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Pierre, <br>
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For my analysis, I assumed someone without much geodetic knowlegde doing a point in polygon in projected coordinates would treat these coordates as unprojected cartesian coordinates. Are you saying that is an incorrect assumption?
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I'm not sure if I understand your question correctly. I think the answer might be the RD column of my table. This is the deviation between a conformally projected geodesic of an ellipsoid with a line y=ax+b in +proj=sterea.<br>
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Regards, Jochem<br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> PROJ <proj-bounces@lists.osgeo.org> on behalf of Pierre Abbat <phma@bezitopo.org><br>
<b>Sent:</b> Sunday, March 29, 2020 9:00:01 AM<br>
<b>To:</b> proj@lists.osgeo.org <proj@lists.osgeo.org><br>
<b>Subject:</b> Re: [PROJ] How does proj deal with ellipsoid with respect to reprojection</font>
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<div class="PlainText">On Sunday, 29 March 2020 02:28:57 EDT Lesparre, Jochem wrote:<br>
> Doing point in polygon in a projection will result in occasional wrong<br>
> conclusions. A point near de edge can seem to be inside the polygon while<br>
> it's outside, or the other way around, since a straight line in the<br>
> projection deviates from the geodesic.<br>
<br>
> I analysed this problem for the Netherlands (51 - 55 degrees north) in the<br>
> azimuthal projection (+proj=sterea) of the national coordinate reference<br>
> system RD (epsg:28992) and in plate-caree projection (+proj=lonlat). The<br>
> deviation depends on the length, orientation and location of a polygon<br>
> segment. I computed the maximum possible deviation in the Netherlands for<br>
> both projections to advise the Dutch government not to allow any segments<br>
> longer than 200 m in a new digital storage system for policy and zoning<br>
> borders.<br>
<br>
When doing point in polygon in the spherical stereographic projection, you are <br>
checking circular arcs, not straight lines, in the plane. A geodesic projects <br>
to a circle. How much does a geodesic of an ellipsoid, projected conformally <br>
onto a sphere, differ from a geodesic of a sphere?<br>
<br>
Pierre<br>
-- <br>
When a barnacle settles down, its brain disintegrates.<br>
Já não percebe nada, já não percebe nada.<br>
<br>
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