Shape

A conformal map preserves the property of shape, so feature outlines on the map are the same as they are on a globe or on the earth.

Mathematically, shape is a matter of angles. In the graphic below, the red lines AB and CD represent the axes of a circle on the earth’s surface. They intersect at 90 degree angles. A pair of perpendicular green lines inclined at 45 degrees to the red lines also make 90 degree angles. The same goes for any pair of perpendicular lines that intersect at the center of the circle.

If all these angles stay the same when the circle is projected onto a map, then the map is conformal. A conformal map preserves angles.

 

Compare circles

 

A circle on a sphere and the same circle projected onto a conformal map. The mathematics described above actually apply to infinitely small circles, not to the very large circles shown here.

 

The fact that a map is conformal doesn't mean it has uniform scale. (No map does.)

 

Mercator projection

 

The Mercator projection is conformal. Angles are not changed by the projection process. Scale, on the other hand, is changed a lot. As you move from the equator to the poles, distance and area is increasingly distorted.

 

Look what happens to a circle when it is projected onto a non-conformal map—it becomes an ellipse.

 

Circle and ellipse

 

On the left, AB and CD make 90 degree angles. So do their projected counterparts A'B' and C'D' on the right. On the left, perpendicular lines EF and GH also make 90 degree angles. However, their projected counterparts E'F' and G'H' do not.

 

In the graphic above, the projected ellipse is stretched from side to side. (It could have been stretched from top to bottom or in an oblique direction.) In any case, there is only a single pair of intersecting lines on the ellipse whose angles are not distorted. These lines are the major and minor axes.

Back in Module 2, Flattening the Earth, you learned that conformality breaks down for large regions, like continents. A planar shape can't be faithful to a spherical shape at large sizes because their mathematical properties are different. (For example, a triangle drawn on a sphere has more than 180 degrees.) That's why conformal maps are often described as “preserving angles locally” or “maintaining local angular relationships.”