Chapter 1: Context and Concepts
What is it?
A fundamental problem confronting mapmakers is that the Earth is round and the paper we put our maps on is flat. When we represent the round Earth on the flat paper, some distortion (perhaps a lot, depending on how much of the spherical Earth we are trying to show) is inevitable. Map projection is so called because it assumes that we have put a light source in the middle of a transparent globe (figure 1.9). The shadows (grid) made on a nearby surface are the projection.4 Their characteristics will vary according to where the surface is placed. If the surface touches the globe, there will be no distortion at that point or along that line in the case
of a cylinder being fitted over the globe, touching along the Equator. Away from the point or line of contact, distortion increases. Among the most common
projections are the cylindrical (already described) and the conical, for which a cone is fitted over the globe, like a hat, with the top of the cone over the pole (see figure 1.9). The cylinder or the cone is cut and flattened to create the map. The cylindrical projection tends to have much more distortion at high latitudes (closer to the poles) compared with the conical.
The better known projections include the venerable Mercator5 (useful for navigation), the Albers conical equal-area6,
and the Lambert conformal conic7 (the last two are frequently used for U.S. maps). Another well-known format is
the Robinson, now the default world
map projection used by the National Geographic Society. Its advantage is that it minimizes high-latitude distortion of areas compared with most other cylindrical projections. U.S. States are typically represented by either the Lambert conformal conic or the transverse8 Mercator, depending on the size and shape of the State. For example, Dent (1990, pp. 72-73) noted that for Tennessee a conical equal-area projection would be appropriate, with its standard parallel (the line of latitude where the projection cone touches the State) running through the east-west axis of the State. Projections are a highly technical branch of cartography, and readers who want to learn more are referred to standard texts in cartography such as Campbell (1993), Dent (1990), and Robinson et al. (1984).
Why we don't need to worry
Map projections are vitally important for cartographers concerned with representing large areas of the Earth's surface owing
to the distortion problem and the myriad choices and compromises available in
various projections and their numerous specialized, modified forms. But crime analysts do not need to be overly concerned with map projections because police jurisdictions are small enough so that map projection (or Earth curvature) is not a significant issue. However, there is the possibility that analysts will deal with maps with different projections and that those maps will not fit properly when brought together. Streets and boundaries would be misaligned and structures misplaced. However, this misalignment can also occur for reasons unconnected with projection, as explained below. Although crime analysts do not need to worry about projections per se, a related issue, coordinate systems, generally needs to be given more attention because the analyst probably will encounter incompatible coordinate systems.
What are the differences between projections and coordinate systems? Projections determine how the latitude and longitude grid of the Earth is represented on flat paper. Coordinate systems provide the x-y reference system to describe locations in two-dimensional space. For example,
latitude and longitude together are a coordinate system based on angular measurements on the Earth's sphere. But there
are other ways of referring to points. For instance, all measurements could be based on distances in meters and compass directions with respect to city hall. That would also be a coordinate system. Distances in feet and directions could be based on the police chief's office as a reference point. The following discussion provides some details on commonly used coordinate