A map projection refers to any of the numerous techniques employed in cartography to depict the three-dimensional surface of the Earth or other spherical objects on a two-dimensional plane.

While these map projection methods often involve mathematical calculations, some also rely on graphical approaches.

## Using a globe versus a map

A globe, being three-dimensional, is the only way to depict the Earth without distortions in shape, area, distance, or map scale. With their accurate metric properties, globes can effectively display spatial relationships on the Earth’s surface.

Globes present certain drawbacks, such as the challenge of creating large-scale maps, difficulties in taking measurements, the inability to view the entire world simultaneously, and the inconvenience of handling and transporting a globe as opposed to a foldable map.

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Flat maps, being two-dimensional, inherently distort one or more properties, complicating the accurate representation of spatial relationships. Despite their distortions, flat maps offer numerous advantages:

- Creating large or even medium-scale globes is impractical
- Measurements on maps are easier
- Maps are more convenient to carry
- World maps allow for viewing the entire world at once instead of having to turn the globe

Only a globe can maintain a consistent scale across its entire surface, whereas the map scale on flat maps varies from point to point and may also differ in various directions from a single point, as seen in Azimuthal maps.

## Developable surfaces

Developable surfaces in map projections refer to simple geometric shapes, such as cylinders, cones, or flat planes, onto which the Earth’s curved surface can be “unfolded” or “projected.”

These surfaces help cartographers create two-dimensional maps from the three-dimensional Earth while minimizing distortion in specific properties like area, shape, distance, or direction.

## Map projection distortions

Cartographers employ different types of map projections depending on the purpose of the map and the area being represented. These projections, while useful, inherently introduce distortions in at least one of the following properties: area, shape, direction, distance, and scale.

Map projections inherently distort one or more of the following:

- Area-preserving projection – Also known as equal area or equivalent projection
- Shape-preserving projection – Referred to as conformal or orthomorphic
- Direction-preserving projection – Includes conformal, orthomorphic, and azimuthal projections (only from the central point)
- Distance-preserving projection – Known as equidistant, which displays the accurate distance between one or two points and all other points

Creating a map projection that simultaneously preserves both area and shape is impossible.

## Map projection categories

Map projections are generally classified into several categories based on their properties and the surfaces they are projected onto.

The main categories of map projections are:

- Cylindrical Projections: These projections are created by wrapping a cylinder around the Earth and projecting its features onto the cylindrical surface. Examples include the Mercator, Transverse Mercator, and Miller Cylindrical projections.
- Conic Projections: In this category, a cone is placed over the Earth, and the features are projected onto the conical surface. Common conic projections are the Lambert Conformal Conic and Albers Equal-Area Conic projections.
- Azimuthal Projections: Also known as planar or zenithal projections, these projections use a flat plane that touches the Earth at a single point. The Earth’s features are projected onto the plane. Examples of azimuthal projections include the Azimuthal Equidistant, Stereographic, and Orthographic projections.
- Pseudocylindrical Projections: These projections resemble cylindrical projections but use curved lines instead of straight lines for meridians and parallels. Some popular pseudocylindrical projections are the Sinusoidal, Mollweide, and Goode Homolosine projections.

Map projections can also be categorized based on the properties they preserve:

- Equal-area (equivalent) projections: These projections maintain the correct proportions of areas, such as the Albers Equal-Area Conic and Mollweide projections.
- Conformal (orthomorphic) projections: These projections preserve local angles and shapes, such as the Mercator and Lambert Conformal Conic projections.
- Equidistant projections: These projections preserve true distances from one or two points to all other points, such as the Azimuthal Equidistant projection.
- Azimuthal projections: These projections preserve directions from a central point, which includes some conformal, orthomorphic, and azimuthal projections.
- Compromise projections: These projections seek to balance the various distortions inherent in map projections, such as the Robinson and Winkel Tripel projections.

It is important to note that no map projection can preserve all properties perfectly, as each type involves some degree of compromise or distortion.

## Cylindrical Projections

### List of cylindrical map projections

- Mercator
- Transverse Mercator
- Oblique Mercator
- Cylindrical Equal-Area
- Miller Cylindrical
- Equidistant Cylindrical
- Cassini

### Mercator Projection

The Mercator projection, developed by Gerardus Mercator in 1569, is a cylindrical projection that preserves angles and shapes locally, making it particularly useful for navigation.

However, this projection significantly distorts the size of landmasses near the poles, causing them to appear much larger than they are in reality.

For example, Greenland appears almost as large as the entire continent of Africa on Mercator maps. In realty, the continent of Africa is about 14 times larger than Greenland.

This effect can lead to misconceptions about the relative sizes of countries and continents.

### Transverse Mercator Projection

The Transverse Mercator projection is a variation of the Mercator projection, where the cylinder is rotated 90 degrees.

This map projection is often used for large-scale mapping of regions with a predominantly north-south extent, such as the U.S. Geological Survey’s topographic maps which use the Universal Transverse Mercator map projection.

This projection reduces distortion for regions with a small east-west extent, while distortion increases as one moves away from the central meridian.

