Computing polygon area with decimal degree coordinates

Dear Listers,

The function areapl() of the package splancs computes polygon areas  in 
the coordinate units. This means in square meters when using UTM or 
Lambert projections but in "square degrees" when using longlat degrees.

Does anybody knows a R function (or an algorithm) to compute the area 
directly (without projecting or projecting internally), eg in square 
meters, of a polygon whose node coordinates are given in decimal degrees?

I think it could be done internally in the sp/src/Rcentroid.c function if 
Area2() was rewritten to call sp_gcdist() on each of the four segments in:

  area = (b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1]);

but it would only be acceptable for larger areas. As it is, the area of 
SpatialPolygons objects is really only used to create the plot order (to 
plot larger polygons before smaller ones). In fact we only have the 
measurement at the Polygon object level sensibly - above that we don't 
really know whether multiple polygons in a Polygons object are holes or 
not, so summing the component Polygon object areas in a Polygons object 
may be wrong.

Roger

Thanks for any hint,

Patrick

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Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no