CGAL users discussion list

[Mariette Yvinec <>]

You may find the answer to your question
in the CGAL documentation.
I quote below the definition of Alpha-shapes in CGAL's user manual
http://www.cgal.org/Manual/last/doc_html/cgal_manual/Alpha_shapes_3/Chapter_main.html

More precisely, the definition of alpha shapes is based on an underlying triangulation that may be a Delaunay triangulation in case of basic alpha shapes or a regular triangulation (cf. 35.3) in case of weighted alpha shapes.

Let us consider the basic case with a Delaunay triangulation. We first define the alpha complex of the set of points S. The alpha complex is a subcomplex of the Delaunay triangulation. For a given value of α, the alpha complex includes all the simplices in the Delaunay triangulation which have an empty circumsphere with squared radius equal or smaller than α. Here ``empty'' means that the open sphere do not include any points of S. The alpha shape is then simply the domain covered by the simplices of the alpha complex (see [EM94]).

mahdavi wrote:

hi all
I use alpha complex ,my program is used regular triangulation  for  weighted
points and I  want to  grow points  by constant alpha(a). please anybody say
me that in weighted alpha  complex must be used alpha or square alpha ,
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Which is instruction correct?
1:Alpha_shape_3  as(P1.begin(), P1.end(), a, Alpha_shape_3::GENERAL);
2:Alpha_shape_3  as(P1.begin(), P1.end(), a^2 ,Alpha_shape_3::GENERAL);
thanks.
  

-- 
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis