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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

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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This is the abbreviated version, containing approximately 71% of the total text.

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

The conversion from spherical to planar earth coordinates
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
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:

...