Convergence

[Kees Krikke-3]

Hello,


I've made a piece of s/w that uses proj's convergence calculation to
find the true north for a given grid north.

When testing with a utm and lcc projection i found some confusing
results regarding the sign (direction) of the convergence.

To demonstrate this i modified proj.exe so it prints the convergence (in
deg) at the end of the line when using the -S flag:


C:\proj-4.6.1\src>proj -vS +proj=utm +datum=WGS84 +lon_0=3
#Universal Transverse Mercator (UTM)
#       Cyl, Sph
#       zone= south
# +proj=utm +datum=WGS84 +lon_0=3 +ellps=WGS84 +towgs84=0,0,0
2 52
431350.30       5761510.32      <0.999658 0.999658 0.999316 1.20783e-006
0.999658 0.999658 -0.788041>
4 52
568649.70       5761510.32      <0.999658 0.999658 0.999316 8.54066e-007
0.999658 0.999658 0.788041>
4 52.1
568496.62       5772632.28      <0.999658 0.999658 0.999315 0 0.999658
0.999658 0.789115>

 From the above results it seems that for utm the convergence is
negative when west and positive when east of lon_0.
If you calculate two utm positions along the same longitude east of
lon_0, you see that the easting reduces when going northwards.

 From this is seems that TrueNorth = GridNorth + convergence


I used the same points for a lcc projection:

C:\proj-4.6.1\src>proj -vS +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3
+lat_1=50 +lat_2=54
#Lambert Conformal Conic
#       Conic, Sph&Ell
#       lat_1= and lat_2= or lat_0
# +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3 +lat_1=50 +lat_2=54 +ellps=WGS84
# +towgs84=0,0,0
2 52
-68634.11       472.08  <0.999392 0.999392 0.998785 0.000355057 0.999395
0.999389 0.788173>
4 52
68634.11        472.08  <0.999392 0.999392 0.998785 0.000355708 0.999395
0.999389 -0.788173>
4 52.1
68481.15        11591.10        <0.999393 0.999393 0.998787 0.000434814
0.999397 0.99939 -0.788173>


The convergence sign west and east of the origin are opposite of the
signs found with the utm. But what confuses me is that when i calculate
two positions along a longitude east of the origin, the easting reduces
when going northwards just like with the utm projection.

 From this is seems that TrueNorth = GridNorth - convergence


I think that either the convergence for lcc or utm has the wrong sign.
But i can't tell which one because i don't know how convergence is defined.


Any thoughts about this?

Regards,

Kees Krikke

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Proj mailing list
Proj@...
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[Noel Zinn-2]

Pardon my proj4 syntax density, but are you in the south with TM and the
north with LCC?  If so, that's the reason.  -Noel

-----Original Message-----
From: proj-bounces@...
[mailto:proj-bounces@...] On Behalf Of Kees Krikke
Sent: Monday, September 15, 2008 10:28 AM
To: PROJ.4 and general Projections Discussions
Subject: [Proj] Convergence

Hello,


I've made a piece of s/w that uses proj's convergence calculation to
find the true north for a given grid north.

When testing with a utm and lcc projection i found some confusing
results regarding the sign (direction) of the convergence.

To demonstrate this i modified proj.exe so it prints the convergence (in
deg) at the end of the line when using the -S flag:


C:\proj-4.6.1\src>proj -vS +proj=utm +datum=WGS84 +lon_0=3
#Universal Transverse Mercator (UTM)
#       Cyl, Sph
#       zone= south
# +proj=utm +datum=WGS84 +lon_0=3 +ellps=WGS84 +towgs84=0,0,0
2 52
431350.30       5761510.32      <0.999658 0.999658 0.999316 1.20783e-006
0.999658 0.999658 -0.788041>
4 52
568649.70       5761510.32      <0.999658 0.999658 0.999316 8.54066e-007
0.999658 0.999658 0.788041>
4 52.1
568496.62       5772632.28      <0.999658 0.999658 0.999315 0 0.999658
0.999658 0.789115>

 From the above results it seems that for utm the convergence is
negative when west and positive when east of lon_0.
If you calculate two utm positions along the same longitude east of
lon_0, you see that the easting reduces when going northwards.

