TransMundi (Map Projections web app)

Introduction

Earth's surface is a slightly flattened sphere (oblate ellipsoid). Map projections are representations of parts of the earth's surface or celestial sphere onto a plane surface. The transition of features from a sphere to a flat surface has imperfections resulting to a distorted view of the world. We seek to demonstrate one of the factors that leads to a skewed view of the world map from reality, visually and interactively.

Definition

A map projection is a systematic transformation of latitudes and longitudes of locations from the curved surface of sphere or an ellipse into locations on a plane.

Background

The maps functions that map points on the sphere onto a plane. A sphere cannot be mathematically represented on a plane surface without distortion (Carl Friedrich Gauss), hence all map projection representations are distorted. On the transition from a spherical globe to a plane surface the following spatial properties are often distorted from reality:

Equal-area maps preserve areas, azimuthal projections preserve direction, conformal maps preserve angles (i.e. country boundaries displayed on maps are the same as they are on earth), and equidistant maps preserve distances. Limitless map projections can be made, however each projection is specifically tailored to a specific purpose. Some examples include the following: The Mercator projection is designed for nautical purposes; Robison's is used on Goode's Atlas; Miller cylindrical is used for world maps (note it's similar to Mercator but it's not useful for navigation).

Distance

A fundamental question people ask themselves when looking at a map is "What is the shortest distance between point A and B?". This may seem trivial at first, which is drawing a straight line from point A to B, but this is not the case. An accurate approximation of a distance on Earth's surface is obtained using an assumption that the Earth is a perfect sphere. Therefore, the shortest path on a map between two points can be achieved with the application of great circle notion. A great circle is defined to be the unique intersection of a sphere's surface and a plane that passes through the centre of the sphere. The shortest distance between points are traced by geodesics Therefore, this shortest distance between two points can be found by first finding the great circle of the Earth that contains these points of interest.

Great circles are commonly used to develop routes for air and sea navigation because of their accuracy in calculating shortest path between two points on the globe. Sailors and pilots using great circles constantly change bearings over long distances, rahter than using Rhumb lines. These are lines that cross the longitudes at the same angle (constant bearing).

Interactive section

The program below focuses on the distortion of distances in different map projections. The web app uses geodesic lines to visually draw the shortest route between two points and the haversine formula to calculate the distance between the points.

Program description

This program consists of two maps. Each map projection can be changed by selecting a type listed in the corresponding drop-down menu bars.

Points of interest on the Earth's surface can be marked with red circles by clicking on the first map. The path of shortest distance between the consecutively selected points is represented by a green curve. This same path is also displayed on the map 2 allowing comparison between the two different projection types. Note that the projection map types can be changed at any time leaving the previously selected points unaffected. The shortest path distance between the two most recently selected points, and the total path distance from the first selected point to the last, are both displayed before map 1.

The program can be restarted by clicking the refresh page button.

Click on the Map.

It is important to note that the path route displayed on maps between points A and B is not always used for navigation purposes due to natural features i.e. weather and mountains etc

Acknowledgements

This project was funded by the Carnegie Trust.

For further reading

Map projections Links

Contact: Thamsanqa Moyo, tammymoyo0164 at yahoo.com