Hello,
I want to compute Alpha shapes of weighted points in 2D (and later 3D). When I compare my own implementation with CGAL, I get very different results for the alpha values of the simplices. I tried this basic example: point 0: 4 5.7 weight 16 point 1: 2.5 5 weight 4 point 2: 3 3 point 3: 6 4 weight 9 point 4: 8 3 We get the triangles 012 and 024, which is fine. They should have squared radius 6.06 and 11.79, but CGAL gives me 2.15 and 6.62. I don't know where these numbers come from. Just to be clear, my definition for the weighted Alpha shape is the following: A simplex is contained in the Alpha shape of radius r if the smallest sphere orthogonal to all its points (AB orthogonal if d(A,B)^2weight_Aweight_B=0) has weight <= r^2. For triangle 012 I compute solve (4  x)^2 + (5.7  y)^2  16  w = 0, (2.5  x)^2 + (5  y)^2  4  w = 0, (3  x)^2 + (3  y)^2  0  w = 0 to get the center (x,y) and weight/radius^2 w of this weighted circumsphere, which indeed gives w=6.06... Why is the alpha value in CGAL 2.15? The correct value does not even appear in the list of alpha values (which are 0.685 1.0625 2.15052 5.8225 6.25 6.6212). Did I understand something wrong about how to use alpha shapes in CGAL? Thanks for your help, Kathi  You are currently subscribed to cgaldiscuss. To unsubscribe or access the archives, go to https://sympa.inria.fr/sympa/info/cgaldiscuss 
Hello, What is your version of CGAL? There was a bug in AS_2 till not so
long ago where it failed to use weights sometimes. As far as I
remember the bug fix came with CGAL 4.12. With master, and the
following test
code, I get the following output: Alpha Shape computed Faces... face: Alpha values which seem to be what you expect. Mael On 06/04/2018 05:03 PM, Kathi Oe wrote:
Hello, 
Hello, The weighted alpha shape computation works now (on this basic
example) with CGAL 4.12. Thanks for your help, Mael. :) Best, Am 08.06.2018 um 15:20 schrieb Kathi
Oe:

Hello, Great! This pull request might solve that issue, it fixes a problem with the insertion of a range of weighted points in a Regular_triangulation_2 using EPECK). I'll try to reproduce it, but do you still have by any chance some problematic code? Thanks, Mael

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