# Map Projections

A map projection is a way to view the earth on a 2-dimensional surface. Because the earth is roughly spherical, it is difficult to represent on the flat surface of a map. This creates a need for a map projection, which is created from a mathematical model of the earth. Many different map projections exist. This is because of the distortion caused by projecting a three-dimensional surface onto a two-dimensional one. The specific distortion varies depending upon the mathematical formulas used to create the projection.

## Contents

## From Sphere to Projection

A modern map projection is made from a geographic coordinate system, which is based on a reference ellipsoid, which in turn is a simplification of a geoid.

- A geoid is a representation of the strength of the earth’s gravity and is used as a basis for determining sea level. Gravity across the earth is not constant; it pulls more strongly in some region than in others, due to the different landforms on the earth. Therefore, the geoid is undulating; it has many bumps and bulges around its surface.
^{[1]}Geoids are mathematically complex, so reference ellipsoids are used to make the computations of making a projection simpler. - An ellipsoid resembles a sphere, but the horizontal axis, sometimes referred to as the equatorial axis, is longer than the vertical axis. Because of the undulating nature of the geoids, reference ellipsoids are not perfect. A reference ellipsoid is meant to simply describe the surface of the geoid, but because of the geoid’s complexity, reference ellipsoids are usually most accurate for only a portion of a geoid’s surface. Therefore, mapmakers will a geoid and ellipsoid that best fits the region being mapped. Should the mapmaker change regions, a different ellipsoid may need to be used.
^{[2]} - Datums and Geographic Coordinate Systems are based on the reference ellipsoid. Datums use control points to connect to the surface of the earth and geographic coordinate systems, which are based on datums, are three-dimensional models of the earth with lines of latitude and longitude. From this geographic coordinate system, a projection is used to make a two-dimensional map.

## Distortion in map projections

The process of projecting a three-dimensional surface onto a two-dimensional one results in distortion in angle, area, direction, or distance in a map. Many times map projections are created to preserve one specific property.

- A map that preserves angles, also known as conformality, has the same scale from one point on that map in all directions, and shape is preserved locally around that point.
- A map that preserves area is known as an equal area map. All areas on the map are directly proportional to the area they represent on the earth’s surface.
- A map preserves direction when the angle from one point on a line to another is correctly portrayed in all directions. This is known as azimuthality.
- A map that preserves distance, known as an equidistant map, accurately portrays distances from the center of the map to all other points on the map.
^{[3]}

Due to the different properties preserved and the properties that are distorted, different map projections have different uses. A map requiring calculations of area needs an equal-area projection, while someone calculating different paths from a single point would likely use an equidistant map. It is the cartographer’s job to know which type of projection is needed for the map being made. However, some maps do not completely preserve any properties, but rather slightly distorts all of them, creating a map that is good for general reference mapping.

## Map categories

Most map projections fall into three main categories: cylindrical, conic, and azimuthal. A cylindrical projection is created by projecting the earth onto a cylinder. A basic cylindrical projection acts much like if a piece of paper was wrapped around the earth so that only the equator actually touched the page and the rest of the earth was projected onto it. A conic projection is created by projecting the spherical earth onto a cone, so that the widest part of the cone is the edges of the map. An azimuthal map projects the earth’s surface onto a plane, it is sometimes known as a planar projection ^{[4]}
<gallery>
File: USGS map Albers conic tall.gif|Conic Projection
File: Cylindrical Projection|Cylindrical Projection
</gallery

## References

- ↑ US Department of Commerce, N. O. and A. A. (n.d.). What is the geoid? Retrieved May 26, 2016, from http://oceanservice.noaa.gov/facts/geoid.html
- ↑ . Ellipsoids | The Nature of Geographic Information. (n.d.). Retrieved May 26, 2016, from https://www.e-education.psu.edu/natureofgeoinfo/c2_p15.html
- ↑ Map Projections. Dana, P.H. The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder. 1999. Retrieved May 25, 2016, from http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html
- ↑ Map Projections. Dana, P.H. The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder. 1999. Retrieved May 25, 2016, from http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

## Extermal links

- Map Projections – From United States Geological Survey (USGS)
- The Nature of Geospatial Information Chapter 2 – Penn State University open textbook