Map Projections: Understanding Globe-to-Map Transformations…

What Are Map Projections?

Map projections are mathematical methods used to represent the three-dimensional surface of the Earth on a two-dimensional map. Each projection has unique properties, such as preserving angles (conformal), areas (equiareal), or distances (equidistant).

The choice of projection depends on the purpose of the map and the region being mapped. For instance, navigators prefer Mercator projections because they preserve angles and shapes locally, making it easier to plot courses.

Tissot’s Indicatrix: Visualizing Distortions

To understand how map projections distort the Earth's surface, we use Tissot’s indicatrix. These are small circles drawn on a globe that transform into ellipses when projected onto a flat map. The shape and size of these ellipses reveal the nature of distortion in terms of area and angle.

For example, in an equiareal projection like the Lambert azimuthal equal-area projection, Tissot’s ellipses are circles, indicating that areas are preserved but angles may be distorted.

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Comparing Projections: Mercator vs. Equal-Area

The Mercator projection is well-known for its conformal property, which means it preserves local angles and shapes. However, this comes at the cost of distorting areas, making regions near the poles appear much larger than they are in reality.

In contrast, equal-area projections like the Lambert azimuthal equal-area projection preserve the true size of features but distort their shape. This makes them ideal for thematic maps where accurate area representation is crucial.

Measuring Distances on Maps

When measuring distances on a map, it’s important to consider the type of projection used because the scale can vary across different parts of the map. Great-circle distances are the shortest path between two points on a sphere and do not change with the projection.

For instance, if you measure the distance between two cities using a ruler on an equal-area projection, it will be more accurate than on a Mercator projection for long distances.

Frequently asked questions

Why are there so many map projections?

Different projections are needed to balance various properties like angle preservation (conformal), area accuracy (equiareal), and distance representation. Each serves a specific purpose based on the intended use of the map.

Can one projection be perfect for all purposes?

No, no single projection can perfectly preserve angles, areas, and distances simultaneously. The choice depends on the specific needs of the map's users, such as navigation or thematic analysis.

How do Tissot’s ellipses help in understanding projections?

Tissot’s ellipses provide a visual representation of how shapes and areas are distorted under different projections. They help identify the nature and extent of these distortions, allowing cartographers to choose appropriate projections for specific applications.

What is the significance of great-circle distances in map projections?

Great-circle distances represent the shortest path between two points on a sphere and are not affected by the projection. They are crucial for accurate navigation and distance measurement, especially over long distances or near the poles.

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Everything above runs in your browser — open Map Projections: Tissot Circles, Area and Angle Distortion, Globe-to-Map Morph and Real Distances and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Map Projections: Tissot Circles, Area and Angle Distortion, Globe-to-Map Morph and Real Distances simulation