 From this is seems that TrueNorth = GridNorth + convergence


I used the same points for a lcc projection:

C:\proj-4.6.1\src>proj -vS +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3
+lat_1=50 +lat_2=54
#Lambert Conformal Conic
#       Conic, Sph&Ell
#       lat_1= and lat_2= or lat_0
# +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3 +lat_1=50 +lat_2=54 +ellps=WGS84
# +towgs84=0,0,0
2 52
-68634.11       472.08  <0.999392 0.999392 0.998785 0.000355057 0.999395
0.999389 0.788173>
4 52
68634.11        472.08  <0.999392 0.999392 0.998785 0.000355708 0.999395
0.999389 -0.788173>
4 52.1
68481.15        11591.10        <0.999393 0.999393 0.998787 0.000434814
0.999397 0.99939 -0.788173>


The convergence sign west and east of the origin are opposite of the
signs found with the utm. But what confuses me is that when i calculate
two positions along a longitude east of the origin, the easting reduces
when going northwards just like with the utm projection.

 From this is seems that TrueNorth = GridNorth - convergence


I think that either the convergence for lcc or utm has the wrong sign.
But i can't tell which one because i don't know how convergence is defined.


Any thoughts about this?

Regards,

Kees Krikke

_______________________________________________
Proj mailing list
Proj@...
http://lists.maptools.org/mailman/listinfo/proj

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[Kees Krikke-3]

Noel,

No i'm not in the south. The line with zone= and south appears because i
use the -v flag.

I always use the -v option with proj. It gives some additional
information about parameters that can be used with a projection (like
zone and south for utm) and a complete list of parameters that are
actually used. This allows you to see all the parameters including those
not set by directly by the user.


Regards,

Kees


Noel Zinn wrote:

> Pardon my proj4 syntax density, but are you in the south with TM and the
> north with LCC?  If so, that's the reason.  -Noel
>
> -----Original Message-----
> From: proj-bounces@...
> [mailto:proj-bounces@...] On Behalf Of Kees Krikke
> Sent: Monday, September 15, 2008 10:28 AM
> To: PROJ.4 and general Projections Discussions
> Subject: [Proj] Convergence
>
> Hello,
>
>
> I've made a piece of s/w that uses proj's convergence calculation to
> find the true north for a given grid north.
>
> When testing with a utm and lcc projection i found some confusing
> results regarding the sign (direction) of the convergence.
>
> To demonstrate this i modified proj.exe so it prints the convergence (in
> deg) at the end of the line when using the -S flag:
>
>
> C:\proj-4.6.1\src>proj -vS +proj=utm +datum=WGS84 +lon_0=3
> #Universal Transverse Mercator (UTM)
> #       Cyl, Sph
> #       zone= south
> # +proj=utm +datum=WGS84 +lon_0=3 +ellps=WGS84 +towgs84=0,0,0
> 2 52
> 431350.30       5761510.32      <0.999658 0.999658 0.999316 1.20783e-006
> 0.999658 0.999658 -0.788041>
> 4 52
> 568649.70       5761510.32      <0.999658 0.999658 0.999316 8.54066e-007
> 0.999658 0.999658 0.788041>
> 4 52.1
> 568496.62       5772632.28      <0.999658 0.999658 0.999315 0 0.999658
> 0.999658 0.789115>
>
>  From the above results it seems that for utm the convergence is
> negative when west and positive when east of lon_0.
> If you calculate two utm positions along the same longitude east of
> lon_0, you see that the easting reduces when going northwards.
>
>  From this is seems that TrueNorth = GridNorth + convergence
>
>
> I used the same points for a lcc projection:
>
> C:\proj-4.6.1\src>proj -vS +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3
> +lat_1=50 +lat_2=54
> #Lambert Conformal Conic
> #       Conic, Sph&Ell
> #       lat_1= and lat_2= or lat_0
> # +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3 +lat_1=50 +lat_2=54 +ellps=WGS84
> # +towgs84=0,0,0
> 2 52
> -68634.11       472.08  <0.999392 0.999392 0.998785 0.000355057 0.999395
> 0.999389 0.788173>
> 4 52
> 68634.11        472.08  <0.999392 0.999392 0.998785 0.000355708 0.999395
> 0.999389 -0.788173>
> 4 52.1
> 68481.15        11591.10        <0.999393 0.999393 0.998787 0.000434814
> 0.999397 0.99939 -0.788173>
>
>
> The convergence sign west and east of the origin are opposite of the
> signs found with the utm. But what confuses me is that when i calculate
> two positions along a longitude east of the origin, the easting reduces
> when going northwards just like with the utm projection.
>
>  From this is seems that TrueNorth = GridNorth - convergence
>
>
> I think that either the convergence for lcc or utm has the wrong sign.
> But i can't tell which one because i don't know how convergence is defined.
>
>
> Any thoughts about this?
>
> Regards,
>
> Kees Krikke
>
> _______________________________________________
> Proj mailing list
> Proj@...
> http://lists.maptools.org/mailman/listinfo/proj
>
>

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[Mikael Rittri-2]

I think you are right that PROJ.4 is inconsistent here.

