Tissot Indicatrices

The Tissot indicatrix shows the deformation for a map projection. It takes a small circle on the earth's surface, and projects that circle on the map projection. You should look at two things:

A map cannot be both conformal and equal area.  If you have a large scale map of a small area, it may be "almost perfect" and it may not be apparent which of the two properties is correctly preserved and which is slightly distorted. This is the goal of a lot of projections, to be close enough that distances, areas, and shapes can all be measured easily.  As the area mapped gets larger, and the map scale smaller, this becomes increasingly impossible and you must make decisions and compromises.

Tissot indicatrices on conformal Mercator projection.

Three planar projections, which map half of the earth onto a circle, with the Tissot indicatrices and the values of h and k. The h and k values measure the distortion in two directions, stretching or squeezing.  Two have h' and k', indicating that there is angular distortion as well.
  • Left map is conformal, with h=k at all points, and the circles stay circular.
  • Center map is equal area; h'*k' ≈ 1.  Also note that in the lower right section of the map there is minimal distortion.
  • Right map is neither equal area nor conformal, but has other properties which are useful in some situations.

You can also look at where the values change.  For example, for the commonly used map projections:

In MICRODEM, overlay Tissot indicatrices from the Cartography menu choice of a map menu. You must have the cartography options enabled on the options form.

 

Tissot references and extensions


Last revision 1/5/2019