Integrating Past, Present, and Future Approaches - Spatial Mathematics: Theory and Practice through Mapping - page 219

Information Network (CIESIN)'s Gridded Population of the World (GPW)
( http://sedac.ciesin.columbia.edu/gpw/ ). Originally produced by Waldo Tobler,
Uwe Deichmann, Jan Gottsegen, and Kelley Maloy from the University of
California Santa Barbara, with partial support from CIESIN under a US
National Aeronautics and Space Administration (NASA) grant, the GPW is
a raster representation of the global population. The purpose of GPW is to
provide a spatially disaggregated population layer that is compatible with the
data sets from social, economic, and Earth science fields. One of its innova-
tions is the generation of a uniform set of population data around the world,
including vast areas not covered by any national census. It accomplished this
through algorithms that used input units at the national and administrative
unit level of varying resolutions. With the addition of a Global Rural-Urban
Mapping Project (GRUMP), the estimates incorporated the use of satellite data,
such as the NASA night-time lights data set, as well as buffered settlement
centroids, the technique of which should by now be familiar to the reader of
this topic.
The native grid cell resolution is 2.5 arc-minutes, corresponding to about 5
kilometers at the Equator, although aggregates at coarser resolutions are also
provided. Separate grids are available for population count and density per
grid cell. The GRUMP data provide resolution to 30 arc-seconds, which is
about 1 kilometer at the Equator. The GRUMP data also provide a point data
set of all urban areas with populations of greater than 1000 persons, in Excel,
Comma Separated Values (CSV), and shapefile formats. In the activity section
of this chapter, you will have the opportunity to examine these data sets for
yourself.
10.3 A non-Euclidean future?
This topic has dealt with mapping in the Euclidean world; what might happen
in a non-Euclidean view of it all is a fascinating future prospect. The mate-
rial below offers a non-Euclidean cartographic connection, enabling us to
see all perspective projections within the framework of projective geometry.
Recall that in Chapter 9 we discussed the role of Euclid's parallel postulate in
relation to the development of a class of non-Euclidean geometries. Here we
probe those connections further to display a theorem involving map projec-
tion in the non-Euclidean world.
10.3.1 Projective geometry
The overarching non-Euclidean geometry, with points at infinity treated as
ordinary points, is called “projective” geometry. The language of projective
geometry is dual: “Two points determine a line” and its dual, “two lines deter-
mine a point.” The words “line” and “point” may be interchanged in any