions greater than three such structures are referred to as " n-dimensional isosurface ". In dimensions less than two such structures do not make sense.
Relationship between Isopotentialen and field lines
Especially in electric, magnetic and gravitational fields are considered in addition to the contour lines of the potential, the Isopotentialen, the always perpendicular thereto field lines.
Types of isolines
The following alphabetical list of isolines does not claim to be complete.