Lab 5

The first picture is the conformal projection: Mercator and Stereographic map. The stereographic projection is a mapping tat projects a sphere onto a plane. It is the conformal projection because it preserves the original angles. However, it doesn't preserve distance or areas of the original figures. This projects is extremely useful in mathematics fields such as complex analysis, geology and cartography. However, the limitation of this projection is the extreme distortion as seen in the picture. The shape, equator, latitude, longitude are distorted by the projection. Therefore, this map will be hard for people to use. The second projection is Mercator. In his projection, latitude and longitude are in right angle. It preserves the angles and shapes. However, as the map goes to the poles. The scale increases and becomes infinite. This map is commonly used in navigation and is used for areas near the equator.

The second picture is equal area projection: cylindrical equal area and Behrmann equal area cylindrical projection. These two projections are similar. They both map longitudes as vertical lines and latitude as horizontal lines. They preserve the area of original figures. However, it distort the direction and distance especially near the poles. These projections is hard for use in research areas. However, they give people a clear view of world map.  The difference between the two projection is: Berhamn projection is narrower than the cylindrical equal area projection.

The third picture is equidistant projection: two point equidistant and azimuthal projection. Both projections preserve distance of the original maps. For the two point equidistant projection, distances from any point on the map to two control points scale to the geodesic distances of the same points on the sphere. This However, it distort the areas and directions. This projection is commonly used for use in measuring distance between two points accurately such as air routes. For azimuthal projection, it also preserve the distance, but not as well as the two point equidistant map. It shows distance and directions accurately from the center point, but distort shapes and size elsewhere.

In this lab, we measure the distance between Washington DC and kabul for each projection. For the conformal projection: The distance between two cities is 10164 miles for Mercator and 9960 miles for Stereographic projections. For equal area projection, the distance between two cities for the Berhamn projection is 8781 miles, which is a little less than the cylindrical projection: 10108 miles. For equidistant projection, the distance is 6648 miles for two point equidistant projection and 8341 miles for azimuthal projection. The true distance between two cities is around 6934 miles. Therefore, from the measurement above, we can see that the conformal projection and equal area projection both distort the distance between the two cities. Equidistant projections preserve the distant well: two point equidistant projection is nearly the same as the geodesic distant while azimuthal is a little bigger than 6934 miles. Therefore, form this lab, we can get the idea that each projection has their own purpose in use. If we want to measure the distant accurately, we would better choose the equidistant projections, especially the two point equidistant projection.