CGAL users discussion list

Thank you for your reply!
I have actually just the point coordinates and their connectivity indices.
Following your suggestion I have to construct the circles for the center
of the spheres and the couples of points defining each side of the polygon
and derive the supporting planes associated to each arc
(c.supporting_plane ()) with their normal. So did you mean the angle
between the normal vectors for two consecutive sides? Moreover, which
function in the spherical kernel can I use to calculate the angle?
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.
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!

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