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b3m2a1
b3m2a1
6:18 AM
Slowly I find I spend less and less time on the main site and more here
I haven't read the whole new question list for a given day in months
 
 
6 hours later…
Szabolcs
Szabolcs
12:15 PM
I have seen OrderingBy in the planning notebook in some Twitch streams, but I do not know which livestream it was discussed in. Does anyone understand the point of OrderingBy? Wouldn't OrderingBy[list, f] be the same as Ordering[f /@ list]?
SortBy is genuinely useful (actually very useful), but I do not get OrderingBy.
 
J. M. is computer-less
J. M. is computer-less
12:58 PM
it could maybe be useful if they also make an operator form: OrderingBy[f] @ list
@kickert, if you're interested in having a gathering of MSE members in the conference, consider making a post on Meta.
 
 
3 hours later…
kickert
kickert
4:24 PM
@J.M.iscomputer-less Done!
 
Meta
Meta
4:55 PM
0
Q: Meet at Wolfram Technology Conference?

kickertI am curious who all is currently attending the Wolfram Technology Conference in Champaign. Would love to put a face with a name for the people I have learned from on SE. Perhaps a meet up? Or feel free to come introduce yourself. -Ben Kickert

discussion
 
Szabolcs
Szabolcs
5:18 PM
@HenrikSchumacher
Urquhart graph
In computational geometry, the Urquhart graph of a set of points in the plane, named after Roderick B. Urquhart, is obtained by removing the longest edge from each triangle in the Delaunay triangulation. The Urquhart graph was described by Urquhart (1980), who suggested that removing the longest edge from each Delaunay triangle would be a fast way of constructing the relative neighborhood graph (the graph connecting pairs of points p and q when there does not exist any third point r that is closer to both p and q than they are to each other). Since Delaunay triangulations can be constructed in...
> The Urquhart graph was described by Urquhart (1980), who suggested that removing the longest edge from each Delaunay triangle would be a fast way of constructing the relative neighborhood graph
> Although it was later shown that the Urquhart graph is not exactly the same as the relative neighborhood graph,[2] it can be used as a good approximation to it.
I feel less stupid now.
 
Henrik Schumacher
Henrik Schumacher
=D
That's indeed something what you found there!
 
Szabolcs
Szabolcs
@Henrik One thing that bother me about Nearest is that it can return points at a distance <= d, but not at a distance < d, which would be useful in some cases.
I can filter, but it's unpleasant and affects performance
 
Henrik Schumacher
Henrik Schumacher
And sometimes, I would love if it would return points >=d....
But <d is equivalent to <= d(1-$MachinePrecision), no?
Alternatively, a function Farthest would do...
 
Szabolcs
Szabolcs
hmm
 
Henrik Schumacher
Henrik Schumacher
Oops. I meant <= d(1-$MachineEpsilon)
 
Szabolcs
Szabolcs
5:28 PM
yes, I got that
I was playing with beta skeletons of various point distributions, including random ones, regular lattices, and things inbetween
With the original implementation, the skeleton of a triangle lattice has no edges for beta >= 2, and has all edges for beta < 2. I wanted it to have all edges for beta==2 as well.
 
Henrik Schumacher
Henrik Schumacher
Aaah.
 
Szabolcs
Szabolcs
it's something very minor, but I want to get the implementation right
and consistent between the various cases: lune-based, circle-based, etc.
 
Henrik Schumacher
Henrik Schumacher
See: The epsilon trick seems to work: nf[{1. - $MachineEpsilon, 1.}, {[Infinity], (1. - $MachineEpsilon)}]
Oh. with nf = Nearest[{0}]
I get {{0}, {}} as answer.
So in short: Nearest[{0.}, {1. - $MachineEpsilon,
1.}, {\[Infinity], (1. - $MachineEpsilon)}] returns {{0}, {}} for me.
That tells me that Nearest does no any tolerance stuff.
 
Chris K
Chris K
any news on v12 release date at WTC?
2
 
Henrik Schumacher
Henrik Schumacher
Another example: Nearest[
CirclePoints[3.] -> Automatic,
CirclePoints[3.],
{\[Infinity], Sqrt[3] (1. - $MachineEpsilon)}
]
returns {{1}, {2}, {3}} (correct)
Nearest[
CirclePoints[3.] -> Automatic,
CirclePoints[3.],
{\[Infinity], Sqrt[3]}
]
returns {{1, 2}, {2, 1, 3}, {3, 2}}
Hmmm. Well, that's not really a sign for reliability...
 
Szabolcs
Szabolcs
6:05 PM
@HenrikSchumacher This question with relative neighbourhood graphs:
4
Q: Error in Mesh Region during concave hull

Giovanni BaezI have the following data: Data.csv It crates the following image: Im trying to make a concave hull so that I can create an outline of the region. I have tried to use all versions of the alphaShapes2D code found in this answer. I think have pinpointed the issue, it seems my points are too clo...

plotting error mesh
There's still work to be done though because I forgot about when: 1. there are duplicate points 2. there are less than 3 points 3. there are less than 3 non-collinear points
 
Henrik Schumacher
Henrik Schumacher
Why do you have to catch these cases? Is it because DelaunayMesh complains otherwise?
 
Szabolcs
Szabolcs
DelaunayMesh is inconsistent, it seems. DelaunayMesh[{{0,0}}] gives a mesh containing a single point. Okay, that's not unreasonable. But then DelaunayMesh[{{0,0},{1,0}}] should contain two points and one line. Instead it gives EmptyRegion[2]
So does DelaunayMesh[{{0, 0}, {1, 0}, {2, 0}, {3, 0}}]
@HenrikSchumacher Yes, but it's easy to work around
The joys of making a package robust ...
Without deleting duplicates, I get really messed up results like
and I do not yet understand what exactly goes wrong in this case. It even has crossing edges
Ah yes ... DelaunayMesh removed any duplicates
 
Henrik Schumacher
Henrik Schumacher
Hmm. Weird...
 
 
3 hours later…
Szabolcs
Szabolcs
9:03 PM
If anyone is willing to write small test cases or benchmarks for IGraph/M, please contact me. Any amount of help would be most welcome, even just adding a single test.
 

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