Tissot’s Indicatrix: Measuring Distortion in Map Projections

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

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

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.

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.

Tissot's indicatrix for the Mercator map projection. Image: Stefan Kühn CC BY 2.0
Tissot’s indicatrix for the Mercator map projection. Image: Stefan Kühn CC BY 2.0

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