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I am concerned with how QGIS (version 2.8.1) and ArcGIS (version 10.0) draw "perpendicular bisecting lines" when Thiessen/Voronoi polygons are created. When using either program to create these polygons, it appears the bisecting lines are NOT perpendicular to the line connecting two nearest points. See attached image: Thiessen polygons were created from the "H Locations". We created 3, 5, and 7 mile non-overlapping buffers around these "H Locations". We expected the Thiessen polygon boundaries to line up with the buffer intersections (a perpendicular line drawn at the half-way point between two H locations), however they do not. It appears the Thiessen polygon boundaries are at the half-way point between the two points, but are not perpendicular with the line connecting those two points. Is this a projection issue?? Thiessen Boundaries vs. Buffer Intersections

In other words...

This (Thiessen Polygons either program created): enter image description here

Doesn't look like this (what we expect them to look like): enter image description here

Additional information: The first step was creating the shapefile of these “H locations” using the program Alteryx. I brought in an Excel document with names and coordinates of 6 locations (in Germany), and output to a SHP. I did not select a projection in the output tool. I also created non-overlapping trade areas/buffers around these 6 points, also in Alteryx. I created 3 mile buffers and 200 mile buffers. I brought all 3 files into ArcGIS, and the buffers looked like ovals. I changed to layout view, accessed data frame properties > coordinate system, and selected “The World from Space” projection. I modified this projection with the latitude and longitude of central Germany. The buffers adjusted to a more circular shape as I expected. I then created Voronoi polygons in ArcGIS, and the result was not as I expected. In the attached image, you can see the intersections of the 200 mile non-overlapping buffers are showing perpendicular to the lines connecting two nearest points – you can see that the Voronoi polygon boundaries are not perpendicular to the lines connecting two nearest points.

enter image description here

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    Given that there are two softwares that are giving the same results, I would suspect that there is something in the way the data is being interpreted that is causing the issue. The incorrect interpretation of the projection may be it. That being said it is difficult to see how that amount of distortion could occur unless it is treating projected data as unprojected. Could you provide a bit more information on the projection and maybe a small sample of points to work with? – MickyT Jan 26 '16 at 0:04
  • Thank you for your reply! I added more info to the original question, but I am not sure how to attach a file. The data I used to create the SHP is as follows: H Location Lat Lon H1 50.111616 8.682105 H2 52.512855 13.405404 H3 53.598318 7.195703 H4 48.131242 11.584122 H5 48.777861 9.180817 H6 51.30347 9.438596 – Jaimie Jan 27 '16 at 22:16
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    @MickyT is correct. The problems began with "I did not select a projection in the output tool." You also need to be aware that depending on the projection, lines that are truly perpendicular may look far from perpendicular on a map. If you want to check perpendicularity visually, then please use a conformal projection both for the analysis and the mapping. – whuber Jan 27 '16 at 23:02
  • @whuber would your answer to this question be appropriate here. I would say picking an appropriate projection would be best, but I wouldn't know which one to suggest. – MickyT Jan 28 '16 at 1:17

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