[Proj] OT: Geotrans's Neys Projection - Modified Lambert Conformal Conic
proj-admin at remotesensing.org
proj-admin at remotesensing.org
Mon Apr 19 22:10:52 EDT 2004
The more I cogitate on this description the more questions I have.
1: if one uses the basic Lambert equations for the 2 parallel case and
where neither parallel is 90d then the factor n will be less than 1.
n is used in the equation; theta=n(lon-lon_0) where theta is the
polar coordinate angle and the extent of the parallel arcs.
When (lon-lon_0)=180 and n<1 then theta will be less than 180 and
total extent of the parallels will leave a gap opposite the central
meridian. If n=1 then there will be closure and the parallels will
make a full circle.
2: If n=1 then only *one* parallel is involved in determining the
remainder
of the computations *and* the second standard parallel is at the
pole. The projection is secant.
3: It is unclear and apparently unspecified how Ney tinkered with the
LCC
to "extend to form complete concentric circles" and why [s]he did not
simply modify the basic equation to perform the single parallel
method.
Also, is this tweaking fully conformal? I would be *very* suspicious
because the seemingly obvious method was ignored.
Sorry to not include the full math but it is impossible to make a clean
description in simple ascii text.
On Apr 19, 2004, at 2:07 PM, proj-admin at remotesensing.org wrote:
> The GeoTrans documentation says:
>
> "A.1.25 NEY?S (MODIFIED LAMBERT CONFORMAL CONIC) PROJECTION
> The Ney's (Modified Lambert Conformal Conic) projection is a conformal
> projection in which the projected parallels are expanded slightly to
> form
> complete concentric circles centered at the pole. As shown in Figure
> A-27,
> the projected meridians are radii of concentric circles that meet at
> the
> pole. Ney's is a limiting form of the Lambert Conformal Conic. There
> are
> two parallels, called standard parallels, along which the point scale
> factor is one. One parallel is at either ¡Ó71 or ¡Ó74 degrees. The other
> parallel is at ¡Ó89 59 59.0 degrees, depending on which hemisphere the
> first
> parallel is in.
> Ney's (Modified Lambert Conformal Conic) is used near the poles. Scale
> distortion is small 25¢X to 30¢X from the pole. Distortion rapidly
> increases
> beyond this.
> The Easting\X and Northing\Y coordinates range from -40,000,000 to
> 40,000,000.
>
>
> "? 1st Standard Parallel ? A latitude value that specifies one of
> the
> two the parallels where the point scale factor is 1.0. The 1st
> Standard
> Parallel is either „b71 or „b74 degrees. The hemisphere of the Origin
> Latitude determines the sign.
>
> ? 2nd Standard Parallel ? A latitude value that specifies one of
> the
> two the parallels where the point scale factor is 1.0. The 2nd
> Standard
> Parallel is fixed at „b89 59 59.0 degrees. The hemisphere of the Origin
> Latitude determines the sign."
>
> Other than these specifics regarding the choice for the Standard
> Parallels,
> the Ney's Projection is a standard Lambert Conformal Conic in a secant
> (POLAR) case.
>
> Note that: "Ney?s (Modified Lambert Conformal Conic) projection
> coordinates
> consist of two fields labeled Easting/X and Northing/Y. The legal
> values
> for the Easting/X and the Northing/Y fields are optionally signed real
> values, with up to three decimal places, in meters. The coordinates
> must
> designate a point that is located within the boundaries of the
> specified
> Ney?s (Modified Lambert Conformal Conic) projection."
>
> Ney's Projection is a POLAR (aspect) Projection.
>
> GeoTrans does have its warts, but this explanation is crystal-clear to
> a
> practitioner in the field.
>
> Cliff Mugnier
> LOUISIANA STATE UNIVERSITY
>
_____________________________________
Jerry and the low riders: Daisy Mae and Joshua
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