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Does anybody know why there a gap appearing between two point layers create with ESRI and QGIS when I a reproject, from the same source file, to Robinson ?

The source coordinate system and destination coordinate system share the same datum. It seems there's a shift depending on the technology used to reproject.

Here are the steps to reproduce:

I'm using a shapefile point layer in Lat/Long WGS84 Coordinate System and I reproject it to Robinson (EPSG 54030) using the Tool "Project" in ArcMap

I do the same thing in QGIS. I take the same point layer in WGS84 Lat/Long and reproject it to Robinson (EPSG 54030) using the "Save as.."

Result in QGIS

Download the sample point data here


At the request of mkennedy, here is the cs2cs conversion of regular 10° points:

deg_E   deg_N   sph_X     sph_Y      ell_X       ell_Y
 10       0   943711.34    0        944768.52       0
 10      10   939370.28 1068322.39  940422.59   1069519.16
 10      20   926913.31 2136644.78  927951.66   2139038.32
 10      30   905962.87 3204967.3   906977.76   3208557.61
 10      40   869724.36 4271566.44  870698.65   4276351.58
 10      50   819047.09 5320935.04  819964.61   5326895.73
 10      60   753647.9  6328948.79  754492.16   6336038.68
 10      70   678150.95 7267177.19  678910.63   7275318.12
 10      80   586327.84 8093403.95  586984.66   8102470.44
 10      90   502243.15 8615503.11  502805.77   8625154.47

Scaling the results leads to the factors in https://en.wikipedia.org/wiki/Robinson_projection.

  • when I try it directly in GDAL, I get the same results as QGIS. I wonder if ESRI is using a different source projection than 4326, as the degree unit in the prj file is slightly different from that in the 4326 spec (see spatialreference.org/ref/epsg/4326/html)? (0.017453292519943295 vs. 0.01745329251994328) – neuhausr Sep 2 '15 at 14:25
  • How big/long are the differences? – bugmenot123 Sep 2 '15 at 14:46
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    Distance between points from both layer are roughly from 6 to 8 km – Jerome Alary Sep 2 '15 at 15:04
  • I did try to reproject using the same angular units ((0.017453292519943295 vs. 0.01745329251994328) but i.m getting the same result – Jerome Alary Sep 2 '15 at 15:06
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    The projections are set up differently--PROJ.4 has pre-calculated values every 5 degrees before it interpolates. Esri uses the table from the original paper, which isn't as dense. I'll have to see what a developer thinks. Esri also has a Robinson (ARC/INFO) version. That gives different answers. It was implemented by a contractor probably 25-30 years ago (before me) and we're still not sure why it's different. – mkennedy Sep 2 '15 at 16:36
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The original paper describing the Robinson projection included a table of values at every 5 degrees along the equator and the central longitude. Those values are used to interpolate intermediate coordinates

This same table is what Esri is using.

The PROJ.4 code has a much expanded table with each 5 degree value having an additional 3 values (possibly done for performance reasons).

An Esri developer thinks that there are different interpolations occurring.

Another possibility is that PROJ.4 is calculating a sphere from the given WGS84 datum while Esri is using the semimajor axis of WGS84, but I haven't been able to check this yet.

Note: I'm getting much closer values (X<1m, Y<120m) if I specify a sphere in PROJ.4 but haven't managed an exact match yet.

  • Can you add which kind of interpolation ESRI uses between the 5° tabulated values? – AndreJ Sep 7 '15 at 6:13
  • @mkennedy : do you know any way I can match the ESRI Robinson 54030 by using ogr proj4? I need to reproject shapefile using ogr / qgis – Jerome Alary Sep 21 '15 at 19:34

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