CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

RGrey wrote:
> I'm looking to use CGAL to specify coordinates and radii for 'N'
> circles/discs, and then calculate the intersection/union (i.e. surface area)
> of the discs.
>
> Example 17.4.4 from -
> <http://www.cgal.org/Manual/3.5/doc_html/cgal_manual/Boolean_set_operations_2/Chapter_main.html>
> on boolean set operations, provides an example of how to generate the union
> of N = 8 identical discs.  Can I extend this example to calculate an exact
> surface area for discs of different radii?
>
> Thanks for any help!
Hello,


If what your are looking for is computing the area of a union of disk,
you may want to use the 2D weighted alpha shape to get a combinatoric
description of the boundary of the union of the disks.
Then from this description you will be able to compute the area
by applying Gauss' formula to each disk restricted to its power
cell (3D version is described here http://hal.inria.fr/inria-00409374).

Alternatively, you can also use an inclusion-exclusion formula
restricted to the simplices of the weighted alpha complex as described
here
http://www.cs.duke.edu/~edels/Papers/2007-J-03-IndependentComplexes.pdf


S.