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Algorithm for Rapidly Updating the Projection Center of a Sphere On a Computer Plot

IP.com Disclosure Number: IPCOM000102430D
Original Publication Date: 1990-Nov-01
Included in the Prior Art Database: 2005-Mar-17
Document File: 3 page(s) / 64K

Publishing Venue

IBM

Related People

Fleming, RH: AUTHOR

Abstract

The conversion from spherical to planar earth coordinates has historically been a major loading problem in combat control display systems. Spherical coordinates are stored in latitude and longitude and are invariant. Planar earth coordinates are derived by projecting the spherical coordinates, and vary depending on the projection center. Since a cathode ray tube (CRT) approximates a plain, planar earth coordinates must be generated as part of the display process. This article describes an algorithm for generating planar earth coordinates.

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Algorithm for Rapidly Updating the Projection Center of a Sphere On a Computer Plot

       The conversion from spherical to planar earth coordinates
has historically been a major loading problem in combat control
display systems.  Spherical coordinates are stored in latitude and
longitude and are invariant.  Planar earth coordinates are derived by
projecting the spherical coordinates, and vary depending on the
projection center. Since a cathode ray tube (CRT) approximates a
plain, planar earth coordinates must be generated as part of the
display process.  This article describes an algorithm for generating
planar earth coordinates.

      The inventive method will now be described with reference to
the block diagram in the figure.

      Step 1 - The latitude and longitude coordinates are initially
provided and stored in a computer system.  As stated previously,
latitude and longitude coordinates are invariant (Block 10).

      Step 2 - The latitude and longitude coordinates are converted
to Euclidian space coordinates (Block 20) in accordance with the
following algorithm:
      X = Re x cos(lat) x sin(lon)
      Y = Re x sin(lat)
      Z = Re x cos(lat) x cos(lon)
where Re is radius of the earth
       lat is degrees latitude
       lon is degrees longitude

      Step 3 - A projection center is then selected in Block 30.

      Step 4 - The rotation matrix (R) is then calculated in Block 40
as follows:

       ...