### Miller Cylindrical Projection

The Miller Cylindrical projection is a modified version of the Mercator projection, developed by Osborn Maitland Miller in 1942. This projection attempts to minimize distortion in the high latitudes by slightly compressing the spacing of parallels.

Although it still overstates the size of areas near the poles, the distortion is less pronounced than in the standard Mercator projection.

## Conic Projections

### List of conic map projections

- Albers Equal Area Conic
- Lambert Conformal Conic
- Equidistant Conic
- Bipolar Oblique Conic Conformal
- Polyconic
- Bonne

### Lambert Conformal Conic Projection

The Lambert Conformal Conic projection is a conic map projection that maintains accurate shapes and angles over small areas.

This map projection is particularly suitable for mapping regions with a predominantly east-west extent, such as the United States. This projection is widely used for aeronautical charts because it preserves angles, making it helpful for navigation.

### Albers Equal-Area Conic Projection

The Albers Equal-Area Conic projection is another conic map projection that preserves the area at the expense of shape and angle. It is particularly useful for displaying regions with a significant east-west extent, such as the continental United States.

This projection is often employed for thematic maps that require accurate representation of areas, such as population density or land use.

## Azimuthal Projections

### List of azimuthal map projections

- Orthographic
- Stereographic
- Gnomonic
- General Perspective (vertical and tilted)
- Lambert Azimuthal Equal-Area
- Azimuthal Equidistant
- Modified-Stereographic Conformal

### Azimuthal Equidistant Projection

The Azimuthal Equidistant projection is a planar projection that maintains accurate distances from the center point to any other point on the map. This projection is frequently used for polar maps, where the center point represents the North or South Pole.

It is also commonly utilized for radio and telecommunications planning, as it accurately represents the distances between the central point and other locations.

### Stereographic Projection

The Stereographic projection is a planar projection that preserves angles and shapes locally, making it conformal. It is often used for mapping polar regions and for creating star charts in celestial cartography.

This projection is also the basis for the popular Polar Stereographic projection, which is used for representing high-latitude regions with minimal distortion.

## Orthographic Projection

The Orthographic projection is a planar projection that represents the Earth as if viewed from an infinite distance, giving the appearance of a globe on a flat surface.

This map projection is often used for artistic purposes and for visualizing the Earth from space, as it provides a unique, aesthetically pleasing perspective.

## Pseudocylindrical Projections

### List of pseudocylindrical and miscellaneous map projections

- Van der Grinten
- Sinusoidal
- Mollweide
- Eckert IV and VI

### Sinusoidal Projection

The Sinusoidal projection, also known as the Sanson-Flamsteed or Mercator Equal-Area projection, is a pseudocylindrical projection that maintains accurate area representation.

This map projection is particularly useful for representing the entire world or large regions while preserving the relative sizes of different areas. However, the Sinusoidal projection introduces distortion in shape and distance, which increases towards the edges of the map.

### Mollweide Projection

The Mollweide projection, developed by Karl Mollweide in 1805, is a pseudocylindrical equal-area projection that is well-suited for global maps.

This projection balances the preservation of area with a visually pleasing representation of the Earth, making it a popular choice for thematic maps that require accurate area representation, such as climate or vegetation maps.

### Goode Homolosine Projection

The Goode Homolosine projection, created by John Paul Goode in 1923, is a pseudocylindrical projection that combines the Sinusoidal and Mollweide projections to minimize distortion.

The projection resembles an orange peel, with the map interrupted along specific lines of longitude to reduce distortion. This projection is useful for displaying global data while minimizing distortions in both area and shape.

## Compromise Projections

### Robinson Projection

The Robinson projection, developed by Arthur H. Robinson in 1963, is a compromise projection that seeks to balance the various distortions inherent in map projections.

While it does not maintain perfect accuracy in any of the properties (area, shape, direction, distance, or scale), the Robinson map projection provides a visually appealing representation of the world that is suitable for general-purpose maps, such as wall maps and atlas maps.

### Winkel Tripel Projection

The Winkel Tripel projection, developed by Oswald Winkel in 1921, is another compromise projection that aims to minimize distortions in area, direction, and distance. It is often considered to be one of the best compromise projections for world maps, and it has been adopted as the standard projection for world maps by the National Geographic Society since 1998.

## Different map projections serve different mapping needs

Different types of projections are suited for different purposes, with some prioritizing the preservation of area, shape, direction, distance, or scale. Understanding the various types of map projections and their characteristics is crucial for cartographers, GIS professionals, and anyone working with maps to make informed decisions about the best projection to use for their specific needs.

## References

Fran Evanisko, American River College, lectures for Geography 20: “Cartographic Design for GIS”, Fall 2002

Snyder, J. P. (1982). *Map projections used by the US Geological Survey* (No. 1532). US Government Printing Office.

Snyder, J. P. (1987). *Map projections–A working manual* (Vol. 1395). US Government Printing Office.

*This article was originally written on December 27, 2002 and has since been updated.*

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