It is not possible to develop a map projection that does not lead to some disortion of the patterns that appear on the surface of the earth. The extent to which different projections distort the original images can be studied with Maple. The simplest way to look at map distortion is plot simple shapes in rectangular coordinates.
Some examples follow.
A better approach, developed by Tissot, is to project the image of circles drawn on the surface of a sphere. To do this we make use of some conversion procedures. We have automated the creation of distortion images in a procedure included in the Maps package. The procedure must be accessed using the readlib command. In what follows we show some representative examples.