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I was convinced that Voronoi polygons were created so that each location in a polygon is closer to the origin point present in that polygon than to any other seeds

In Snow's famous case study in Soho, London (see screenshot), when I compare the Voronoi partitioning to the distances to the nearest point, I realize that some deaths (red figures) are in the polygon of a pump (white figure) while they are closer to another pump.

How can this be explained?

enter image description here

Map projection is EPSG 3857 (WGS84). Reprojection to British national grid gives me the same result.

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  • how are you calculating the distances?
    – Ian Turton
    Oct 20, 2022 at 7:24
  • Map projection or data/calculation projection (BTW EPSG 3857 is a Mercator projection with highly distorted measurements in meters, not degrees on an ellipsoid like WGS84)? Can you replicate the result in other software? Oct 20, 2022 at 7:24
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    It is not the map projection that matters but the data projection. Have you tried reprojecting the data first?
    – JGH
    Oct 20, 2022 at 13:00
  • My data have different projections.
    – Wilcar
    Oct 20, 2022 at 15:37
  • Ok, works great with save as and all data with EPSG 3857 (WGS84)
    – Wilcar
    Oct 20, 2022 at 15:42

1 Answer 1

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It is not the map projection that matters but the data projection.

As a rule of thumb, for any processing, all data must be in the same projection even if some tools allow some sort of on-the-fly reprojection. 3857 should however not be used for anything related to distances, as it highly distorts them.

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