Introduce compatibility for cs2cs-style proj-strings into the 4D API.

Parameters such as towgs84, nadgrids and geoidgrids was previously only
handled by pj_transform(). This commit add a compatibility layer in
proj_create() by calling the pj_cs2cs_emulation_setup() function. This
function sets up a handful of predefined transformation objects on the
PJ object that is being created. Each of these transformation objects
are related to the cs2cs-style parameters we are trying to emulate in
the 4D API. That is, if the +towgs84 parameters is used we create
P->helmert with the parameters specified in +towgs84. Similarly for
+axis, +nadgrids and +geoidgrids. When these transformation objects
exists we use them in the prepare and finalize functions in pj_fwd/
pj_inv. If no cs2cs-style parametes are specified we skip those
parts of the prepare and finalizing steps.

Co-authored-by:Thomas Knudsen <thokn@sdfe.dk>
Co-authored-by:Kristian Evers <kristianevers@gmail.com>

4 files changed, 182 insertions, 16 deletions

diff --git a/test/gie/4D-API_cs2cs-style.gie b/test/gie/4D-API_cs2cs-style.gie
new file mode 100644
index 00000000..853df993
--- /dev/null
+++ b/test/gie/4D-API_cs2cs-style.gie
@@ -0,0 +1,161 @@
+===============================================================================
+
+Test the 4D API handling of cs2cs style transformation options.
+
+These tests are mostly based on the same material as those in
+more_builtins.gie, since we are testing the same kinds of things,
+but provided through a different interface.
+
+===============================================================================
+
+
+<gie>
+
+-------------------------------------------------------------------------------
+Test the handling of the +towgs84 parameter
+-------------------------------------------------------------------------------
+This example is from Lotti Jivall: "Simplified transformations from
+ITRF2008/IGS08 to ETRS89 for maritime applications". The original
+XYZ data (cf. more_builtins.gie) have been transformed to LPZ using
+this command: echo x_val y_val z_val | cct -It0 proj=cart ellps=GRS80 --
+
+NOTE: Here, the ellipsoid has been swapped to WGS84, to align with
+      the WGS84 ellipsoid used in the cs2cs emulation introduced by
+      pj_cs2cs_emulation_setup()
+-------------------------------------------------------------------------------
+operation proj=latlong ellps=WGS84
+          towgs84 =  0.676780,  0.654950, -0.528270,
+                    -0.022742,  0.012667,  0.022704, -0.010700
+-------------------------------------------------------------------------------
+tolerance 0.05 mm
+direction forward
+
+accept    13.4999969828397   54.9999995493206   -0.6034
+expect    13.4999906103972   54.9999957469562   -0.6374
+
+direction inverse
+
+accept    13.4999906103972   54.9999957469562   -0.6374
+expect    13.4999969828397   54.9999995493206   -0.6034
+-------------------------------------------------------------------------------
+
+
+
+-------------------------------------------------------------------------------
+This example is a random point, transformed from ED50 to ETRS89 using KMStrans2.
+
+NOTE: Signs swapped wrt. KMStrans2, which apparently uses frame rotation.
+-------------------------------------------------------------------------------
+operation proj=latlong ellps=intl
+          towgs84 =  081.07030, 089.36030, 115.75260,
+                     000.48488, 000.02436, 000.41321, 0.540645
+-------------------------------------------------------------------------------
+tolerance  0.1 mm
+# echo SWAPPED and trimmed - expect succcess
+# accept     16.819999997    55.170000002        61.0
+accept     16.82    55.17        61.0
+expect     16.8210462130   55.1705688946       29.0317
+-------------------------------------------------------------------------------
+This commented-out version of the example above was used to detect the sign
+discrepancy between KMSTrans2 and PROJ.
+-------------------------------------------------------------------------------
+operation proj=latlong ellps=intl
+          towgs84 =  -081.07030, -089.36030, -115.75260,
+                     -000.48488, -000.02436, -000.41321, -0.540645
+-------------------------------------------------------------------------------
+# echo NOT SWAPPED - Expect failure
+# accept     16.8210462130   55.1705688946       29.0317
+# expect     16.819999997    55.170000002        61.0
+-------------------------------------------------------------------------------
+
+
+
+-------------------------------------------------------------------------------
