CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

 wrote:
> Hi!
> I would like to calculate the surface area of polygons on the surface of a
> sphere. In order to define the polygons I have a first file providing the
> coordinates of 3D points and a second file listing the indices of a
> sequence of points in the first file that are to be connected. I was able
> to find only function evaluating the polygon area in 2D (for example
> polygon_area_2). Can anyone provide me any suggestion?
> Thanks in advance!

There is no function in CGAL that will directly give you the result.
I guess the points on the sphere are connected with great circles
(circle on the sphere which center is that of the sphere). In that case,
the geodesic curvature of a great circle being 0, the area computation
is simply limited to A=(2 pi - sum(theta_i) ) * r0^2 where r0 is the
radius of the sphere and theta_i are the internal angle at each point
of the polygon (angle between -pi/2 and pi/2 between the oriented
incident circular arc).
Again as you have only great circles, it is equivalent to computing
the angle between normal vectors of supporting planes, which can be done
using CGAL.


S.