Before I read your post, I thought there was a standard sign convention
for meridian convergence, although I could never remember which way it went.  
But I have done some googling now, and the situation seems as bad as for
the rotation angles in a 7-parameter transform.  

If I use a slash and a backslash to describe how a piece of a meridian
looks in a projected grid, then:

The National Land Survey of Sweden agrees with +proj=utm, and says:
  \ has positive meridian convergence,
  / has negative.  
http://www.lantmateriet.se/templates/LMV_Meridiankonvergens.aspx?id=11496&lang=EN 

But the Ordnance Survey of Great Britain agrees with +proj=lcc, and says:
  \ has negative meridian convergence,
  / has positive.
http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidetonationalgrid/page19.html

I didn't search further.  Possibly, there might be a clear majority
viewpoint among all national mapping agencies, but I got tired.

Best regards,

--
Mikael Rittri
Carmenta AB
Box 11354
SE-404 28 Göteborg
Visitors: Sankt Eriksgatan 5
SWEDEN
Tel: [phone]
Mob: [phone]
mikael.rittri@...
www.carmenta.com

-----Original Message-----
From: proj-bounces@... [mailto:proj-bounces@...] On Behalf Of Kees Krikke
Sent: den 15 september 2008 17:28
To: PROJ.4 and general Projections Discussions
Subject: [Proj] Convergence

Hello,


I've made a piece of s/w that uses proj's convergence calculation to find the true north for a given grid north.

When testing with a utm and lcc projection i found some confusing results regarding the sign (direction) of the convergence.

To demonstrate this i modified proj.exe so it prints the convergence (in
deg) at the end of the line when using the -S flag:


C:\proj-4.6.1\src>proj -vS +proj=utm +datum=WGS84 +lon_0=3
#Universal Transverse Mercator (UTM)
#       Cyl, Sph
#       zone= south
# +proj=utm +datum=WGS84 +lon_0=3 +ellps=WGS84 +towgs84=0,0,0
2 52
431350.30       5761510.32      <0.999658 0.999658 0.999316 1.20783e-006
0.999658 0.999658 -0.788041>
4 52
568649.70       5761510.32      <0.999658 0.999658 0.999316 8.54066e-007
0.999658 0.999658 0.788041>
4 52.1
568496.62       5772632.28      <0.999658 0.999658 0.999315 0 0.999658
0.999658 0.789115>

 From the above results it seems that for utm the convergence is
negative when west and positive when east of lon_0.
If you calculate two utm positions along the same longitude east of
lon_0, you see that the easting reduces when going northwards.

 From this is seems that TrueNorth = GridNorth + convergence


I used the same points for a lcc projection:

C:\proj-4.6.1\src>proj -vS +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3
+lat_1=50 +lat_2=54
#Lambert Conformal Conic
#       Conic, Sph&Ell
#       lat_1= and lat_2= or lat_0
# +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3 +lat_1=50 +lat_2=54 +ellps=WGS84
# +towgs84=0,0,0
2 52
-68634.11       472.08  <0.999392 0.999392 0.998785 0.000355057 0.999395
0.999389 0.788173>
4 52
68634.11        472.08  <0.999392 0.999392 0.998785 0.000355708 0.999395
0.999389 -0.788173>
4 52.1
68481.15        11591.10        <0.999393 0.999393 0.998787 0.000434814
0.999397 0.99939 -0.788173>


The convergence sign west and east of the origin are opposite of the
signs found with the utm. But what confuses me is that when i calculate
two positions along a longitude east of the origin, the easting reduces
when going northwards just like with the utm projection.

 From this is seems that TrueNorth = GridNorth - convergence


I think that either the convergence for lcc or utm has the wrong sign.
But i can't tell which one because i don't know how convergence is defined.


Any thoughts about this?

