Hi

(GMT version 6.3.0)

I’m trying to understand the importance of the region specified on the -R option when using mapproject to convert between geographic coordinates and Cartesian. For the same input coordinates and projection it seems that the region affects how the transformation is done, resulting in differences in the result. e.g.

```
$~>echo "-137000.0 11000.0" | gmt mapproject -Jt-17.927/64.463/1:1 -R-23/-7/60/66 -I -C -F -V
mapproject [INFORMATION]: Processing input table data
mapproject [INFORMATION]: Using spherical projection with authalic latitudes
mapproject [INFORMATION]: Transform -2.30000000e+01/-7.00000000e+00/6.00000000e+01/6.60000000e+01 <- -2.83125208e+05/6.08385783e+05/-5.14521453e+05/1.98117729e+05 [m]
mapproject [INFORMATION]: Reading Data Table from Standard Input stream
mapproject [INFORMATION]: Writing Data Table to Standard Output stream
-2.07948097e+01 6.46830641e+01
mapproject [INFORMATION]: Projected 1 points
mapproject [INFORMATION]: Input extreme values: Xmin: -1.37000000e+05 Xmax: -1.37000000e+05 Ymin: 1.10000000e+04 Ymax 1.10000000e+04
mapproject [INFORMATION]: Output extreme values: Xmin: -2.07948097e+01 Xmax: -2.07948097e+01 Ymin: 6.46830641e+01 Ymax 6.46830641e+01
mapproject [INFORMATION]: Mapped 1 x-y pairs [m] to lon-lat pairs
```

Yields a different results than

```
$~> echo "-137000.0 11000.0" | gmt mapproject -Jt-17.927/64.463/1:1 -R-23/-8/60/66 -I -C -F -V
mapproject [INFORMATION]: Processing input table data
mapproject [INFORMATION]: Transform -2.30000000e+01/-8.00000000e+00/6.00000000e+01/6.60000000e+01 <- -2.82888271e+05/5.52531638e+05/-4.97396944e+05/2.07039344e+05 [m]
mapproject [INFORMATION]: Reading Data Table from Standard Input stream
mapproject [INFORMATION]: Writing Data Table to Standard Output stream
-2.07821645e+01 6.45340166e+01
mapproject [INFORMATION]: Projected 1 points
mapproject [INFORMATION]: Input extreme values: Xmin: -1.37000000e+05 Xmax: -1.37000000e+05 Ymin: 1.10000000e+04 Ymax 1.10000000e+04
mapproject [INFORMATION]: Output extreme values: Xmin: -2.07821645e+01 Xmax: -2.07821645e+01 Ymin: 6.45340166e+01 Ymax 6.45340166e+01
mapproject [INFORMATION]: Mapped 1 x-y pairs [m] to lon-lat pairs
```

The only difference being that the region in the latter call is 1 degree wider in the longitude. I note that the smaller region triggers ` spherical projection with authalic latitudes`

so presumably this is the cause of the difference (about 16.64 km) here but I assume that the projection should be unique so asking for some help on how to know which region is appropriate to use.