Tissot’s Indicatrix: Measuring Distortion in Map Projections

Elizabeth Borneman

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Tissot’s indicatrix is a mathematical contrivance used in cartography to characterize local distortions in map projections. A major problem in cartography has always been how to accurately depict a three-dimensional object onto a two-dimensional surface.

Maps are Always Distorted

Different map projections have different problems with their individual distortions; distances between objects and the objects themselves are often inaccurate in some way.

Who Created the Tissot’s Indicatrix to Measure Map Distortion?

Tissot’s indicatrix was created by a French mathematician named Nicolas Auguste Tissot between 1859-1871. He showed how the geometry of putting an object like a globe onto a map creates an ellipse that has axes indicating two directions along a scale of maximal and minimal points on a map.

A circular map of the world centered on the North Pole.  The oceans are blue and the land masses are greens and browns.
A world map centered on the North Pole in the Lambert Azimuthal equal area map projection. The overlaid Tissot’s indicatrix ellipses shows how distortion is greatest at the edges of the map. Map: Caitlin Dempsey.

How Distortion is Shown on a Map

The indicatrix not only shows where the map’s distortions are, but how much they are distorted using a scale of magnitude.

A Robinson world map with circles showing how the poles are more distorted than by the Equator.
A Tissox matrix overlaid onto a world map using the Robinson Projection. Distortion is more prominent towards the poles as compared to the Equator. Map: Caitlin Dempsey, Natural Earth data.

Tissot found a way to indicate how much a map’s points were distorted using his scale. Distortion varies across a map, which makes the scale important for knowing what is the most distorted and what is only slightly distorted.

The best way to visualize Tissot’s indicatrix is by overlaying circles on to a map. When Tissot’s indicatrix is applied, the circles are altered in size and/or shape based on how much distortion applies to that part of the map.

A world map using the Mercator map projection with red circles showing that the high latitudes are much more distorted than by the Equator.
Tissot’s indicatrix for the Mercator map projection. Map: Caitlin Dempsey, Natural Earth data.

Tissot’s indicatrix can be used to understand and visualize the distortions that occur in different map projections. Linear, angular, and areal distortion can be seen, as well as the magnitude of the distortion.

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About the author
Elizabeth Borneman
My name is Elizabeth Borneman and I am a freelance writer, reader, and coffee drinker. I live on a small island in Alaska, which gives me plenty of time to fish, hike, kayak, and be inspired by nature. I enjoy writing about the natural world and find lots of ways to flex my creative muscles on the beach, in the forest, or down at the local coffee shop.

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