Hi, I just noticed that on this page:

http://postgis.net/docs/using_postgis_dbmanagement.html#PostGIS_Geography

there are a number of references to “sphere” when they should instead say 
“spheroid”, and to “great circle arc” when they should instead say “geodesic”.

This is clear from the subsequent discussion, in particular in the FAQ section:

http://postgis.net/docs/using_postgis_dbmanagement.html#idp32988960

where it says


4.2.3.1.


Do you calculate on the sphere or the spheroid?



By default, all distance and area calculations are done on the spheroid. You 
should find that the results of calculations in local areas match up will with 
local planar results in good local projections. Over larger areas, the 
spheroidal calculations will be more accurate than any calculation done on a 
projected plane.

All the geography functions have the option of using a sphere calculation, by 
setting a final boolean parameter to 'FALSE'. This will somewhat speed up 
calculations, particularly for cases where the geometries are very simple.


So in

4.2. PostGIS Geography Type

the corrected documentation would change:

The basis for the PostGIS geographic type is a sphere. The shortest path 
between two points on the sphere is a great circle arc. That means that 
calculations on geographies (areas, distances, lengths, intersections, etc) 
must be calculated on the sphere, using more complicated mathematics. For more 
accurate measurements, the calculations must take the actual spheroidal shape 
of the world into account, and the mathematics becomes very complicated indeed.

to:

The basis for the PostGIS geographic type is a spheroid, a “squashed” sphere 
whose polar diameter is smaller than its equatorial diameter. The shortest path 
between two points on the sphere is a great circle arc, and on a spheroid it’s 
a similar arc called a geodesic. That means that calculations on geographies 
(areas, distances, lengths, intersections, etc) will provide more accurate 
measurements, but the calculations must take the actual spheroidal shape of the 
world into account, and the mathematics becomes very complicated indeed.

and in

4.2.3.3. What is the longest arc you can process?

the corrected documentation would change:

We use great circle arcs as the "interpolation line" between two points. That 
means any two points are actually joined up two ways, depending on which 
direction you travel along the great circle. All our code assumes that the 
points are joined by the *shorter* of the two paths along the great circle. As 
a consequence, shapes that have arcs of more than 180 degrees will not be 
correctly modelled.

to:

We use geodesics as the "interpolation line" between two points (these are 
great circle arcs on spheres). That means any two points are actually joined up 
two ways, depending on which direction you travel between them. All our code 
assumes that the points are joined by the *shorter* of the two paths. As a 
consequence, shapes that have arcs of more than 180 degrees will not be 
correctly modeled.

Cheers,

— Andy

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