[OpenLayers-Users] Distance errors on Google maps

[Jennifer Strahan]

Hi Peter, 

Back in Oct/Now I wrote to Tim Schaub asking about measurements when 
working with Spherical Mercator and he sent me a few responses that I'm 
copying below for you. 

Regards,
Jennifer


*First response:
*Regarding the measure control, this provides planar instead of geodesic 
measures (as is true with ArcMap and other GIS software).  So, when you 
measure a length, you are getting the straight-line distance between 
points on a projected plane instead of the shortest distance between 
points on a spheroid.  Same goes for area - planar area instead of 
surface area of a spheroid.

So, yeah, your spatial reference system is important.  And spherical 
mercator will be worse the farther you are from the equator. So, for a 
couple points around San Francisco:

point 1: -13625500, 4551200
point 2: -13625250, 4551200

planar distance: 250 m
geodesic distance: 198 m

That is pretty bad.

The solution with lines is to use a geodesic calculation (which we 
provide with OpenLayers.Util.distVincenty).  For areas, this is more 
complicated - as it involves dividing an arbitrary polygon into 
triangles and running spheroid areas on those (which we don't have a 
function for in the library).

One solution would be to transform the polygon to a more appropriate 
projection before calculating the area.  I can't get in to more detail 
on this now, but if you haven't found another solution, we can talk more 
about this.

Tim

*A few weeks later he sent this:*
Hey-

In case you don't see it on the OL dev list, I've put up a patch to do 
geodesic measures with the measure control.

This assumes that you have provided the proj4js definitions for your map 
projection.

http://trac.openlayers.org/ticket/1819

Let me know if it works for you.

Tim



Peter Robins wrote:
> I have a program that displays kml linestrings on either topo maps or google. 
> I'm using getLength() to display the length of the segments, and noticed 
> significant errors on the google display, in some cases 60% or more. I'm 
> also using the scaleline, which is also wrong on Google.
>
> Thinking this was probably some error in my logic, I tried some simple tests. 
> The topo maps conveniently include a 1km grid, so I drew some 1km lines on 
> the grid (as close as I could make it) and saved them to kml. This gave me 
> coordinates that I knew were 1km apart (on the topomap projection). I then 
> used the Google api:
>
> var p1 = new GLatLng(42.87420777239693,-8.547039046722437);
> var p2 = new GLatLng(42.87483907990915,-8.534868375601192);
> alert(p1.distanceFrom(p2));
>
> This gave me 0.995km, so Google agrees that these 2 points are 1km apart. 
> (Google's docs say their calculations may be up to 0.3% out because of the 
> spherical assumption they use; this is no problem at the scales I'm using.)
>
> I then took OL's spherical mercator example page, and added my kml file. The 
> scale line incorrectly showed the 1km line as well over 1km long. I then did:
>
> var p1 = new OpenLayers.Geometry.Point(-8.534868375601192,42.87483907990915);
> p1.transform(map.displayProjection, map.projection);
> var p2 = new OpenLayers.Geometry.Point(-8.547039046722437,42.87420777239693);
> p2.transform(map.displayProjection, map.projection);
> alert(p1.distanceTo(p2));
>
> This gave me 1.358km.
> Thinking there might be some problem with the spherical mercator calculations, 
> I tried removing 'sphericalMercator: true' and using proj with different 
> projection objects. I found several defs on spatialreference.org, 
> and used SR-ORG:6 and SR-ORG:6627; I also used the new EPSG:3785. These defs 
> are all very similar, so I was not surprised to get the same error: 1358m.
>
> Those 2 points are in Spain, EPSG:23030, but I also tried other places. One 
> 5.2km line in GB, as measured on OS maps, EPSG:27700, was 8.4km according to 
> OL Google getLength().
>
> I would expect discrepancies when dealing with different projections. I would 
> expect rounding errors when transforming lots of points on a linestring. But 
> these errors are so large the figures are effectively useless.
>
> Am I doing something wrong, or missing some vital step somewhere? Is it an 
> error in OL's calculations? Or is it one of those complicated projection 
> issues, where it would be simpler to use Google's api not OL if I want 
> linestring lengths?
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> http://openlayers.org/mailman/listinfo/users
>   


-- 
Jennifer Strahan, GIS Specialist
GreenInfo Network - www.greeninfo.org -
Information and Mapping in the Public Interest

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