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 a projection?
Projection is a method of transferring a three-dimensional image onto a flat surface. In this case, the transfer is carried out with strict observance of mathematical laws and rules in order to reduce the effect of distortion.
Distortions arise in any case, only their types can be different. Depending on the purpose of the destination of the resulting flat image, use a certain type of projection, which is performed according to its own rules and gives one of the types of distortion.
Projections are most widely used in compiling maps and plans of the earth's surface of various sizes. For mapping, there are also different types of projection, each of which has a different purpose.
Use for cards
Even in ancient centuries, people began to create images of the Earth. The information on them was incomplete, highly distorted and sometimes even incorrect. The continents on the old maps were too large, the shape of the banks did not correspond to the real ones. Since then, the process of compiling maps has changed dramatically, improving their methods, but to date it is impossible to completely get rid of distortions.
An Earthless model of the Earth is a globe. It more accurately reflects the shape and dimensions 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 suited for the above purposes, although it does provide less accurate information.
Types of projections
To date, cartography has three main types of projection, 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 tightly adjacent to the equatorial line and representing the figure of a cylinder, we can define this variety. When projecting, 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 distortions will be observed at the equator, and the greatest - at the poles.
- Conical projection. It is formed when a plane in the shape of a cone comes in contact with the globe. In this case, the parallels will be depicted 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 greatest - at the places of their greatest removal.
- Azimuthal projection. Formed when the plane touches the globe. When projecting, a 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 depicted as concentric circles remote 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 that are outwardly similar to one of the three groups of projections, but performed according to other mathematical laws. These include polyconic, pseudocylindrical, plural.
Azimuth projection
The azimuthal projection of the Earth has become widespread due to the preservation of the azimuth of lines on the resulting picture plane without distortion. The point from which the projection is conducted 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 isocolates. In the image obtained in the azimuthal cartographic projection, the isokols have the form of concentric circles. Distortion increases as you move away from the point of contact of the plane and the globe. As a result, the touch point itself has the greatest accuracy.
Types of Distortion
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 a plane.
- Equal-sized - 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 associated with the calculation of dimensional values.
- Equiangular - projections that leave the corners of objects almost unchanged, but distort their size.
- Equidistant - projections at which angles and areas of objects are distorted, but the scale is preserved along the main path. They are mainly used in geoinformatics and computer systems.
- Arbitrary - projections that can distort all 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 continent of Eurasia may be the same size as Australia.
Projection Subtypes
In addition to the types of distortion, there are other elements of the projection. Depending on this, subgroups of azimuthal projection types are distinguished.
Depending on the position of the tangent or secant plane of the projection, there are:
- Polar - the picture plane touches the globe at one of the poles.
- Transverse - the picture plane touches the globe in place of 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, the points of view distinguish between:
- central - the point from which the projection is carried out is located in the center of the globe;
- stereographic - the point of view is located at a distance from the point of contact at a distance equal to the diameter of the globe;
- external - the point of view is removed from the globe at any possible distance;
- orthographic - there is no point of view or it is removed at an infinite distance, and projection is performed using parallel lines.
The most common of the above are the Lambert azimuthal projection, polar and transverse projections.
Lambert Projection
Lambert’s equal azimuthal projection is performed on different parts of the Earth. It allows you to save with small distortion of the area and their relationship, but greatly changes angles and shapes. The scale on such a map in the direction of meridians and parallels will vary in different ways. With distance from the center horizontally, it will decrease by 0.7 times, and vertically - increase by 1.4 times.
On a map made in such a projection, the equator and the middle meridian will be depicted as straight lines perpendicular to each other. The remaining meridians and parallels are convex lines.
The 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 quite large areas, so it is used to map entire continents, regions, as well as hemispheres. It is widely used to create maps of the western and eastern hemispheres due to small distortion values. Also used to project onto the plane of mainland Africa. The disadvantage is the large distortions that arise 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 performed with minimal distortion in a cylindrical or conical projection. The picture plane, as a rule, hardly touches the Arctic and Antarctica, and this area is mapped with very large errors in size and shape. However, the polar azimuthal 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 azimuthal projection is used to create maps of the western and eastern hemispheres.
The smallest distortions in this case arise at the equator and the surrounding areas, and the greatest at the poles. Therefore, to create pole maps, it is advisable to use a different projection in order to create more accurate information.
Projection application
Azimuthal projection is one of the most important cartographic projections. It is suitable for mapping large areas of the earth's surface, as well as for creating maps of individual countries or continents. This is very important due to the fact that other methods of transferring images to the plane - cylindrical and conical versions - are suitable only for the hemispheres or the entire Earth.
Projection Selection
The choice of projection type depends on such groups of factors as:
- The location, shape and size of the mapped area.
- Purpose and purpose of creating a map.
- Type of application tasks that will be solved using a map.
- The characteristic of the selected projection is the amount of distortion, as well as the shape of the meridians and parallels.
The significance of factors can be determined in an arbitrary order depending on the conditions and purpose of the work.