
Comments and Discussions



Hi,
I'm looking for a fast way to determine the location of a specified point (x,y) within your VoronoiGraph in C#.
Your VoronoiGraph only returns a list of edges and vertices of the graph. Are they in any specific order?
It would be great if there was an easy way to create a structure for a single Voronoi cell and a list of its neighbor cells.
Is there a fast way to determine in which cell my specified point is? (In literature a logarithmic runtime is said)
Thanks for your help in advance!





In the special case of 3 data points, all FixedPoints are equal to the unique Vertize, isn't wrong??
i made a test with: (0,0);(10,0);(0,10).
and for each edge the fixedPoint is equal to (5,5).
I hope your answer BenDi... Excellent tool!!
cheers





That's the proper result: for any three sites  except when they are perfectly aligned (in any direction), there will be only one vertex, shared by the three edges.





somebody have a free C# code, to generate the Polygon for each data point using a boundary polygon that could be the convex hull(or extended convex hull) of the data points.
thks.





Ben,
For following another set of points, algorithum misses the vertex by almost 250 mt.
NODE_ID EASTING NORTHING
6 10494.00016 10092.53629
7 10290.7531 10684.97519
8 9947.773702 11043.95948
9 9776.284008 11059.26798
10 10991.95541 10217.30055
11 10057.01902 10092.5363
It gives 8 edges and 3 vertex, but due to wrong location of vertex 3, egde no 6,7 and 8 have not come out properly. Actual location of vertex 3 should be 9819.40,10578.40. I strongly feel that it should have 4 vertexes.
Could you please look into it.
Thanks,
Sunil Terkar





Hi,
sorry to hear about that, the only problem I can image is double rounding...
I think what you need is a version of the algorithm based on the decimal class, not on double  should be done by replacing all occurences of 'double' with 'decimal'  please try it.
cheers,
Ben





Ben
Ok, will give try for this & get back to you. I have one more observation wrt last message, even program doesn't sorts correctly all site nodes on y coordiantes...does it could be the another reason for not producing correct vertex..
Regards,
Sunil Terkar





Ben,
Tried decimal type also, still its reporting 3 vertex at wrong coordinates. Even this circle at this vertex is not an empty circle.
Please look into this problem.
Thanks,
Sunil Terkar





I tried the numbers above, and with BenDi's version, I got 5 vertices:
y:10277.582825767151, x:10313.499324681763
y:10489.718951040446, x:9870.995694254938
y:10497.621153995677, x:10719.098572868817
y:10504.131065614873, x:9950.369665759434
y:13717.0357506786, x:12076.964532715061
(not 3 as you report, and neither 4 as you anticipate.)





Ben,
I have passed on following points to this algorithum,seems its generating atleast one less vertex and one less edge. I have compared voronoi diagram generated by these points wih standard GIS software like MapInfo, is it the thing that you need to address ?
1 399380.8371 5526801.89
2 400882.095 5525038.395
3 402256.1277 5524122.657
4 399247.2089 5525471.661
5 401383.9145 5523790.174
Regards,
Sunil Terkar





I tried it, and BenDI's version correctly reports 4 vertices:
y:5530625.902209154, x:405647.4244046288
y:5526166.085865074, x:400398.8301785578
y:5524717.980236851, x:401702.70591802325
y:5523959.683474038, x:399813.0172873341
Are you saying your GIS software is reporting 5 vertices?





Hello: I'm working on a project that involves finding the medial axis of
vector polygons and was hoping from all that I've read that using the voronoi would allow me to do this.
has anyone has experience w/ working w/ this project and finding the medial axis?
thanks,
Proctor





Thank you very much for posting this! It's a great starting point for developing my own Voronoi solver.





How does the code return the rays (ie sides with only one vertex and a direction). From what I can tell VVertexB is just set to NaN. But how does one generate the rays from this information?






Hi!
For (partly) infinite edges I provided two properties do make drawing easier: FixedPoint and DirectionVector. FixedPoint is either the (one) Vertex that exists or the middle between the two data points. DirectionVector is orthogonal to the connecting line between the data points (this is a property of all voronoi edges).
The secret to getting the direction of an infinite edge is in the voronoi algorithm itself  it provides edges with 'left' and 'right' data points. This gives a direct way to calculating the direction from the vertex. It goes in the direction where LeftData is left and RightData is right. Simple
Cheers,
Ben





Do you mean that the Voronoi edge ray must start at VVertexA and must have the direction of the line made by the points LeftData and RightData (i.e. from LeftData to RightData comes first). If yes, then your algorithm is wrong. Just test it on a rectangle and you will see the result. If I misunderstood you, please explain how to get the rays in more details.
VladovsoftSoftware products for fitness and health club management, storehouses, shops and barcode generation.





They start in VVertexA and go orthogonal to the line from LeftData to RightData, so that LeftData is on the left and RightData is on the right.





Ok, thanks. But what about the vertices. I made a simple polygon generator to test the algorithm and I saw that the location of the vertex for 3 points (i.e. a triangle) is sometimes out of the triangle. But it should be the center of the inscribed circle, shouldn't it ?
VladovsoftSoftware products for fitness and health club management, storehouses, shops and barcode generation.





No, Voronoi Vertex of a triangle is the center of it's outer circle, which is only inside the triangle for max(angle)<90 degree. (see wiki[^])
B.





Ok, thanks for the info. I was planning to use Voronoi diagrams for finding the Maximum Inscribed Circle in a simple polygon, but I guess I should read some more information about its properties to determine if it will work for me.
VladovsoftSoftware products for fitness and health club management, storehouses, shops and barcode generation.





According to this, if I take RightDataLeftData, I get the vector from left to right. Then swapping X and Y and negating one gets an orthogonal vector. Taking the nonunknown point and adding the orthogonal vector should produce the correct ray, with LeftData on the left and RightData on the right. However in some cases it does not, and the ray is cast in the wrong direction, as if LeftData and RightData are in the wrong order.
Do you have a correction for me, or updated version of this code?





Hi,
sorry, I dont have any free time at the moment... can you verify whether the left/right data points are actually wrong?
B.





I solved this the same way many other implementations do  don't try to draw the unbounded edges, just contain the points you want to draw within a much larger triangle or square.
With this, I don't have any issues.





Hello BenDi,
I tried to fix the ray problem many people seem to have. I verified the left/right data points and they really seem to be wrong. If I draw a green/blue line from RightData to LeftData (where the left part of the line is green and the right part is blue) you can see in the picture below, that the right/left side is sometimes wrong.
https://www.dropbox.com/s/1o4zl2izmkuv96d/voronoi_ray_problem.png[^]
Do you have any idea where I could fix that problem? How do you decide which one is the left and which one the right point?
It would be kind if you could help me with this problem, or at least give me a hint. Drawing the rays correctly is really necessary for me and I can't skip them.
Peh







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