Regards,

Kees Krikke

_______________________________________________
Proj mailing list
Proj@...
http://lists.maptools.org/mailman/listinfo/proj

_______________________________________________
Proj mailing list
Proj@...
http://lists.maptools.org/mailman/listinfo/proj

[Charles Karney]

I believe the convention is:

    meridian convergence = bearing of grid north (measured clockwise
          from true north)

This is the sign convention suggested by those little figures at the
bottom of large scale maps (USGS and UKOS for example) which indicate
the bearing of magnetic and grid north relative to true north.  (And the
universal convention is, I believe, that "bearings" are measured
clockwise.)

This is consistent with

http://www.lantmateriet.se/templates/LMV_Meridiankonvergens.aspx?id=11496&lang=EN

The UK OS page

http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidetonationalgrid/page19.html

seems to have it backward.  However, the previous page


http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidetonationalgrid/page18.html

says

    true bearing = grid bearing + convergence

which is consistent with the convention (assuming bearing are always
measured clockwise from the reference direction).

--
Charles Karney <ckarney@...>
Sarnoff Corporation, Princeton, NJ 08543-5300

URL: http://charles.karney.info
Tel: [phone]
Fax: [phone]

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[Kees Krikke-3]

Thanks Charles for your clarification. So i suppose that proj's
convergence calculation for lcc is not correct. I will try to submit a
bug report for this.

Regards,

Kees krikke

On 9/17/2008, "Charles Karney" <ckarney@...> wrote:

>I believe the convention is:
>
>    meridian convergence = bearing of grid north (measured clockwise
>           from true north)
>
>This is the sign convention suggested by those little figures at the
>bottom of large scale maps (USGS and UKOS for example) which indicate
>the bearing of magnetic and grid north relative to true north.  (And the
>universal convention is, I believe, that "bearings" are measured
>clockwise.)
>
>This is consistent with
>
>http://www.lantmateriet.se/templates/LMV_Meridiankonvergens.aspx?id=11496&lang=EN
>
>The UK OS page
>
>http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidetonationalgrid/page19.html
>
>seems to have it backward.  However, the previous page
>
>
>http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidetonationalgrid/page18.html
>
>says
>
>    true bearing = grid bearing + convergence
>
>which is consistent with the convention (assuming bearing are always
>measured clockwise from the reference direction).
>
>--
>Charles Karney <ckarney@...>
>Sarnoff Corporation, Princeton, NJ 08543-5300
>
>URL: http://charles.karney.info
>Tel: [phone]
>Fax: [phone]
>
>

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[Gerald I. Evenden-3]

Something does appear to be broken.  

To fix: comment out the last assignment statement in the file proj_lcc.c.

P->spc = fac;

to

/* P->spc = fac; */

This forces the software to do numerical estimation of scale, blah, blah
rather than use the analytic equations within lcc.

At the moment, I do no know whether the procedure that calls fac or fac itself
is the problem but something is broken in more ways than just the
convergence.

Recompile and link.


On Monday 22 September 2008 5:04:18 am Kees Krikke wrote:

> Thanks Charles for your clarification. So i suppose that proj's
> convergence calculation for lcc is not correct. I will try to submit a
> bug report for this.
>
> Regards,
>
> Kees krikke
>
> On 9/17/2008, "Charles Karney" <ckarney@...> wrote:
> >I believe the convention is:
> >
> >    meridian convergence = bearing of grid north (measured clockwise
> >           from true north)
> >
> >This is the sign convention suggested by those little figures at the
> >bottom of large scale maps (USGS and UKOS for example) which indicate
> >the bearing of magnetic and grid north relative to true north.  (And the
> >universal convention is, I believe, that "bearings" are measured
> >clockwise.)
> >
> >This is consistent with
> >
> >http://www.lantmateriet.se/templates/LMV_Meridiankonvergens.aspx?id=11496&
> >lang=EN
> >
> >The UK OS page
> >
> >http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystem
> >sinfo/guidetonationalgrid/page19.html
> >
> >seems to have it backward.  However, the previous page
> >
> >
> >http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystem
> >sinfo/guidetonationalgrid/page18.html
> >
> >says
> >
> >    true bearing = grid bearing + convergence
> >
> >which is consistent with the convention (assuming bearing are always
> >measured clockwise from the reference direction).
> >
> >--
> >Charles Karney <ckarney@...>
> >Sarnoff Corporation, Princeton, NJ 08543-5300
> >
> >URL: http://charles.karney.info
> >Tel: [phone]
> >Fax: [phone]
>
> _______________________________________________
> Proj mailing list
> Proj@...
> http://lists.maptools.org/mailman/listinfo/proj

--
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist
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