[Proj] OT: Geotrans's Neys Projection - Modified Lambert Conformal Conic

[proj-admin at remotesensing.org]

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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