From 7b3b638b6f93d1634fa3a96af4608c94b352db0f Mon Sep 17 00:00:00 2001 From: Howard Butler Date: Sun, 3 Sep 2023 13:58:07 -0500 Subject: [PATCH] Doc updates from jidanni (#3858) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Update nzmg.rst Here I am taking a guess at which grid this is referring to and thus trying to make it clearer. * Update transformation.rst Note: I have only mentioned that the +'s went away. Apparently the author is using +init files here, and showing only their contents. However even if the user placed the example snippets seen in the boxes into files in the current directory, there is no complete working example! I am saying that earlier in this book, the user was able to run the examples shown. But now if the user wishes to continue running them, he has to put the +'s back, or use some special syntax that you haven't shown yet in a complete working example! * Always use the cleanest examples. Move repetitive default into text explanation. P.S., maybe one day even consider changing the default +ellps=GRS80 to +ellps=WGS84... but no big deal... * Update docs/source/apps/proj.rst * Update x_0.rst These are meters and one cannot just use e.g., +units to change it. * Remove redundant optional default parameters! We get the exact same answer without the clutter that doesn't make things any more clearer. * 50 U.S. isn't grammatical P.S., perhaps add a reference to where this projection came from. * Remove parameter that is default anyway Make example less cluttered. * Update cart.rst Simplify via defaults. * Can remove default parameter. Shorten string by removing redundancies. * Update som.rst showing relation of the two lines Mentioning how the two lines are related. * Update rhealpix.rst Got rid of - default -f setting Eliminated ellipse emphasis and just used the default. * Update geoc.rst Defaults shown clear as day at the bottom of the page already. * Update topocentric.rst Wipe off items that aren't the focus of the issue and don't affect outcome here. * Update unitconvert.rst Use and explain defaults. One day this page should mention what the default time etc. units are too. * Update set.rst Simplify by removing default parameters. * Update push.rst Eliminate default reuse, getting same calculation. * Update xyzgridshift.rst Don't repeat defaults. * Update vertoffset.rst GRS80 already implied and documented. * Update hgridshift.rst Reduce chance of too wide example going off the screen! * Update geogoffset.rst Add '+' to match rest of book. * Update differences.rst Add actual EOF notation. * Update helmert.rst Reduce horizontal scrolling, at least on desktop. Also one day maybe add '+' before each... or maybe not. * Update defmodel.rst Example causes scrolling horizontally, even on desktop. * Update bertin1953.rst Remove src. * Update cass.rst - Less horizontal scrolling, which was seen even on desktop. - Zapped default meter parameter. * Update s2.rst Clean off testing residue. Perhaps one day also hyperlink "Quadrilateralized Spherical Cube" page. * Update tmerc.rst Trimming defaults reduces horizontal scrolling. * Update y_0.rst These are meters and one cannot just use e.g., +units to change it. * Update unitconvert.rst Mention defaults. I only listed the ones I know. The rest I didn't list. --------- Co-authored-by: 積丹尼 Dan Jacobson --- docs/source/apps/cct.rst | 2 -- docs/source/apps/proj.rst | 1 + docs/source/operations/conversions/cart.rst | 4 ++-- docs/source/operations/conversions/geoc.rst | 4 ++-- docs/source/operations/conversions/push.rst | 10 +++++----- docs/source/operations/conversions/set.rst | 2 +- .../operations/conversions/topocentric.rst | 6 +++--- .../operations/conversions/unitconvert.rst | 18 +++++++++--------- docs/source/operations/options/x_0.rst | 2 +- .../operations/projections/bertin1953.rst | 2 +- docs/source/operations/projections/cass.rst | 10 ++++++++-- docs/source/operations/projections/gall.rst | 4 ++-- docs/source/operations/projections/gs50.rst | 4 ++-- docs/source/operations/projections/healpix.rst | 2 +- docs/source/operations/projections/lsat.rst | 2 +- docs/source/operations/projections/nzmg.rst | 4 ++-- .../source/operations/projections/rhealpix.rst | 4 ++-- docs/source/operations/projections/s2.rst | 2 +- docs/source/operations/projections/som.rst | 2 +- docs/source/operations/projections/tmerc.rst | 4 ++-- .../operations/transformations/defmodel.rst | 3 ++- .../operations/transformations/geogoffset.rst | 6 +++--- .../operations/transformations/helmert.rst | 3 ++- .../operations/transformations/hgridshift.rst | 4 +++- .../operations/transformations/vertoffset.rst | 2 +- .../transformations/xyzgridshift.rst | 4 ++-- docs/source/usage/differences.rst | 10 ++++++---- docs/source/usage/transformation.rst | 4 +++- 28 files changed, 69 insertions(+), 56 deletions(-) diff --git a/docs/source/apps/cct.rst b/docs/source/apps/cct.rst index e2199510c8..71968c30c8 100644 --- a/docs/source/apps/cct.rst +++ b/docs/source/apps/cct.rst @@ -49,8 +49,6 @@ file referenced by the {object_reference} must contain a valid .. versionadded:: 8.0.0 - - Description *********** diff --git a/docs/source/apps/proj.rst b/docs/source/apps/proj.rst index 327cc393ce..9c3754a939 100644 --- a/docs/source/apps/proj.rst +++ b/docs/source/apps/proj.rst @@ -206,6 +206,7 @@ The following script EOF will perform UTM zone 12 forward projection. +The default +ellps=GRS80 is used as no +ellps was specified. The geographic values of this example are equivalent and meant as examples of various forms of DMS input. The x-y output data will appear as three lines of:: diff --git a/docs/source/operations/conversions/cart.rst b/docs/source/operations/conversions/cart.rst index 239b1772d1..0daca0b9ce 100644 --- a/docs/source/operations/conversions/cart.rst +++ b/docs/source/operations/conversions/cart.rst @@ -27,9 +27,9 @@ longitude=90, latitude=0 and the third axis (Z) points to the North pole. Usage ################################################################################ -Convert geodetic coordinates to GRS80 cartesian coordinates:: +Convert geodetic coordinates to cartesian (uses default +ellps=GRS80):: - echo 17.7562015132 45.3935192042 133.12 2017.8 | cct +proj=cart +ellps=GRS80 + echo 17.7562015132 45.3935192042 133.12 2017.8 | cct +proj=cart 4272922.1553 1368283.0597 4518261.3501 2017.8000 Parameters diff --git a/docs/source/operations/conversions/geoc.rst b/docs/source/operations/conversions/geoc.rst index 6ee32ea65d..bd12618e55 100644 --- a/docs/source/operations/conversions/geoc.rst +++ b/docs/source/operations/conversions/geoc.rst @@ -63,11 +63,11 @@ Usage Converting from geodetic latitude to geocentric latitude:: - +proj=geoc +ellps=GRS80 + +proj=geoc Converting from geocentric latitude to geodetic latitude:: - +proj=pipeline +step +proj=geoc +inv +ellps=GRS80 + +proj=pipeline +step +proj=geoc +inv Parameters ################################################################################ diff --git a/docs/source/operations/conversions/push.rst b/docs/source/operations/conversions/push.rst index a1f4423a74..a0dbed1ceb 100644 --- a/docs/source/operations/conversions/push.rst +++ b/docs/source/operations/conversions/push.rst @@ -46,10 +46,10 @@ operation but the vertical part is kept exactly as the input was. $ echo 12 56 12.3 2020 | cct +proj=pipeline \ +step +proj=push +v_3 \ - +step +proj=cart +ellps=GRS80 \ + +step +proj=cart \ +step +proj=helmert +x=3000 +y=1000 +z=2000 \ - +step +proj=cart +ellps=GRS80 +inv \ - +step +proj=pop +v_3 \ + +step +proj=cart +inv \ + +step +proj=pop +v_3 12.0056753463 55.9866540552 12.3000 2000.0000 @@ -58,9 +58,9 @@ Note that the third coordinate component in the output is the same as the input. The same transformation without the push and pop operations would look like this:: $ echo 12 56 12.3 2020 | cct +proj=pipeline \ - +step +proj=cart +ellps=GRS80 \ + +step +proj=cart \ +step +proj=helmert +x=3000 +y=1000 +z=2000 \ - +step +proj=cart +ellps=GRS80 +inv \ + +step +proj=cart +inv 12.0057 55.9867 3427.7404 2000.0000 diff --git a/docs/source/operations/conversions/set.rst b/docs/source/operations/conversions/set.rst index 635d08d32f..8c1d5418e8 100644 --- a/docs/source/operations/conversions/set.rst +++ b/docs/source/operations/conversions/set.rst @@ -47,7 +47,7 @@ the reverse direction. +step +proj=vgridshift +grids=nlgeo2018.gtx \ +step +proj=push +v_3 \ +step +proj=set +v_3=43 \ - +step +proj=cart +ellps=GRS80 \ + +step +proj=cart \ +step +proj=helmert +x=-565.7346 +y=-50.4058 +z=-465.2895 +rx=-0.395023 +ry=0.330776 +rz=-1.876073 +s=-4.07242 +convention=coordinate_frame +exact \ +step +proj=cart +inv +ellps=bessel \ +step +proj=hgridshift +inv +grids=rdcorr2018.gsb,null \ diff --git a/docs/source/operations/conversions/topocentric.rst b/docs/source/operations/conversions/topocentric.rst index 14019965d9..4c0d3d135b 100644 --- a/docs/source/operations/conversions/topocentric.rst +++ b/docs/source/operations/conversions/topocentric.rst @@ -57,7 +57,7 @@ Convert geocentric coordinates to topocentric coordinates, with the topocentric origin specified in geocentric coordinates:: echo 3771793.968 140253.342 5124304.349 2020 | \ - cct -d 3 +proj=topocentric +ellps=WGS84 +X_0=3652755.3058 +Y_0=319574.6799 +Z_0=5201547.3536 + cct -d 3 +proj=topocentric +X_0=3652755.3058 +Y_0=319574.6799 +Z_0=5201547.3536 -189013.869 -128642.040 -4220.171 2020.0000 @@ -65,8 +65,8 @@ Convert geographic coordinates to topocentric coordinates, with the topocentric origin specified in geographic coordinates:: echo 2.12955 53.80939444 73 2020 | cct -d 3 +proj=pipeline \ - +step +proj=cart +ellps=WGS84 \ - +step +proj=topocentric +ellps=WGS84 +lon_0=5 +lat_0=55 +h_0=200 + +step +proj=cart \ + +step +proj=topocentric +lon_0=5 +lat_0=55 +h_0=200 -189013.869 -128642.040 -4220.171 2020.0000 diff --git a/docs/source/operations/conversions/unitconvert.rst b/docs/source/operations/conversions/unitconvert.rst index 13ca922886..7de98b8dad 100644 --- a/docs/source/operations/conversions/unitconvert.rst +++ b/docs/source/operations/conversions/unitconvert.rst @@ -26,16 +26,16 @@ of that. Many North American systems are defined with coordinates in feet. For example in Vermont:: - +proj=pipeline - +step +proj=tmerc +lat_0=42.5 +lon_0=-72.5 +k_0=0.999964286 +x_0=500000.00001016 +y_0=0 - +step +proj=unitconvert +xy_in=m +xy_out=us-ft + +proj=pipeline \ + +step +proj=tmerc +lat_0=42.5 +lon_0=-72.5 +k_0=0.999964286 +x_0=500000.00001016 \ + +step +proj=unitconvert +xy_out=us-ft Often when working with GNSS data the timestamps are presented in GPS-weeks, but when the data transformed with the `helmert` operation timestamps are expected to be in units of decimalyears. This can be fixed with `unitconvert`:: - +proj=pipeline - +step +proj=unitconvert +t_in=gps_week +t_out=decimalyear + +proj=pipeline \ + +step +proj=unitconvert +t_in=gps_week +t_out=decimalyear \ +step +proj=helmert +epoch=2000.0 +t_obs=2017.5 ... Parameters @@ -44,16 +44,16 @@ Parameters .. option:: +xy_in= or Horizontal input units. See :ref:`distance_units` and :ref:`angular_units` - for a list of available units. `` is the conversion factor + for a list of available units. Default: meter. `` is the