MI Re: polyhedric projection

[Cliff Mugnier - University of New Orleans]

Terry,

The Polyhedric is a very old projection used mainly in the 19th Century.  It is
a sheet-by-sheet sort of thing, where adjoining sheets are individual and
separate projections.  The graticule fits together more or less when you attempt
to paste two or more sheets together, but trying many sheets will result in
physical holidays.  It is similar to the screwy way the old American Polyconic
works, but it is a different projection.  It was invented for mapping by
planetable and alidade.  It was extensively used by the Austro-Hungarian Empire.

I don't think John P. Snyder did much with it because the USGS did not use it.

This is still used by the Germans for their small scale topographic maps
intended for sale to tourists for hiking.  It's still found in (formerly Dutch)
Indonesia, Tampico, and was probably used a LONG time ago in Aruba, Curacao, and
Sint Maartin.  Argentina used to use it, and Uruguay still (I think) uses it for
their 1:200,000 military topo series.

Mathematically, the closest thing current canned software packages might come is
the Local Space Rectangular (LSR) where the geocentric coordinates of an origin
point (center of the sheet) is used as a point of tangency to the ellipsoid.  A
three-dimensional orthogonal rotation matrix is computed to "pop" all geocentric
coordinates into a tangent plane (or secant plane if you want to diddle with a
scale factor).  Just constrain all of your transformed plane coordinates to
local Z=0 meters.  The inverse is just as easy since the inverse of a direction
cosine matrix (orthogonal coordinate system) is equal to its transpose.

In this implementation, the LSR is the same as a Polyhedric ("Polyeder" in
Dutch), and is an ellipsoidal gnomonic.  I have discussed this in a couple of my
past columns in "Photogrammetric Engineering and Remote Sensing."

The equations are in the third and fourth editions of the Manual of
Photogrammetry.

-- 
Clifford J. Mugnier ([EMAIL PROTECTED])
The Topographic Engineering Laboratory
Department of Civil and Environmental Engineering
UNIVERSITY OF NEW ORLEANS
New Orleans, Louisiana  70148

Voice and Facsimile: (504) 280-7095
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Terry D. Peterson wrote:
> 
> Dr. Mugnier,
> 
>   Just a quick question.  According to a client who is using our
> software old Japanese geologic maps are drawn in the polyhedric
> projection which I had never even heard of before his email.  In doing a
> search on the net, I did find some information but no equations, etc.
> Unfortunately, I am unable to locate our copy of the latest Synder
> book.  Do you happen to know anything about this projection?
> 
>   Thank you in advance for any help that you can provide.
> 
> ==========
> Terry D. PETERSON
> MicroImages Technical Sales Engineer
> MicroImages, Inc.
> 11th Floor - Sharp Tower
> 206 South 13th Street
> Lincoln, NE 68508-2010
> voice: 402.477.9554
> fax: 402.477.9559
> email: [EMAIL PROTECTED]
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