Week 3 - Lab 3A

The process of map projection essentially involves the conversion of an image from a three-dimensional surface unto one that is two-dimensional. Such a process inherently involves distortions along the way. Depending on which properties a cartographer wants to preserve, different methods of map projection will be used. Map projections can generally be classified by two main qualities: (1) by developable surface and (2) by preserved properties. The most common types of developable surfaces historically used by cartographers are the plane, the cone, and the sphere. With the advent of computers and geospatial technology, unorthodox planar surfaces are now used in map projections. The above three sets of maps depict three common methods of projection, as characterized by preserved properties - Conformal, Equal Area, and Equidistant, respectively.

The Conformal projection preserves angles locally. Its visually highlighting characteristic is the intersection of parallels and meridians at right angles. The benefit to such a projection is that local shapes are correctly preserved without much distortion. Looking at the Mercator projection, the latitudinal and longitudinal demarcations intersect uniformly in 90 degree angles. But as portions of the map move away from the equator, the images are increasingly distorted. Antarctica looks as though it covers nearly a third of Earth's surface. The distortions are clearly seen by observing the 30x30 World Graticule, as the grids become more elongated as they approach larger latitudes. The Gall Stereographic projection was developed as a way to improve the distortions found with the Mercator projection. And it does so by using the same cylindrical projection method but has the plane intersect at 45 degrees North and South to reduce stretching. The differences in methods produce rationally different results when measuring the distance between Washington DC and Kabul. The Mercator projection indicated a distance of 10,135.44 miles, while the Gall Stereographic projection showed the distance to be 7,141.04 miles. The actual distance between the two capital cities is 6,923.39 miles. The Gall Stereographic projection does a better job at estimating the distance because it somewhat adjusts for distortion and because both DC and Kabul reside within the 45 degrees North-South region, where distortion for the Gall projection is the lowest.

Equal-Area projections attempt to maintain proportionality between areas on a map. Unlike conformal projection, the latitudinal and longitudinal angles are not always perpendicular. However, the relative sizes of countries are presented in a much more accurate manner. Equal-Area projections do not attempt to render perfect size proportionality across the entire globe, but rather focuses on specific areas. The Sinusoidal projection is centered along the Prime Meridian. Thus, all parallels that intersect this central meridian do so in perpendicular fashion. Portions of the map that extend further away from the Prime Meridian experience greater distortion. This serves as an explanation for the over-exaggerated distance (8,117.75 miles) between DC and Kabul as purported by the Sinusoidal projection. The Bonne projection is also an Equal-Area projection that centers itself along the Prime Meridian. Distortions are slightly better accounted for as one moves away from the center. Thus, the distance between DC and Kabul, according to the Bonne projection is 6,732.80 miles. Due to the method of projection and intended preservation of area, Equal-Area projections are typically more useful for mapping out smaller areas, such as continents or countries, rather than the entire globe.

Equidistant projections preserve the distance between the center of projection to any other area on the map. And therefore these projections were the closest towards asserting the distance between DC and Kabul. In the Equidistant Conic projection, all latitudes run parallel to each other at a uniform distance. As the name suggests, the projection involves mapping out the globe unto a cone. Out of the six map projections, this one was the most accurate in determining the distance between DC and Kabul. It was roughly 50 miles short, at 6,971.74 miles, in its calculation. The Equidistant cylindrical projection is similar to the Equidistant Conic projection, but uses a cylinder as its two-dimensional plane. Each grid in the 30x30 graticule is the same size. Both Equidistant projections employ standard parallels - the latitude at which the two-dimensional plane tangentionally (or secantly) intersects the three-dimensional globe. That intersection then becomes the reference point from which equal distance is given.

Projections are an essential part of mapping. The type of projection used will determine the distortion of the map as well as the preserved qualities of the map. As each map is used for different purposes, the type of projection will be decided upon that underlying basis.