[PROJ] How does proj deal with ellipsoid with respect to reprojection

[Pierre Abbat]

On Sunday, 29 March 2020 03:33:18 EDT Lesparre, Jochem wrote:
> Pierre,
> 
> 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?

I'm not sure if it's a valid assumption or not, but it's not what I was doing. 
I was writing code to do two related things:
* When excerpting a geoid file, write a KML file which shows the boundary;
* Determine whether a point is in the boundary of a projection.
For the first, I figured a precision of a meter is good enough. For the second, 
boundaries are several kilometers larger than the jurisdiction covered by the 
projection, because sometimes a survey includes parts of two counties, or even 
parts of two states, and the coordinates need to be shown in both projections.

The code I wrote treats the coordinates as spherical and the lines between 
points as spherical geodesics (arcs of great circles). When drawing the 
northern or southern boundary of an excerpt of a geoid file in a geolattice 
format, the boundaries are parallels of latitude, so I have to subdivide them 
into enough points that the spherical geodesics between them approximate the 
parallels of latitude within a meter. The KML code uses the point-in-polygon 
test to determine which boundary is inside which.

The code I wrote has to handle polygons anywhere on the Earth. Point 196, the 
point that is projected to infinity, lies inside UTM zone 10 South. The 
boundary of that zone (which hasn't been entered yet) is projected inside-out, 
so points inside the zone are outside its projection, but the program returns 
the correct answer because the area of the projection is negative. The 
attached file shows two parallelograms, one around the antipode of point 196, 
which is near Arabia, and one around point 196, which is in the Pacific, as 
projected.

> 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.

I looked up the projection used in the Netherlands; it's a conformal 
projection from the ellipsoid to the sphere, followed by a stereographic 
projection. I'm asking for the deviation between a conformally projected 
geodesic of an ellipsoid (which is a plane curve not easily expressible in 
closed form) and a conformally projected geodesic of a sphere (which is an arc 
of a circle).

Pierre
-- 
Don't buy a French car in Holland. It may be a citroen.
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