The Shape of the Earth
The level of the Earth’s oceans, its plains,
mountains and valleys, of course defines the true shape of the
Earth. Because there is no simple mathematical model to represent
this, a concept called a “Geoid” is defined. This is a three
dimensional surface defined by mean sea level and its imagined
continuation under the continents at the same level of gravitational
potential. Because this surface cannot be easily represented
mathematically (short of equations with hundreds of terms), other
concepts need to be used when calculations need to be performed.
As a first approximation we can consider the shape of the earth as a
sphere with a radius of approximately 6400 kilometres (c. 4000
Miles). Because of centrifugal force due to the Earths rotation as
well as the fact that the Earth is not a completely solid object,
the Earth actually bulges at the Equator and is flattened at the
poles. To better model this shape an ellipsoid is normally used.
This is a planar ellipse which is rotated around the North / South
Polar Axis to form a three dimensional surface. An ellipse in GIS
applications is normally represented by the Equatorial Radius, which
in mathematical terms is the semimajor axis of the ellipse and a
socalled flattening factor, which represents how much the ellipse
differs from a circle. During the effort to map the Earth over the
last couple of centuries more accurate values for these terms have
been obtained as time and technology progresses. Another
complication is that different values for these parameters can yield
better fits to the Geoid when we restrict over interest to certain
regions. Different countries and regions have historically used
their own values for the basis of their maps.
The above book excerpt is from:
Super SQL
Server Systems
Turbocharge Database Performance with C++ External Procedures
ISBN:
0976157322
Joseph Gama, P. J. Naughter
http://www.rampantbooks.com/book_2005_2_sql_server_external_procedures.htm
.
