Re: [Geographiclib-users] Find S12 using planimeter

[Charles K. <cha...@sr...>]

The errors you get will very much depend on the type of polygon.  0.1m^2
per edge is a worst case; it appears that the errors cancel to some
extent.

Version 1.37 allows you to compile GeographicLib with Boost or MPFR
allowing you to use either quad or arbitrary precision.  So perhaps you
can gauge the errors in your case yourself.  (I can possibly get you a
binary version of GeographicLib + MPFR for Windows.)  If you are on a
Linux machine you can also compile using long doubles and get an extra
11 bits of precision.

As a practical example...  I have a dataset of the boundaries of Poland
which has

     67801 edges
     mean edge 53m
     min edge 0.06m
     max edge 10km

Planimeter gives the area as 312679715911.98608 m^2.  The true area is
312679715911.9856346137 m^2.  So the error in this case is less than
0.001 m^2.

   --Charles

On 2014-09-18 15:39, Mike Toews wrote:
> Great, thanks, I think that clears up my questions with my assumptions
> on the quadrilateral for S12. And yes, the absolute error of residual
> with the technique described previously increases approaching the
> (1-f)*180 deg edges.
>
> The planimeter approach is what I'm interested in. Out of curiosity,
> are there any test datasets that can be used to check the accuracy of
> polygon area calculations? Also, how does the error of polygon area
> calculation accumulate? For instance, I see the expected error of S12
> is 0.1 m^2. Does the error relate to the number of vertices in the
> polygon in combination to the length of each edge? I just looking for
> a general idea, nothing exhaustive.
>
> Thanks in advance,
> -Mike
>

-- 
Charles Karney <cha...@sr...>
SRI International, Princeton, NJ 08543-5300

Tel: +1 609 734 2312
Fax: +1 609 734 2662