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
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)^2-weight_A-weight_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,
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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
code, I get the following output:
Alpha Shape computed
which seem to be what you expect.
On 06/04/2018 05:03 PM, Kathi Oe wrote:
The weighted alpha shape computation works now (on this basic
example) with CGAL 4.12. Thanks for your help, Mael. :)
Am 08.06.2018 um 15:20 schrieb Kathi Oe:
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?
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