[OSRS-PROJ] Lambert Conformal Conic 1SP

[Clifford J Mugnier]

Costa Rica Zona Norte is defined as:

Latitude of Origin: 10º 28'N
Scale Factor at Origin: 0.99995696

and

Costa Rica Zona Sud is defined as:

Latitude of Origin: 9º 00
Scale Factor at Origin: 0.99995696

Both are secant Lambert Conical Orthomorphic projections.

Costa Rica is NOT tangential, it is secant as are ALL other Lambert
Conformal Conics established by Army Map Service's Inter American Geodetic
Survey in the 1950's.

If it's tangential, then Scale Factor at Origin is equal to UNITY.  Still
PERIOD.  Notice above parameters have Scale Factors at Origin less than
unity.  Still PERIOD.

Latitude at Origin has nothing to do with the False Origin where False
Northing is equal to zero.  Of course, False Northing is arbitrary in that
the design area of a zone will supposedly not have any negative Northing
values.  Of course, in North Africa, the Lambert zones DO, in fact, have
occasion to go to zero with False Northings and they have actually
implemented False Northings at False Origin.  That has nothing to do with
"Tangent" or "Secant" developed surfaces.  Incidentally, those Lamberts are
French Army Truncated Cubic math models, and the fully conformal equations
will NOT work.

With proper mathematical programming, I assert, rather than imply, that
there is only ONE set of equations necessary to implement both "Tangent"
and "Secant" developed surfaces.  John P. Snyder ignored the British
Definition because USGS had no need for it.  People with applications
outside of the US, on the other hand, DO have such a need.

Check out Thomas' SP251.  If the proper math model is programmed, then only
ONE equation is needed for either definition of secant Lamberts.  Only the
equations for the coefficients need change.  Paul D. Thomas said it all on
this topic back in 1952.  This is not "new" stuff.

Cliff Mugnier
LOUISIANA STATE UNIVERSITY



On Sun, 2003-02-09 at 16:52, Clifford J Mugnier wrote:
...
> The fully conformal Lambert has its developed surface in either a tangent
> case or a secant case.  Period.  If we consider a tangent case, then the
> scale factor at the latitude of origin is equal to unity.  If we consider
a
> secant case, then the scale factor at the latitude of origin is less than
> unity.  Period.

The inference, if not outright assertation, is that scale is not
specified for the tangential form of LLC.  That seems peculiar
as I have specs for Costa Rica Norte y Sud, Cuba Norte y Sud as
well as several other central American countries that use LLC
tangential with k_0 specified.  k_0 with tangential is merely an
alternative to secant usage and totally up to local cartographers in
selection.

Also, latitude of origin for the secant form is arbitrary and does
not necessarily have to be at the point of unity scale factor.
Unity scale factor occurs at the two standard parallels for
secant LLC.

As an aside, changing the formulas for secant to tangent only
requires the replacement of one equation.

PERIOD.

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