Tuesday, August 19, 2008

Projections 101

A map projection takes the three-dimensional form of the Earth and represents it on a flat surface. The Earth’s surface is projected onto a developable surface such as a cylinder or cone and then “unrolled” to produce a flat plane. Depending on the shape of the developable surface, the projection can be planar/azimuthal (plane), cylindrical (cylinder) or conic (cone). No map projection can be perfect; all have distortions. However, a projection can be designed to fit specific needs, maintaining one or more these properties – true shape, true area, true distance or true direction – allowing certain distortions to be minimized.


A map that preserves shape is known as a Conformal Projection. The map scale is constant across the map and the angle between any two lines on the map is the same as the corresponding original lines on the Earth. The parallels and meridians intersect at right angles. However, the angles are only preserved at the local level and are not expected to be true beyond the intersection point.

The Mercator Projection is a cylindrical projection of the Earth, meaning that the parallels and meridians are straight and perpendicular to each other. Distances are only true along the equator and as distance away from the equator increases, the map stretches both east-west and north-south, causing the poles to be extremely distorted. According the Mercator Projection, the distance between Washington D.C. and Baghdad is approximately 8,400 miles, while the actual distance is 6,200 miles; and Antarctica appears to be larger than all other land masses combined while Greenland appears to be larger than South America. On the other hand, the east-west scale and the north-south scale remain the same relative to each other, meaning that the shapes are essentially true as well.

A typical Stereographic Projection is an azimuthal projection on a plane, where direction is true only from the center point of the projection and scale and thus distortion of areas increases away from the center point. The Gall Stereographic Projection on the other hand is a cylindrical projection that when first created, claimed to present real size proportion, having no distance, area or shape distortion. However, while area distortion is absent, in actuality, the Gall Projection contains shape and distance distortion. Antarctica and Greenland are still significantly oversized and the distance from Washington D.C. to Baghdad is approximately 5,900 miles, over 3,000 miles less than the real distance.



Equal-area Projections are projections that maintain the same proportional relationship to the corresponding areas on the Earth, although shape may not be preserved, especially at high latitudes. In the Mollweide Projection, the Earth is projected onto a 2:1 ellipse, where the equator is twice the length of the central meridian. The parallels are straight, but are compressed near the poles, while the aside from the central meridian, the meridians are projected as elliptical arcs equally spaced at the equator. This results in the elongation of shapes in the north-south direction, especially towards the poles. In addition, scale is only true along the standard parallels and according to the Mollweide Projection, the distance from Washington D.C. to Baghdad is approximately 6,600 miles.

Like the Mollweide Projection, in the Sinusoidal Projection, shapes are increasingly distorted away from the central meridian and near the poles. In the Sinusoidal Projection, the polar region is overcrowded, while the Mollweide Projection spaces the meridians, but creates more extreme angular distortion. The Sinusoidal Projection is a pseudo-cylindrical projection that preserves not only area, but distances along the horizontals. According to the projection, the distance from Washington D.C. to Baghdad is approximately 6,700 miles, which is fairly reasonable compared to the actual distance of 6,200 miles, and may have to do with the fact Washington D.C. and Baghdad are located on nearby parallels.

Equidistant Projections show distances from the center of the projection to be equidistant to any other place on the map in all directions. In the Equidistant Cylindrical Projection, all meridians are equally spaced straight vertical lines and all parallels are equally spaced straight horizontal lines. The scale is true and therefore equidistant along all the meridians, however because the poles are represented as straight lines equal in length to the equator, distortion of both shape and area increases towards the poles. According to the Equidistant Cylindrical Projection, the distance from Washington D.C. to Baghdad is approximately 4,200 miles, over 2,000 miles shorter than the actual.

In the Equidistant Conic Projection, distances are true along the meridians and one or two standard parallels, and distortion increases away from the standard parallels. In this map, areas north of the equator are well represented in direction, shape and area. According to the projection, the distance from Washington D.C. to Baghdad is approximately 6,300 miles, almost identical to the actual distance of 6,200 miles. However, the map is extremely distorted south of the equator, showing Australia as similar in size to North America.

1 comment:

Butter said...

your blog is cool. i l00ve the maps ;)