Robinson Projection

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Introduction

Robinson projection is a compromise projection designed by Arthur H. Robinson in 1963 at the request of the Rand McNally Company. It was developed using graphic design rather than mathematical equations to provide a balanced visual effect for world maps. The projection is a pseudo-cylindrical projection. The meridians are regularly distributed curves that imitate elliptical arcs. They are concave to both sides with the central meridian as the center and do not intersect the parallels perpendicularly. The parallels are unequally distributed straight lines. The equator, the poles, and the central meridian are all projected as straight lines. The length of the central meridian is 0.5072 times the length of the projected equator, and the length of the polar line is 0.5322 times the length of the equator. The graticule is symmetrical along the equator and the central meridian. It is neither conformal nor equal-area, which will cause shape, area, distance, direction, and angle distortion. Area distortion increases with increasing latitude, but is not affected by changes in longitude. High latitudes will be exaggerated. Angular distortion is moderate near the center of the map and increases toward the edges. Distortion values are symmetrical along the equator and the central meridian.

Projection Composition

The pseudo-cylindrical projection method is adopted to achieve global compromise expression through graphic design. The central meridian is a straight line, the other meridians are curves that are concave toward the center, and the latitudes are unequally spaced straight lines. After projection, the graticule is symmetrical along the equator and the central meridian. The length of the central meridian is 0.5072 times that of the equator, and the length of the polar line is 0.5322 times that of the polar line. Its deformation characteristics are non-equal area and non-equal angle. The area distortion increases with increasing latitude (high latitudes are exaggerated). The angular distortion is smaller near the center and increases at the edges. The overall distortion is minimal within 45° and at the equator, achieving global visual balance.

Pros

Good visual balance: The Robinson projection achieves a relatively balanced compromise between shape, area, distance and direction through graphic design rather than mathematical equations. This design makes the world map more visually beautiful and avoids the serious distortion of other features caused by over-emphasis on a single feature (such as equal area or equal angle).
Small global deformation: In world map drawing, the overall deformation of the Robinson projection is relatively small, which can better show the global geographical distribution. Compared with some traditional projections (such as the Mercator projection), it effectively controls the exaggeration of the area in high-latitude areas while keeping the shape of low-latitude areas relatively accurate.
Suitable for general world maps: Due to its compromise characteristics, the Robinson projection is widely used in map scenes that need to take into account multiple features, such as textbooks, posters, news media, etc. It can provide readers with an intuitive and comprehensive overview of global geography without misleading cognition due to the distortion of a certain feature.
Easy to understand and accept: The visual effect of Robinson projection is consistent with people’s intuitive cognition of the earth. Its soft meridian curves and uniform latitude spacing make the map look more natural. This feature makes it highly acceptable in public education and information dissemination.

Cons

Non-equal area and non-conformal characteristics: The Robinson projection is neither equal area nor conformal, which means that in local areas or specific applications, characteristics such as area, shape, and angle may be significantly distorted. For example, in geographic analysis that requires accurate calculation of area or angle, this projection may not meet the requirements.
Inaccurate direction and distance information: Due to the compromise design of the projection, direction and distance information may be distorted to varying degrees in different areas. In applications such as navigation and measurement across continents or oceans, this distortion may lead to error accumulation and affect the accuracy of the results.
Deformation still exists in high-latitude areas: Although the Robinson projection has controlled the area exaggeration phenomenon in high-latitude areas, compared with polar projections (such as Lambert azimuthal projections), its shape and area performance in polar regions is still somewhat insufficient. For applications that require accurate display of polar geographical features, this projection may not be the best choice.
Lack of mathematical precision: The Robinson projection is implemented through graphic design and lacks a strict mathematical equation description. This makes it difficult to seamlessly integrate and convert with other mathematical model-based projections in certain geographic information system (GIS) applications that require precise calculations.

Application Scenario

Robinson projection is often used to draw general world maps because it compromises shape and area, making the world map more beautiful and less deformed around the world. It is suitable for displaying global maps, so it is often used for world maps in books and posters.

Example

Robinson map projection centered on Greenwich.

The Robinson projection with Tissot’s indicatrix of deformation.

Mercator Projection

Wagner Projection

Lambert Conformal Conic Projection

Longitude / Latitude Projection