Cartographic projecting is used to represent the Earth’s surface on the plane according to strict mathematical rules, as well as the system of meridians and parallels on the Earth, or geographic grid, which, when transferred to the map plane according to a given projecting, becomes the cartographic grid. Cartographic mapping involves transferring the points of the surface of a sphere, or Earth’s ellipsoid, to the map plane using certain mathematical principles. It would be too cumbersome to transfer every point from the Earth’s surface to the plane, so to avoid this difficulty, the Earth’s surface is covered by a system of meridians and parallels that form the aforementioned geographic grid. The purpose of mapping is to represent this grid on the plane. The image of the cartographic grid depends, among other things, on the mapping surface used, and the location on the Earth’s surface of a point, or line of tangency.Some cartographic mappings involve the geometric projection of certain points
from a sphere. We then speak ofprojections. All cartographic projections distort the real image of the Earth’s surface, since a sphere (ellipsoid) is not a surface that can be developed into a plane. It cannot be laid out on a plane without gaps or overlaps and without distortion. The mapping can be done with high accuracy only if the area will be very small, so that a small part of the sphere’s surface will be almost identical to the adjacent plane. Distortions caused by the representation of a sphere, or ellipsoid, on a plane can include;
- The change in length of the same segment on a sphere when mapped to a plane
- Resulting from a change in length a change in the area of any figure that can map onto a figure with a different j area
- The change in angle in the image compared to the original sphere or ellipsoid.
Thus, the basic distortions on maps that result from the inability to represent the surface of a sphere on a plane t distortions of length, area, or angles. Every map is burdened with at least two of these distortions. In every mapping, there are points on the map where there are equal distortions of line, area, or angle.
Connecting these points with each other yields lines of equal distortion, otherwise known as isocols. In some mappings, these lines run along parallels, or, for example, are represented as circles. Due to the presence of distortions, another division of mappings is distinguished:
- Fidelity- they reproduce angles without distortion (they are often used
in marine and aviation communications). - faithful-distance- lines on the map are depicted without distortion.
( They are used, for example, in radio communications) - fidelity-surface preserves the fidelity of the surface (they are most often used in atlases).
There are also a number of projections that do not meet any of the above conditions, but are characterized by small distortions. For this reason, they deform the image of the Earth’s surface very little. These are called intermediate mappings.
Cartographic mappings are divided into four groups depending on the mapping surface:
- Plane projections, also called azimuthal mappings. ( These are, for example, orthographic grid, orthodromic grid, stereographic grid, Lambert grid, Postel grid).
- cylindrical projections(e.g., Merkator grid, Gall grid, square grid)
- conic projections (e.g., Ptolemy grid, Lambert conic grid, Albers grid).
- conventional projections (pseudo-azimuthal, pseudo-oval, pseudo-cone, circular grids)
In addition, plane, cone, cylinder, and conventional mappings can be classified according to the position of the plane, cylinder, or cone in relation to the Earth’s axis. Thus, we distinguish:
- Normal mappings, when the plane of the mapping is perpendicular to the Earth’s axis. The axes of the cone, or cylinder, are in line with the Earth’s polar axis, and the plane is tangent to the sphere at the pole
- transverse mappings when the mapping plane is parallel to the Earth’s axis, or when the axis of a cylinder or cone lies in the plane of the equator
- oblique mappings, when the point of tangency is between the equator and the pole, and the axes of the cylinder or cone are at an intermediate position between the equator and the pole.
Plane (azimuthal) projection
Plane projections are characterized by the fact that circles passing through a diameter perpendicular to the plane of the mapping, or azimuths, are depicted faithfully, without distortion at the main point of the mapping. In the normal position, the meridians form straight lines that intersect at the same angles as the meridians on the sphere. Parallels, on the other hand, are represented as circles with a common center. To determine the position of a point in an azimuthal representation, two coordinates of the point are needed, that is, the radius of the circle and the azimuth. Azimuth is the angle contained between the north direction
and the given direction counted clockwise expressed in angular measure,most often in degrees. In plane mapping, the normal (polar) position is mapped with the least distortion to the polar region, in the immediate vicinity of the point of tangency.When the point of tangency is located on the equator, a transverse plane grid is formed, while if the point of tangency is placed between the pole and the equator then we should talk
about the construction of a diagonal plane grid In plane grids, a distinction is made between central mappings, when the point of projection is at the center of the Earth, stereographic, when the point of projection occurs at the opposite pole, and orthographic, in which the focus of projection is at an infinite distance. Currently, the most widely used azimuthal grids are the Lambert equidistant grid, which preserves the fidelity of the surface. Distortions of distances, and angles in this mapping reach lower values than other azimuthal grids. The second plane cartographic grid that has found widespread use is the Postel parallel azimuthal grid. The meridians in this grid map without distance distortion, so their lengths are consistent with the lengths of the meridians on the sphere. Distortions of surfaces and angles in this grid are relatively small. This mapping is mainly used for mapping circumpolar regions. In oblique position, this grid is mostly used for communication maps.
