[Proj] Grid Systems

Irwin Scollar al001 at uni-koeln.de
Mon Oct 6 14:55:42 EDT 2008

Gerald I. Evenden wrote:

>A far as the Algerian system(s) you are discussing, I finally 
>guessed that you
>are referring to the transition from one grid system to another as one treks
>southward.  So?  What is new about that?  In a little postage stamp size
>state like Massachusetts we have two grid systems: one for the mainland and
>another that covers the islands of Marthasvinyard and Nantucket.  California
>has 6 grid systems with irregular boundaries determined by county borders.
>At least the Algerians and UTM have regular grid boundaries.
>The situation in Algeria is the rule not the exception.
>Welcome to the world of grid systems.

At least the above-mentioned are documented.  In the course of 
implementing the Old Egyptian grid (1907) which has four documented 
(EPSG) areas called Belts, I calculated the grid values at for the 
lat/lons at the corners of each "Belt" to set range checks for user 
data entry and thus discovered that the main "Red Belt" which 
straddles the Nile valley has negative coordinates in the south near 
the border with Sudan, and the "Purple Belt" has one much further 
north and west.

Ragab Hafiez of DASCO in Cairo investigated this at the Egyptian 
Survey Authority at my request and discovered that the most recent 
1:50000 maps have an undocumented False Northing whereby 1,000,000 
was added to the published FN of 810,000 used north of the area in 
question. That has led me to invent my own "Red Extended Belt" south 
of 22 deg 45 min which is not documented in EPSG (but perhaps should be?).

California is in "good" (sic) company with the other side of the 
Pacific.  The Japan grid follows the boundaries of prefectures in 
places cutting across islands and has 19 zones stretching across a 
vast area, not to mention having grids with Bessel and GRS80 
ellipsoid datums as well.  Further entertainment is provided by the 
old Austrian and the old Japan Bessel grids which  have negative E-W 
coordinates as well.

Can anyone suggest a solution or reference to the apparently trivial question:

Given a lat/lon value, in which zone or area does the point fall so 
that the FN, FE and origins  can be determined automatically by 
either table lookup or a point in polygon search?  The first thing 
which comes to mind suggests using the Euler solution to the "point 
in polygon" problem, or more subtly employing data structures like 
KD, BSP or BAR trees but in most cases one doesn't have data for 
boundaries in machine readable form.

Irwin Scollar 

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