conversion factor from the input unit to metre for linear units, or to radian for angular - units. + units. Default if not given: meters. .. option:: +xy_out= or Horizontal output units. See :ref:`distance_units` and :ref:`angular_units` - for a list of available units. `` is the conversion factor + for a list of available units. Deault: meter. `` is the conversion factor from the output unit to metre for linear units, or to radian for angular - units. + units. Default if not given: meters. .. option:: +z_in= or diff --git a/docs/source/operations/options/x_0.rst b/docs/source/operations/options/x_0.rst index ed4020d842..b80787c90f 100644 --- a/docs/source/operations/options/x_0.rst +++ b/docs/source/operations/options/x_0.rst @@ -1,5 +1,5 @@ .. option:: +x_0= - False easting. + False easting, in meters. *Defaults to 0.0.* diff --git a/docs/source/operations/projections/bertin1953.rst b/docs/source/operations/projections/bertin1953.rst index 65afcf62e2..bbed0c80b0 100644 --- a/docs/source/operations/projections/bertin1953.rst +++ b/docs/source/operations/projections/bertin1953.rst @@ -44,7 +44,7 @@ Usage The Bertin 1953 projection has no special options. Its rotation parameters are fixed. Here is an example of a forward projection with scale 1:: - $ echo 122 47 | src/proj +proj=bertin1953 +R=1 + $ echo 122 47 | proj +proj=bertin1953 +R=1 0.72 0.73 Parameters diff --git a/docs/source/operations/projections/cass.rst b/docs/source/operations/projections/cass.rst index 073fe6cc7b..fb3b3576d4 100644 --- a/docs/source/operations/projections/cass.rst +++ b/docs/source/operations/projections/cass.rst @@ -40,12 +40,18 @@ The Cassini-Soldner was also used for the detailed mapping of many German states Example using EPSG 30200 (Trinidad 1903, units in clarke's links):: - $ echo 0.17453293 -1.08210414 | proj +proj=cass +lat_0=10.44166666666667 +lon_0=-61.33333333333334 +x_0=86501.46392051999 +y_0=65379.0134283 +a=6378293.645208759 +b=6356617.987679838 +to_meter=0.201166195164 + $ echo 0.17453293 -1.08210414 | proj +proj=cass \ + +lat_0=10.44166666666667 +lon_0=-61.33333333333334 \ + +x_0=86501.46392051999 +y_0=65379.0134283 \ + +a=6378293.645208759 +b=6356617.987679838 \ + +to_meter=0.201166195164 66644.94 82536.22 Example using EPSG 3068 (Soldner Berlin):: - $ echo 13.5 52.4 | proj +proj=cass +lat_0=52.41864827777778 +lon_0=13.62720366666667 +x_0=40000 +y_0=10000 +ellps=bessel +units=m + $ echo 13.5 52.4 | proj +proj=cass \ + +lat_0=52.41864827777778 +lon_0=13.62720366666667 \ + +x_0=40000 +y_0=10000 +ellps=bessel 31343.05 7932.76 Options diff --git a/docs/source/operations/projections/gall.rst b/docs/source/operations/projections/gall.rst index ba83d45099..6ef99d0fcf 100644 --- a/docs/source/operations/projections/gall.rst +++ b/docs/source/operations/projections/gall.rst @@ -49,12 +49,12 @@ Unlike the Mercator, the Gall shows the poles as lines running across the top an Example using Gall Stereographic :: - $ echo 9 51 | proj +proj=gall +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +units=m + $ echo 9 51 | proj +proj=gall 708432.90 5193386.36 Example using Gall Stereographic (Central meridian 90°W) :: - $ echo 9 51 | proj +proj=gall +lon_0=90w +x_0=0 +y_0=0 +ellps=WGS84 +units=m + $ echo 9 51 | proj +proj=gall +lon_0=90w 7792761.91 5193386.36 Parameters diff --git a/docs/source/operations/projections/gs50.rst b/docs/source/operations/projections/gs50.rst index a5694f9488..5378c25a89 100644 --- a/docs/source/operations/projections/gs50.rst +++ b/docs/source/operations/projections/gs50.rst @@ -1,7 +1,7 @@ .. _gs50: ******************************************************************************** -Modified Stereographic of 50 U.S. +Modified Stereographic of the 50 