In order to transfer the image of a three-dimensional object, it is necessary to use a special projection. In cartography, there are many types of projections for different parts of the earth's surface. One of them is the azimuthal projection.
What is projection?
Projection is a method of transferring a three-dimensional image onto a flat surface. At the same time, the transfer is carried out with strict observance of mathematical laws and rules in order to reduce the effect of distortion.
Distortions occur in any case, only their types can be different. Depending on the destination of the resulting flat image, a certain type of projection is used, which is performed according to its own rules and gives one of the types of distortion.
Projections are most widely used in the preparation of maps and plans of the earth's surface of various sizes. Cartography also has its own types of projection, each of which has a different purpose.
Use for cards
Even in ancient times, people began to create images of the Earth. The information on them was incomplete, severely distorted, and in some places evenwrong. The continents on the old maps were too large, the shapes of the coasts did not correspond to the actual ones. Since then, the process of mapping has changed a lot, improving its methods, but it is still impossible to completely get rid of distortions today.
Deprived of distortion model of the Earth is a globe. It more accurately reflects the shape and size of the globe, conveying its surface in real form. The globe, however, is a three-dimensional figure, and is not always convenient for performing special calculations and solving practical problems. In addition, it is very inconvenient for transportation. A flat map is better for the above purposes, although it provides less accurate information.
Types of projections
To date, there are three main types of projection in cartography, depending on the types of meridians and parallels. Each of them, in addition, has its own subspecies according to the location of the projecting plane and the nature of the distortion.
- Cylindrical projection. If we imagine that the globe can be surrounded by a plane that fits snugly to the equatorial line and represents the figure of a cylinder, we can give a definition of this variety. When projected, the meridians on paper will be straight lines converging at one point of the poles, and the parallels will be straight lines parallel to each other. The smallest distortion will be observed at the equator, and the largest - at the poles.
- Conic projection. It is formed when a cone-shaped plane touches the globe. ATIn this case, the parallels will be shown on the map as concentric circles, and the meridians as their radii. The smallest distortions will also be observed at the points of contact of the plane with the ball of the Earth, and the largest - at the places of their greatest removal.
- Azimuthal projection. Formed when a plane touches the earth. When projecting, the plane can not only touch, but also cross the Earth, which is also one of the types of azimuthal projection. In this case, the parallels will also be shown as concentric circles distant from each other, and the meridians as their radii. In this case, the angle between adjacent meridians will be the same value as the difference in longitudes of the specified location.
There are also conditional views, outwardly similar to one of the three groups of projections, but performed according to other mathematical laws. These include polyconical, pseudocylindrical, multiple.
Azimuthal projection
The azimuthal projection of the Earth has become widespread due to the preservation of the azimuth of the lines on the resulting picture plane without distortion. The point from which the projection is made is called the point of view. The point of contact of the globe with the plane is called the point of contact.
There are lines on the map with the same distortion values. They are called isocoles. On the image obtained in the azimuth map projection, the isocoles look likeconcentric circles. Distortions increase with distance from the point of contact between the plane and the globe. As a result, the touch point itself has the highest accuracy.
Distortion types
Azimuthal projection can be performed in various ways depending on the purpose of the resulting map. The methods differ in the type of distortion resulting from transferring the image to the plane.
- Equal area - projections on which the areas, sizes, lengths of objects are preserved, but the angles and shapes change greatly. Most often used to solve applied problems related to the calculation of dimensional values.
- Equilateral - projections that leave the corners of objects almost unchanged, but distort their sizes.
- Equidistant - projections, in which both the angles and areas of objects are distorted, but the scale along the main trajectory is preserved. They are mainly used in geoinformatics and computer systems.
- Arbitrary - projections that can distort all the given parameters to varying degrees, depending on the purpose and purpose of the map. They are used for various purposes, for example, in maritime affairs to determine routes and trajectories. On such maps, the mainland of Eurasia may have the same size as Australia.
Projection subtypes
Besides the types of distortion, there are other elements of projection performance. Depending on this, subgroups of types of azimuth projection are distinguished.
Depending on the position of the tangent or secantprojection planes are:
- Polar - the picture plane touches the globe at the point of one of the poles.
- Transverse - the picture plane touches the globe at the equator line.
- Slanting - the picture plane touches the globe in any other place (in latitude from 0 to 90 degrees).
Depending on the location of the point of view, there are:
- central - the point from which the projections are made is in the center of the globe;
- stereographic - the point of view is at a distance from the point of contact at a distance equal to the diameter of the globe;
- external - point of view removed from the globe at any possible distance;
- orthographic - there is no point of view or it is removed to an infinite distance, and the projection is performed using parallel lines.
The most common of the above are Lambert azimuth, polar and transverse projections.
Lambert projection
The Lambert equal-area azimuthal projection is performed on different parts of the Earth. It allows you to save with small distortions of the area and their relationship, but greatly changes the angles and shapes. The scale on such a map in the direction of the meridians and parallels will change in different ways. As you move away from the center, it will decrease horizontally by 0.7 times, and increase vertically by 1.4 times.
On a map made in such a projection, the equator and the middle meridian will be shown as straight lines perpendicular to each other. Other meridians and parallelsare convex lines.
Projection can be performed both to create maps of the polar regions (normal projection) and to create maps of all other regions (equatorial and oblique projection).
The projection can cover fairly large areas, so it is used to map entire continents, regions, and hemispheres. It is widely used to create maps of the western and eastern hemispheres due to the low distortion values. Also used for projection onto the plane of the African continent. The disadvantage is the large distortions that occur off the coast of Eurasia.
Maps made in the Lambert projection are commonly used in geography textbooks.
Polar projection
The polar regions of the earth cannot be done with minimal distortion in a cylindrical or conic projection. The picture plane, as a rule, almost does not touch the Arctic and Antarctica, and this area is mapped with very large errors in size and shape. However, the polar azimuth projection allows you to create an accurate image of the polar zones on a flat surface.
In this case, the point of contact coincides with the north or south pole or is in close proximity to them. Meridians on the map are depicted as straight lines emanating from the middle of the map. Parallels are concentric circles, the distance between which increases with distance from the point of contact.
Transverse projection
Transverse azimuth projectionused to create maps of the western and eastern hemispheres.
The least distortion in this case occurs at the equator and nearby areas, and the largest - at the poles. Therefore, to create pole maps, it is desirable to use a different projection in order to create more accurate information.
Applying projection
The azimuthal projection is one of the most important map projections. It is suitable both for mapping large areas of the earth's surface, and for creating maps of individual countries or continents. This is very important due to the fact that other methods of transferring an image to a plane - cylindrical and conical options - are suitable only for the hemispheres or the entire territory of the Earth.
Projection selection
The choice of projection type depends on such groups of factors as:
- Location, shape and dimensions of the mapped area.
- Purpose and purpose of creating the map.
- Type of applied tasks that will be solved using the card.
- Characteristic of the selected projection - the amount of distortion, as well as the shape of the meridians and parallels.
The significance of factors can be determined in any order, depending on the conditions and purpose of the work.
