Map projection

Various projections

The cartographic projection or geographic projection is a graphic representation system that establishes an ordered relationship between the points on the curved surface of the Earth and those on a flat surface (Map). These points are located with the help of a network of meridians and parallels, in the form of a mesh. The only way to avoid the distortions of this projection would be to use a geodetic map, although the distortion is minimized when represented on a spherical map.

In a projected coordinate system, points are identified by Cartesian coordinates (x and y) on a grid whose origin depends on the cases. This type of coordinates are obtained mathematically from the geographic coordinates (longitude and latitude), which are not projected.

The flat representations of the terrestrial sphere are called maps, and those in charge of making them or specialists in cartography are called cartographers.

Properties of map projections

Classifications are usually established based on their main property; the type of surface on which the projection is made: zenithal (a plane), cylindrical (a cylinder) or conical (a cone); as well as the relative disposition between the terrestrial surface and the projection surface (plane, cylinder or cone) and can be tangent, secant or oblique. Depending on the property that a projection possesses, a distinction can be made between:

• equidistant projections, if they retain the distances for some particular point (it is impossible to keep the distances for all points on a flat map).
• equivalent projections, if you retain the surface areas.
• according projections, if they retain the forms (or, what is the same, the angles).

It is not possible to have all the previous properties at the same time, so it is necessary to opt for compromise solutions that will depend on the utility for which the map is intended.

Types of map projections

Depending on which point is considered the center of the map, a distinction is made between polar projections, whose center is one of the poles; equatorial, whose center is the intersection between the line of Ecuador and a meridian; and oblique or inclined, whose center is any other point.

There are three types of basic projections: cylindrical, conical and azimuthal.

Cylindrical projection

Scheme of a cylindrical projection.

The Mercator projection, which revolutionized cartography, is cylindrical and conformal. In it the terrestrial globe is projected on a cylindrical surface. It is one of the most used, although generally in a modified form, due to the large distortions it offers in high latitude areas, which prevents the polar regions from being appreciated in their true proportion. It is used in the creation of some world maps. To correct deformations at high latitudes, pseudocylindrical projections are used, such as the Van der Grinten projection, which is polyconic, with circular parallels and meridians. It is essentially useful for viewing the entire Earth's surface.

• Projection of Mercator
• Peters Projection
• Robinson Projection

Conical projection

Scheme of a conical projection.

The conical projection is obtained by projecting the elements of the earth's spherical surface onto a tangent conical surface, placing the vertex on the axis that joins the two poles. Although the shapes presented are of the poles, cartographers use this type of projection to see countries and continents. There are several types of conical projections:

• Simple conical projection
• Projection according to Lambert
• Multiple conical projection

Azimuthal projection

Scheme of a gnomonic acimutal projection.

In this case, a portion of the Earth is projected on a plane tangent to the globe at a selected point, obtaining an image similar to the vision of the Earth from an interior or exterior point. If the projection is of the first type it is called a gnomonic projection; if it is from the second, spelling. These projections offer greater distortion the greater the distance to the tangential point of the sphere and the plane. This type of projection is mainly related to the poles and hemispheres. Types of projections:

• Orthographic projection
• Stereographic projection
• Gnomonic projection
• Acimutal projection of Lambert

Modified projections

Currently most maps are made based on modified projections or a combination of the above, sometimes with several focal points, in order to correct distortions in certain selected areas as much as possible, even when they occur other new ones in places to which secondary importance is given, such as the great expanses of sea. Among the most common are the Lambert polyconic projection used for educational purposes, and the world maps made according to the Winkel-Tripel (adopted by the National Geographic Society) and Mollweide projections, which have an ellipse shape and fewer distortions.

Conventional projections

Conventional projections were generally created to represent the entire world (world map) and give the idea of maintaining metric properties, seeking a balance between distortions, or simply making the world map "look good". Most of these types of projections distort shapes in the polar regions more than at the equator:

• Aitoff projection
• Bernard J.S. Cahill Projection
• Dymaxion Projection
• Projection of Goode
• Screening of Kavrayskiy VII
• Miller Cylindrical Projection
• Robinson Projection
• Van der Grinten Projection
• Projection of Wagner VI
• Waterman Projection
• Projection of Winkel-Tripel

Robinson's projection was adopted by National Geographic magazine in 1988 but abandoned around 1997 in exchange for the projection of Winkel-Tripel.