U.S. states ******************************************************************************** +---------------------+----------------------------------------------------------+ @@ -24,7 +24,7 @@ Modified Stereographic of 50 U.S. .. figure:: ./images/gs50.png :width: 500 px :align: center - :alt: Modified Stereographic of 50 U.S. + :alt: Modified Stereographic of the 50 U.S. states proj-string: ``+proj=gs50`` diff --git a/docs/source/operations/projections/healpix.rst b/docs/source/operations/projections/healpix.rst index 41bc10dbd7..ec00f90a5d 100644 --- a/docs/source/operations/projections/healpix.rst +++ b/docs/source/operations/projections/healpix.rst @@ -40,7 +40,7 @@ Usage To run a forward HEALPix projection on a unit sphere model, use the following command:: - proj +proj=healpix +lon_0=0 +a=1 -E < 55 12 > EOF 55 12 6115727.86 1553840.13 diff --git a/docs/source/operations/projections/s2.rst b/docs/source/operations/projections/s2.rst index 46ae715e81..e29ab65d23 100644 --- a/docs/source/operations/projections/s2.rst +++ b/docs/source/operations/projections/s2.rst @@ -82,7 +82,7 @@ Usage The following example uses S2 on the right face:: - echo 90 0 | ../bin/proj +proj=s2 +lat_0=0 +lon_0=90 +ellps=WGS84 +UVtoST=linear + echo 90 0 | proj +proj=s2 +lat_0=0 +lon_0=90 +ellps=WGS84 +UVtoST=linear 0.5 0.5 diff --git a/docs/source/operations/projections/som.rst b/docs/source/operations/projections/som.rst index 124fff9194..d3cf437786 100644 --- a/docs/source/operations/projections/som.rst +++ b/docs/source/operations/projections/som.rst @@ -40,7 +40,7 @@ satellite data to be represented accurately as a rectangular array. proj-string: ``+proj=som +inc_angle=98.303820000243860022 +ps_rev=0.06866666666666667 +asc_lon=64.412896137498847793`` - proj-string: ``+proj=som +inc_angle=1.7157253262878522r +ps_rev=0.06866666666666667 +asc_lon=1.1242171183417042r`` + (gives same results as: ``+proj=som +inc_angle=1.7157253262878522r +ps_rev=0.06866666666666667 +asc_lon=1.1242171183417042r``) Parameters ################################################################################ diff --git a/docs/source/operations/projections/tmerc.rst b/docs/source/operations/projections/tmerc.rst index 576ad32733..879f3bf398 100644 --- a/docs/source/operations/projections/tmerc.rst +++ b/docs/source/operations/projections/tmerc.rst @@ -64,12 +64,12 @@ The following table gives special cases of the Transverse Mercator projection. Example using Gauss-Kruger on Germany area (aka EPSG:31467) :: - $ echo 9 51 | proj +proj=tmerc +lat_0=0 +lon_0=9 +k_0=1 +x_0=3500000 +y_0=0 +ellps=bessel +units=m + $ echo 9 51 | proj +proj=tmerc +lon_0=9 +x_0=3500000 +ellps=bessel 3500000.00 5651505.56 Example using Gauss Boaga on Italy area (EPSG:3004) :: - $ echo 15 42 | proj +proj=tmerc +lat_0=0 +lon_0=15 +k_0=0.9996 +x_0=2520000 +y_0=0 +ellps=intl +units=m + $ echo 15 42 | proj +proj=tmerc +lon_0=15 +k_0=0.9996 +x_0=2520000 +ellps=intl 2520000.00 4649858.60 Parameters diff --git a/docs/source/operations/transformations/defmodel.rst b/docs/source/operations/transformations/defmodel.rst index 8d737e6e56..26c4bc38ba 100644 --- a/docs/source/operations/transformations/defmodel.rst +++ b/docs/source/operations/transformations/defmodel.rst @@ -62,4 +62,5 @@ Transforming a point with the LINZ NZGD2000 deformation model: :: - echo 166.7133850980 -44.5105886020 293.3700 2007.689 | cct +proj=defmodel +model=nzgd2000-20180701.json + echo 166.7133850980 -44.5105886020 293.3700 2007.689 | + cct +proj=defmodel +model=nzgd2000-20180701.json diff --git a/docs/source/operations/transformations/geogoffset.rst b/docs/source/operations/transformations/geogoffset.rst index 6ca4f64c83..a1e1c89ae0 100644 --- a/docs/source/operations/transformations/geogoffset.rst +++ b/docs/source/operations/transformations/geogoffset.rst @@ -39,15 +39,15 @@ Examples Geographic offset from the old Greek geographic 2D CRS to the newer GGRS87 CRS:: - proj=geogoffset dlon=0.28 dlat=-5.86 + +proj=geogoffset +dlon=0.28 +dlat=-5.86 Conversion from Tokyo + JSLD69 height to WGS 84:: - proj=geogoffset dlon=-13.97 dlat=7.94 dh=26.9 + +proj=geogoffset +dlon=-13.97 +dlat=7.94 +dh=26.9 Conversion from Baltic 1977 height to Black Sea height:: - proj=geogoffset dh=0.4 + +proj=geogoffset +dh=0.4 Parameters diff --git a/docs/source/operations/transformations/helmert.rst b/docs/source/operations/transformations/helmert.rst index 78f3621c9f..062d13e5ab 100644 --- a/docs/source/operations/transformations/helmert.rst +++ b/docs/source/operations/transformations/helmert.rst @@ -50,7 +50,8 @@ Transforming coordinates from NAD72 to NAD83 using the 4 parameter 2D Helmert: :: - proj=helmert convention=coordinate_frame x=-9597.3572 y=.6112 s=0.304794780637 theta=-1.244048 + proj=helmert convention=coordinate_frame x=-9597.3572 y=.6112 \ + s=0.304794780637 theta=-1.244048 Simplified transformations from ITRF2008/IGS08 to ETRS89 using 7 parameters: diff --git a/docs/source/operations/transformations/hgridshift.rst b/docs/source/operations/transformations/hgridshift.rst index 70aac061d3..5191f9c2b3 100644 --- a/docs/source/operations/transformations/hgridshift.rst +++ b/docs/source/operations/transformations/hgridshift.rst @@ -63,7 +63,9 @@ the coordinate is part of the coordinate tuple. Suppose we want to model the deformation of the 2008 earthquake in Iceland in a transformation of data from 2005 to 2009:: - echo 63.992 -21.014 10.0 2005.0 | cct +proj=hgridshift +grids=iceland2008.gsb +t_epoch=2008.4071 +t_final=2009.0 + echo 63.992 -21.014 10.0 2005.0 | + cct +proj=hgridshift +grids=iceland2008.gsb \ + +t_epoch=2008.4071 +t_final=2009.0 63.9920021 -21.0140013 10.0 2005.0 .. note:: diff --git a/docs/source/operations/transformations/vertoffset.rst b/docs/source/operations/transformations/vertoffset.rst index c9ea3aba45..8b6b571039 100644 --- a/docs/source/operations/transformations/vertoffset.rst +++ b/docs/source/operations/transformations/vertoffset.rst @@ -30,7 +30,7 @@ Examples Vertical offset from LN02 height to EVRF2000 height with horizontal coordinates in ETRS89:: +proj=vertoffset +lat_0=46.9166666666666666 +lon_0=8.183333333333334 \ - +dh=-0.245 +slope_lat=-0.210 +slope_lon=-0.032 +ellps=GRS80 + +dh=-0.245 +slope_lat=-0.210 +slope_lon=-0.032 Parameters ################################################################################ diff --git a/docs/source/operations/transformations/xyzgridshift.rst b/docs/source/operations/transformations/xyzgridshift.rst index ca3ca88127..86c971e16d 100644 --- a/docs/source/operations/transformations/xyzgridshift.rst +++ b/docs/source/operations/transformations/xyzgridshift.rst @@ -45,8 +45,8 @@ NTF to RGF93 transformation using :file:`gr3df97a.tif` grid +proj=pipeline +step +proj=push +v_3 +step +proj=cart +ellps=clrk80ign - +step +proj=xyzgridshift +grids=gr3df97a.tif +grid_ref=output_crs +ellps=GRS80 - +step +proj=cart +ellps=GRS80 +inv + +step +proj=xyzgridshift +grids=gr3df97a.tif +grid_ref=output_crs + +step +proj=cart +inv +step +proj=pop +v_3 Parameters diff --git a/docs/source/usage/differences.rst b/docs/source/usage/differences.rst index 3bc2f54ddf..1b20d71841 100644 --- a/docs/source/usage/differences.rst +++ b/docs/source/usage/differences.rst @@ -37,19 +37,21 @@ PROJ 5, this was handled incorrectly when a custom central meridian was set with :option:`+lon_0`. This caused a change in sign on the resulting easting as seen below:: - $ proj +proj=merc +lon_0=110 + $ proj +proj=merc +lon_0=110 <