Conical projection
Conic projections are mappings to the side of a cone tangent to a sphere or secant, which is then developed into a plane. Cone mappings can be divided into tangential, when the side of the cone meets the sphere along a certain parallel, and secant, when the side of the cone intersects the sphere at two parallels. Cone mappings are very suitable for representing areas extending along mid-latitudes parallels. When the side of the cone is developed into a plane, a grid is created in which the meridians are straight lines ext
from the apex of the cone. Parallels, on the other hand, are arcs of circles. Distortions in cone grids run along the parallels. One of the most popular and yet simplest conic mappings to construct isPtolemy’s straight conic grid. This mapping was known as early as the second century.It is the projection of a geographic grid on the surface of a cone tangent to the globe along the central parallel of the area being mapped. The main idea of this grid is to faithfully reproduce all meridians, and to faithfully reproduce the central parallel. The poles are mapped in this grid as an arc of a circle, while distortions are small. This grid is used to represent mid-latitude areas and is often found in school atlases. Another conic mapping is Lambert’s fiducial cone grid. The apex of the cone in this grid was taken at the Earth’s pole. The cone is then not tangent but secant along the central parallel, which is mapped faithfully. This mapping is easily recognizable because the spacing between the parallels increases as one approaches the pole. Another conic grid that is much more widespread than the previous one is the Albres conic fidelity grid. It was constructed in 1805.Like
in the previous case, this mapping does not preserve surface distortions. The design of this grid followstwo “secant” parallels. Between the secant parallels there is an elongation along the meridians, while a shortening is observed outside. The Albers grid is one of the best conic grids for representing mid-latitudes.
Cylindrical projection
Cylindrical projections are based on using the side of a cylinder as an expandable surface on a plane. The cylinder, as in conic mappings, can be tangent to the sphere or secant along appropriately selected two circles. Normal cylindrical mapping is used to represent equatorial areas and also to present the area of the entire globe. Transverse cylindrical mappings are used to represent areas along a given meridian, while diagonal mappings are used for areas along any great circle. A cylindrical grid, when developed on a plane, consists only of straight lines. The meridian lines are perpendicular to the parallels. The intervals between meridians are equal and their size depends on the circumference of the base of the cylinder. Distortions in cylindrical mappings are the same for all points located on the same parallel. The best-known cylindrical grid was constructed in 1565- 1568 by G. Mercator. Mercator’s goal was to draw up for nautical purposes such a map in which the different wind directions would be represented everywhere by straight lines and which would form the same angles with each other. The principle of the construction of this grid is the faithful representation of the equator. As a fidelity grid, it should show equal linear and surface distortions in the direction of the poles. As one moves away from the equator, the spacing between the parallels increases. and the linear and surface distortions increase. In the Mercator grid, the rhumb line, which is the line that intersects all meridians at a fixed angle, is mapped as a straight line. This is of great benefit to sailors guiding themselves using compasses when traveling. The Mercator mapping makes it possible to measure the course angle directly on the map. A loxodroma is not the shortest line connecting two points on the surface of a sphere. Such a line is an orthodroma. Diagonal and transverse cylindrical mappings are not suitable for representing larger areas, while they have found wide use in topographic maps.
Contractual projection
Among conventional projections, three related groups of mappings are most often distinguished: pseudo-plane, pseudo-cone and pseudo-oval. Pseudo-plane mappings are constructed on the basis of plane meshes; however, they are characterized by a different distribution of distortions.common feature of conic
and pseudo-cone mappings is the representation of parallels as arcs of circles., on the other hand, in pseudo-oval mappings are curved linesthat differ
depending on the assumption of a given mapping. In pseudovalc grids, meridians are represented as curved lines. Often the poles are also reproduced as points. These grids are often used to present the entire globe on overview maps because of the good image of the Earth, and the straightness of the parallels. An example of a pseudo-oval mapping is theMoolviene equidistant grid. This grid is constructed so that the image of the entire globe is an ellipse, with all parallels mapped as straight lines parallel to each other, and perpendicular to the zero meridian. The images of the parallels are arranged in such a way that the fields they create are mapped faithfully. The meridians are determined by dividing the parallels into the appropriate number of sections. This grid is excellent for representing the entire area of the Earth, such as climate maps, faunal maps, etc. Another pseudo-oval grid is the Sanson sine grid. This representation is obtained by taking the central meridian, equator, and parallels as straight lines. The images of the meridians will be curved lines that map to sinusoids. The intervals between the meridians on the parallels follow the intervals on the sphere. The poles are mapped here as points. This is a fiducial grid. Conventional mappings are also widely used in the construction of large-scale maps.
Geographical components
Geographical components are information in the field of physical geography, and economic geography, which are represented by conventional signs rendered by a variety of ways and graphical methods described in detail in a separate chapter
Off-frame description
The off-frame description consists of the information contained in the map legend, i.e. map title and author’s name, publishing institution, map scale, scale, year of publication or map making, explanation of characters and abbreviations along with color scale. Often the type of mapping on the basis of which the map was made is also given. Some maps or city plans are often accompanied by a list of geographical names usually attached to the back of the map, or as a separate booklet. Sheet maps are sometimes accompanied by a corridor containing the emblem and numbering of the surrounding sheets, and thus allowing one to get an idea of the location of a given sheet
