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SQL Server Tips by Gama and Naughter Consulting

 


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 semi-major axis of the ellipse and a so-called 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: 0-9761573-2-2
Joseph Gama, P. J. Naughter

 http://www.rampant-books.com/book_2005_2_sql_server_external_procedures.htm

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