Animated Apollonius diagram

[stla]

Hello,

Could you explain why more edges appear as the radii decrease?

[sloriot]

The diagram should be a partition of the plane, so they are definitely missing edges.

I haven't looked at your code but I did wrote something for Ipe that does something similar here:
https://github.com/CGAL/cgal/blob/master/CGAL_ipelets/include/CGAL/CGAL_Ipelet_base_v7.h#L724

In theory, updating Voronoi_from_tri should be all you need (This is old code, please be indulgent)

[stla]

Hmm that's embarrassing.

My code is here but there's a part done in R and the C++ code can look complicated because originally I didn't find how to use vertices with info. But to sum up, I iterate over the finite faces and I take the dual of each face.

[lrineau]

That is because you only display finite edges. When the radii decrease, the corresponding face switch from "infinite faces" to "finite faces", and same for the edges.

[stla]

That's what I suspected, thanks. Currently trying to deal with all_faces_begin() instead of finite_faces_begin() but getting problems (see the issue I've just opened).

[stla]

So, when I iterate over all the faces, I get some Line_2 as dual of the infinite faces, that's correct? I plotted these lines in blue and I'm lost, they don't help to partition the plane. Observe they are tangent to some circles, I don't know why.

[stla]

I'm able to get the partition without using the dual Line_2s. There's just a problem: I have to manually set the direction of the hyperbolic rays (the blue lines).

Yet I don't know what are these Line_2s. Maybe lines of hyperbolic reflections?

[stla]

I think I get it now. An infinite face has only one finite edge. Its dual line is tangent to the two circles centered at the vertices of this edge. These two circles are on the same side of the line, and the infinite ray must remain in the opposite side.

[stla]

Yeah it works now!

[stla]

Golden spiral. A bit weird.

[stla]

Fermat spiral -> failure :-( Why?

[stla]

Any idea why it fails? The original sites (red points) are not isolated.

[stla]

It works when the weights vary from 1 to 2. It fails when they vary more.

[stla]

I think some circles are contained into other circles. Can it be the reason of the failure?

[sloriot]

Check https://doc.cgal.org/latest/Apollonius_graph_2/classCGAL_1_1Apollonius__graph__2.html#abd505d277047969aac281c3b06d3024e

[stla]

Thanks, I will check that. Let's see what happens on an animation first. The radii vary from 1 to rmax:

We observe that the hyperbolic segments become highly curved. Then it is not surprising that something weird happens.

[stla]