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Geodetic Area Calulation using ellipsoid

SIMONKELLY

I am searching for a method that can take any set of geographic coordinates (world-wide) that constitue a polygon (stored in a pointCollection) with a defined geographic coordinate system (datum, ellipsoid etc) and calculate the Geodetic Surface Area in square metres based on the ellipsoid.

I imagine that somewhere within ArcObjects suite this must exist, and would be very grateful to anyone who could point me in the right direction.

Thanks.

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CharlesKarney

Fridjof,

I hope this works for you. If esri hasn't yet figured out yet what to
do with ellipsoidal areas, it should consider the solution provided by
GeographicLib (it's distributed under the MIT/X11 license).

If it does use this, it would be prudent to update the Vincenty geodesic
method with the more accurate geodesic solution in GeographicLib, so
that everything is consistent. (Vincenty, of course, also has the
problem that the method stops converging for near antipodal points.
This is fixed by GeographicLib.)

--Charles

FridjofSchmidt

Hi Charles,

I had a first glance at the paper and the Javascript implementation and tested with some polygons. This seems to be exactly what I was looking for. Thanks for sharing! Now I will think of a way to integrate this in my ArcGIS environment...

Fridjof

CharlesKarney

I derived an accurate expression for the area between a geodesic and the
equator in

Charles F. F. Karney,
Geodesics on an ellipsoid of revolution,
Feb. 2011,
http://arxiv.org/abs/1102.1215
Errata: http://geographiclib.sourceforge.net/geod-errata.html

This extends work by

J. Danielsen,
The Area under the Geodesic,
Survey Review 30, 61-66 (1989).

From this it is easy to compute the area of an arbitrary geodesic
polygon. GeographicLib includes a class, PolygonArea, and a command line
utility, Planimeter, that does just this. You can access Planimeter
online at

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

Only simple (non-intersecting) polygons are supported. But they can
encircle a pole. The accuracy is about 0.1 m^2 per vertex. The time is
proportional to the number of vertices of the polygon (about 3 us/vertex
on a 3GHz machine).

There's also a Javascript implementation of the same method available at

http://geographiclib.sourceforge.net/scripts/geod-calc.html

Hope this helps.

--Charles

FridjofSchmidt

Hi Fridjof,

We have been working on it but it's a little early to state which software and/release it will be in.

Melita

Hi Melita,

And can you already say something about references you evaluated for calculation methods? We might need an implementation before it is available in ArcGIS...

Fridjof

MelitaKennedy

Hi Melita,

This topic has been around for a while (see http://forums.esri.com/thread.asp?c=93&f=984&t=189688). Are there any news regarding geodetic area calculation in ArcObjects? Will the approximation methods be made available to developers?

Best regards
Fridjof

Hi Fridjof,

We have been working on it but it's a little early to state which software and/release it will be in.

Melita

FridjofSchmidt

No, that functionality doesn't existing within ArcObjects. Methods are generally approximations and we've been comparing some of them this summer.
Melita

Hi Melita,

This topic has been around for a while (see http://forums.esri.com/thread.asp?c=93&f=984&t=189688). Are there any news regarding geodetic area calculation in ArcObjects? Will the approximation methods be made available to developers?

Best regards
Fridjof

MelitaKennedy

I am searching for a method that can take any set of geographic coordinates (world-wide) that constitue a polygon (stored in a pointCollection) with a defined geographic coordinate system (datum, ellipsoid etc) and calculate the Geodetic Surface Area in square metres based on the ellipsoid.

I imagine that somewhere within ArcObjects suite this must exist, and would be very grateful to anyone who could point me in the right direction.

Thanks.

No, that functionality doesn't existing within ArcObjects. Methods are generally approximations and we've been comparing some of them this summer. You'll get reasonable answers just by projecting the polygon to an equal area projection, hopefully centered somewhere near the data. If necessarily, you may want to densify the polygon first. At 10, you can now write code to densify a polygon or polyline with points on a geodesic, loxodrome/rhumb line, great elliptic, or normal section: IPolycurve4 or IPolycurveGeodetic.

Melita

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