[Proj] What is the meaning of the "Mercator 41" projection in EPSG:3752 ?

[Gerald I. Evenden]

On Tuesday 02 September 2008 4:53:58 am Mikael Rittri wrote:
> Hello,
> I am trying to understand the meaning of EPSG:3752,
> "WGS 84 / Mercator 41", used around New Zealand.
>
> I think the EPSG description of the projection is ambiguous:
>
>         Map Projection: Mercator 41
>         Projection Method: Mercator(1SP)
>
>         Parameter Name:
>         Latitude of natural origin      41° S
+lat_ts=-41  ??
>         Longitude of natural origin    100° E
+lon_0=100  ??
>         Scale factor at natural origin   1

Presuming latitude of "natural origin" is latitude of true scale then it is 
implied that k at 41S is 1.

>         False easting                    0 metres
>         False northing                   0 metres

Seems a bit odd that NZ would be using Mercator.  They used to have a unique 
TMish under +proj=nzmg and now I think I read that they went to a new 
projection.  Forgot the reference but probably TM.

> Now, this description contradicts the EPSG Guidance Note 7.2
> (http://www.epsg.org/guides/docs/G7-2.pdf), Table 3 on pages
> 14 - 15, "Summary of Coordinate Operation Parameters required
> for some Map Projections".  Because Table 3 says that
> "Latitude of natural origin" is indeed the first parameter of
> Mercator(1SP), but it should be the equator.  Well, maybe
> Table 3 was meant to say that it is _usually_ the equator,
> but that does not help me.
>
> >From the description of "Mercator 41", I think it is clear
>
> that the projected point with Easting 0 m and Northing 0 m
> represents the "natural origin" at 100° E, 41° S.
>
> But where on the map is the local scale factor equal to 1 ???
>
> Since the scale factor parameter is named "Scale factor at natural origin",
> it would seem that the local scale factor is 1 at latitude 41° S
> (also at 41° N), because that's where the natural origin is located.
>
> On the other hand, if this is the intention, I would have expected
> EPSG to say that the projection method is Mercator(2SP), since it

What, may I ask is "Mercator(2SP)"????  Anytime +lat_ts is spec'ed then there 
are two standard parallels unless it is 0.

> has two standard parallels. So, maybe "Scale factor at natural origin"
> refers to the equator, after all, despite the inconsistent terminology.

Scale factor at natural origin seems a bit whacky.

If +lat_ts is used then it defines k0=1 at that latitude internally and will 
override any +k_0 parameter.  That is, "latitude of true scale" means exactly 
what it says.

I can only imaging +k_0 being used in equitorial zones in the same manner as 
TMs relationship with the CM.

> Does anyone know the truth out there?  A test point should suffice
> to settle the matter (if distinct from 100° E, 41° S).

Amen.  I can't stress the value of reference or test points to help ensure 
that the definition of a projection is understood.

(lat,lon to 0.0001")<->(x,y to millimeters) will suffice.

May the offspring of any cartographer that fails to document their 
grid/projection system with such information suffer the infestation of the 
fleas of a thousand camels.

Something like the above should be the motto of this group.  Certainly our 
standard curse.

> Best regards,

Plain old Mercator as a projection for New Zealand seems a bit strange. I 
can't imagine a poorer projection.

> --
> Mikael Rittri
> Carmenta AB
> Box 11354
> SE-404 28 Göteborg
> Visitors: Sankt Eriksgatan 5
> SWEDEN
> Tel: +46-31-775 57 37
> Mob: +46-703-60 34 07
> mikael.rittri at carmenta.com
> www.carmenta.com
>
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