[Proj] FW: Bad Mercator Projection string?

[Geoff Shipton]

Mikael,

 

Many thanks - my knowledge of these things is somewhat lacking but I did get
as far as figuring out that the scaling factor was likely dependent on the
cosine of the latitude - but of course it's not quite that simple.  My
approach to Geodesy has always been  to know enough to understand when you
need help!

 

Your description will further my understanding.

 

Many thanks.

 

Geoff

 

From: Mikael Rittri [mailto:Mikael.Rittri at carmenta.com] 
Sent: Friday, July 20, 2012 2:42 AM
To: <geoff at tritonimaginginc.com>
Cc: PROJ.4 and general ProjectionsDiscussions
Subject: Re: [Proj] Bad Mercator Projection string?

 


> ... how you arrived at the scaling factor?

You know how a Mercator map enlarges stuff at high latitudes. This
enlargement is known as 

the local scale factor, k, and for Mercator, it depends only on the
latitude, phi. An "ordinary" instance

of Mercator has k = 1 on the equator by definition, and the k at latitude
phi is then 1/cos(phi) if you use

spherical formulas, or slightly different in your case since you use
ellipsoid formulas for WGS84. 

 

Anyway, to make your Mercator instance with latitude of true scale at 41.5
degrees, I computed k

at 41.5 degs for the corresponding ordinary instance, and then used k_0 =
1/k for your instance. 

 

With ellipsoid formulas for Mercator, the formula for k at latitude phi is

 

    k = sqrt(1 - e2 * sin2(phi)) / cos(phi)

 

where e2 is the ellipsoid's first eccentricity squared, defined as 1 -
(b/a)2 where a is the

equatorial radius and b is the polar radius, or as (2-f)*f where f is the
flattening. 

 

(Every 2 above - except the last - should really be a superscript.)

 

The formula for k can be found as Eq. (7-8) at page 44 of

 

John  P. Snyder.

Map Projections: A Working Manual, 1987. 

http://pubs.er.usgs.gov/pubs/pp/pp1395

 

And you can find e2 and other properties of WGS84 at

 

http://home.online.no/~sigurdhu/WGS84_Eng.html

 

Best regards,

 

Mikael Rittri

Carmenta

Sweden

http://www.carmenta.com


20 jul 2012 kl. 01:15 skrev "Geoff Shipton" <geoff at tritonimaginginc.com>:

Hello again Mikael,

 

Many thanks!

 

That seems to have fixed the problem.  As I said I am not a geodesist, can
you give me a clue as to how you arrived at the scaling factor?  I suppose
its some function of the Latitude of true scale? 

 

Geoff

 

From: Mikael Rittri [mailto:Mikael.Rittri at carmenta.com] 
Sent: Thursday, July 19, 2012 10:41 AM
To: <geoff at tritonimaginginc.com>; PROJ.4 and general ProjectionsDiscussions
Cc: proj at lists.maptools.org; Howard Unkeles
Subject: Re: [Proj] Bad Mercator Projection string?

 


I don't know what the trouble is, but maybe GeoTIFF doesn't support Mercator
with

a lat_ts parameter (latitude of true scale). If so, you can try to use a
scale factor instead. 

 

That is, replace your

 

    +lat_ts=41.5

 

by

 

    +k_0=0.750058844766239

 

This will give you an equivalent definition, and maybe it will work better. 

 

Best regards,

 

Mikael Rittri

Carmenta

Sweden

http://www.carmenta.com


18 jul 2012 kl. 19:16 skrev "Geoff Shipton" <geoff at tritonimaginginc.com>:

Hello everyone,

 

We "inherited" this Proj4 string from a previous product - it has always
seemed to work but we are having problems using it with gdalwarp, the warped
.tif image looks valid but has errors in the TIF tags.  If anybody has any
idea what's wrong I would be grateful.  Comparing it with other Mercator
Proj4 strings it looks a bit simple.

 

Here's the string:

 

+proj=merc +datum=WGS84 +lon_0=0 +lat_ts=41.5 +x_0=0 +y_0=2000000

 

I am not a geodesist, be gentle.

 

Many thanks,

Geoff Shipton,
Triton Imaging Inc.
Customer Support.
Capitola CA.
geoff at tritonimaginginc.com

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