The area of a rhumb line polygon

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The area of a rhumb line polygon

Charles Karney
The calculation of the area of a geodesic polygon has been included in
GeographicLib since v1.4 (2010-09).

In the latest version v1.39, I've also included the equivalent
calculation when the edges of the polygon are rhumb lines.  The
formulation is given in

   http://geographiclib.sf.net/html/rhumb.html#rhumbarea

and the online planimeter

   http://geographiclib.sf.net/cgi-bin/Planimeter

implements this area calculation.  I've also worked out the area when
the edges are great ellipses.  For the formulation, see

   http://geographiclib.sf.net/html/greatellipse.html#gearea

An implementation is included in the Matlab package

   http://www.mathworks.com/matlabcentral/fileexchange/47898

Comments are welcome.

   --Charles
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Re: The area of a rhumb line polygon

Noel Zinn (cc)
Thanks for the Matlab versions, Charles.  Why R2014b?  (I'm still running
R2014a, but planning an upgrade to R2015a, which will include the new World
Magnetic Model.)
Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
[hidden email] (email)
http://www.hydrometronics.com (website)

-----Original Message-----
From: Charles Karney
Sent: Tuesday, December 16, 2014 7:14 AM
To: PROJ.4 and general Projections Discussions
Subject: [Proj] The area of a rhumb line polygon

The calculation of the area of a geodesic polygon has been included in
GeographicLib since v1.4 (2010-09).

In the latest version v1.39, I've also included the equivalent
calculation when the edges of the polygon are rhumb lines.  The
formulation is given in

   http://geographiclib.sf.net/html/rhumb.html#rhumbarea

and the online planimeter

   http://geographiclib.sf.net/cgi-bin/Planimeter

implements this area calculation.  I've also worked out the area when
the edges are great ellipses.  For the formulation, see

   http://geographiclib.sf.net/html/greatellipse.html#gearea

An implementation is included in the Matlab package

   http://www.mathworks.com/matlabcentral/fileexchange/47898

Comments are welcome.

   --Charles
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Re: The area of a rhumb line polygon

Charles Karney
Only the toolbox version requires R2014b.  The Matlab release I used was
R2013a and it works with Octave too.  Just click on "Download Zip".

GeographicLib already works with the World Magnetic Model 2015.  You can
download the model from

   https://sf.net/projects/geographiclib/files/magnetic-distrib/

and you are good to go.  Just specify "-n wmm2015" to the MagneticField
utility.  (This will be the default for GeographicLib 1.40 which I will
be releasing later this week.)

While on the subject of great ellipses, I provide a critique of some
papers which advocate great ellipses for the purposes of navigation at

   http://geographiclib.sf.net/html/greatellipse.html#gevsgeodesic

   --Charles

On 2014-12-16 09:01, Noel Zinn (cc) wrote:

> Thanks for the Matlab versions, Charles.  Why R2014b?  (I'm still running
> R2014a, but planning an upgrade to R2015a, which will include the new World
> Magnetic Model.)
> Noel
>
> Noel Zinn, Principal, Hydrometronics LLC
> +1-832-539-1472 (office), +1-281-221-0051 (cell)
> [hidden email] (email)
> http://www.hydrometronics.com (website)
>
> -----Original Message-----
> From: Charles Karney
> Sent: Tuesday, December 16, 2014 7:14 AM
> To: PROJ.4 and general Projections Discussions
> Subject: [Proj] The area of a rhumb line polygon
>
> The calculation of the area of a geodesic polygon has been included in
> GeographicLib since v1.4 (2010-09).
>
> In the latest version v1.39, I've also included the equivalent
> calculation when the edges of the polygon are rhumb lines.  The
> formulation is given in
>
>     http://geographiclib.sf.net/html/rhumb.html#rhumbarea
>
> and the online planimeter
>
>     http://geographiclib.sf.net/cgi-bin/Planimeter
>
> implements this area calculation.  I've also worked out the area when
> the edges are great ellipses.  For the formulation, see
>
>     http://geographiclib.sf.net/html/greatellipse.html#gearea
>
> An implementation is included in the Matlab package
>
>     http://www.mathworks.com/matlabcentral/fileexchange/47898
>
> Comments are welcome.
>
>     --Charles
> _______________________________________________
> Proj mailing list
> [hidden email]
> http://lists.maptools.org/mailman/listinfo/proj
>
> _______________________________________________
> Proj mailing list
> [hidden email]
> http://lists.maptools.org/mailman/listinfo/proj
>

--
Charles Karney <[hidden email]>
SRI International, Princeton, NJ 08543-5300

Tel: +1 609 734 2312
Fax: +1 609 734 2662
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Re: The area of a rhumb line polygon

J Luis
Hi,

I just want to call your attention that GMT has the CM4 magnetic model,  
which the only one that provides an estimate of the magnetic daily  
variation, making it the best (IMO) model to use.

Joaquim


> Only the toolbox version requires R2014b.  The Matlab release I used was
> R2013a and it works with Octave too.  Just click on "Download Zip".
>
> GeographicLib already works with the World Magnetic Model 2015.  You can
> download the model from
>
>    https://sf.net/projects/geographiclib/files/magnetic-distrib/
>
> and you are good to go.  Just specify "-n wmm2015" to the MagneticField
> utility.  (This will be the default for GeographicLib 1.40 which I will
> be releasing later this week.)
>
> While on the subject of great ellipses, I provide a critique of some
> papers which advocate great ellipses for the purposes of navigation at
>
>    http://geographiclib.sf.net/html/greatellipse.html#gevsgeodesic
>
>    --Charles
>
> On 2014-12-16 09:01, Noel Zinn (cc) wrote:
>> Thanks for the Matlab versions, Charles.  Why R2014b?  (I'm still  
>> running
>> R2014a, but planning an upgrade to R2015a, which will include the new  
>> World
>> Magnetic Model.)
>> Noel
>>
>> Noel Zinn, Principal, Hydrometronics LLC
>> +1-832-539-1472 (office), +1-281-221-0051 (cell)
>> [hidden email] (email)
>> http://www.hydrometronics.com (website)
>>
>> -----Original Message-----
>> From: Charles Karney
>> Sent: Tuesday, December 16, 2014 7:14 AM
>> To: PROJ.4 and general Projections Discussions
>> Subject: [Proj] The area of a rhumb line polygon
>>
>> The calculation of the area of a geodesic polygon has been included in
>> GeographicLib since v1.4 (2010-09).
>>
>> In the latest version v1.39, I've also included the equivalent
>> calculation when the edges of the polygon are rhumb lines.  The
>> formulation is given in
>>
>>     http://geographiclib.sf.net/html/rhumb.html#rhumbarea
>>
>> and the online planimeter
>>
>>     http://geographiclib.sf.net/cgi-bin/Planimeter
>>
>> implements this area calculation.  I've also worked out the area when
>> the edges are great ellipses.  For the formulation, see
>>
>>     http://geographiclib.sf.net/html/greatellipse.html#gearea
>>
>> An implementation is included in the Matlab package
>>
>>     http://www.mathworks.com/matlabcentral/fileexchange/47898
>>
>> Comments are welcome.
>>
>>     --Charles
>> _______________________________________________
>> Proj mailing list
>> [hidden email]
>> http://lists.maptools.org/mailman/listinfo/proj
>>
>> _______________________________________________
>> Proj mailing list
>> [hidden email]
>> http://lists.maptools.org/mailman/listinfo/proj
>>
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