There has been a renewed interest in Geometric Geodesy due to the advent of commercial and private applications of the U.S. military's Global Positioning System. Traditionally, the study of geometric geodesy was motivated by the political needs of mapping and surveying of the entire Earth's surface. Today, the motivation for studying geometric geodesy comes from scientific needs where precise point positioning play an important role.
Surveyors working over small regions typically assume the territory to be defined over a flat surface. For larger, national and global surveys, the curvature of the Earth must be taken into account. This curvature can be described utilizing principles of geometry and trigonometry. Geometric geodesy thus falls under the guise of applied geometry.
In a very rudimentary way, we can say that the Earth has the shape of a sphere. But due to the planet's spin, it bulges at the equator and is flattened slightly at the poles. A better term to use for the shape of the Earth is that of an ellipsoid of rotation. There has been considerable work done (mostly in the latter 19th century and early 20th century) in the area of theoretical physics on the topic of figures of equilibrium.
Additionally, considerable geodetic surveying work has been done which considers the geometric implications of the ellipsoid. Lines lying on this ellipsoid of rotation are no longer great circles, which is the case for spheres. On an ellipsoid, or any curved surface for that matter, the curve connecting two points in the shortest distnce is called the geodesic curve. The study of these kinds of curves falls into the mathematical subdiscipline of differential geometry.
Geometric Geodesy confines itself to the study of coordinate systems and angular and linear relationships of geodesic curves on ellipsoids of rotation which best approximate the shape of the whole planet or parts thereof. These mathematically defined surfaces are called datums.
Geometric Geodesy Specifically
Texts on Differential Geometry
Texts on Figures of Equilibrium
Sam Wormley's Maps and mapping (from Iowa State U.)
Mars topographic mapping based on the Mars Observer Laser Altimeter (MOLA)
Last Modified: August 21, 2007