+operation  proj=latlong nadgrids=nzgd2kgrid0005.gsb  ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 1 nm
+accept    173                 -45                  0 0
+expect    172.999892181021551 -45.001620431954613  0 0
+direction inverse
+accept    172.999892181021551 -45.001620431954613  0 0
+expect    173                 -45                  0 0
+-------------------------------------------------------------------------------
+
+
+
+-------------------------------------------------------------------------------
+operation  proj=latlong geoidgrids=egm96_15.gtx  ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 15 cm      # lax tolerance due to widespread bad egm96 file
+accept    12.5 55.5   0
+expect    12.5 55.5 -36.0213
+direction inverse
+accept    12.5 55.5 -36.0213
+expect    12.5 55.5  0
+-------------------------------------------------------------------------------
+operation  proj=merc geoidgrids=egm96_15.gtx  ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 0.1 mm
+accept    12.5 55.5 0
+expect    1391493.63492   7424275.19462  -36.0213
+direction inverse
+accept    1391493.63492   7424275.19462  -36.0213
+expect    12.5 55.5 0
+-------------------------------------------------------------------------------
+
+
+
+-------------------------------------------------------------------------------
+Same as the two above, but also do axis swapping.
+-------------------------------------------------------------------------------
+operation  proj=latlong geoidgrids=egm96_15.gtx  axis=neu ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 15 cm      # lax tolerance due to widely distributed, bad egm96 file
+accept    12.5 55.5  0
+expect    55.5 12.5 -36.0213
+direction inverse
+accept    55.5 12.5 -36.0213
+expect    12.5 55.5  0
+-------------------------------------------------------------------------------
+operation  proj=latlong geoidgrids=egm96_15.gtx  axis=dne ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 15 cm      # lax tolerance due to widely distributed, bad egm96 file
+accept    12.5 55.5  0
+expect    36.0213 55.5 12.5
+direction inverse
+accept    36.0213 55.5 12.5
+expect    12.5 55.5  0
+-------------------------------------------------------------------------------
+operation  proj=merc geoidgrids=egm96_15.gtx  ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 0.1 mm
+accept    12.5 55.5 0
+expect    1391493.63492   7424275.19462  -36.0213
+direction inverse
+accept    1391493.63492   7424275.19462  -36.0213
+expect    12.5 55.5 0
+-------------------------------------------------------------------------------
+
+
+-------------------------------------------------------------------------------
+Some more complex axis swapping.
+-------------------------------------------------------------------------------
+operation  proj=latlong geoidgrids=egm96_15.gtx  axis=nue ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 15 cm      # lax tolerance due to widely distributed, bad egm96 file
+accept    12.5 55.5 0
+expect    55.5 -36.0213 12.5
+direction inverse
+accept    55.5 -36.0213 12.5
+expect    12.5 55.5 0
+-------------------------------------------------------------------------------
+operation  proj=merc geoidgrids=egm96_15.gtx axis=sue ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 15 cm
+accept    12.5 55.5 0
+expect    -7424275.1946 -36.0213  1391493.6349 0.0000
+direction inverse
+accept    -7424275.1946 -36.0213  1391493.6349 0.0000
+expect    12.5 55.5 0
+-------------------------------------------------------------------------------
+</gie>
diff --git a/test/gie/axisswap.gie b/test/gie/axisswap.gie
index ac148a92..190ca3e7 100644
--- a/test/gie/axisswap.gie
+++ b/test/gie/axisswap.gie
@@ -53,9 +53,14 @@ expect      3 -2 1 4
 roundtrip   100
 
 operation   proj=axisswap axis=neu
-tolerance   0.000001 m
-accept      1 2 3 4
-expect      2 1 3 4
+tolerance   0 m
+accept      1 2 3
+expect      2 1 3
+
+operation   proj=axisswap axis=nue
+tolerance   0 m
+accept      1 2 3
+expect      2 3 1
 
 operation   proj=axisswap axis=swd
 tolerance   0.000001 m
diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie
index 3877b58a..e8f1bfe1 100644
--- a/test/gie/builtins.gie
+++ b/test/gie/builtins.gie
@@ -1233,14 +1233,14 @@ Geocentric
 operation +proj=geocent   +ellps=GRS80  +lat_1=0.5 +lat_2=2
 -------------------------------------------------------------------------------
 tolerance 0.00010 mm
-accept  2 1
-expect  222638.981586547 111319.490793274
-accept  2 -1
-expect  222638.981586547 -111319.490793274
-accept  -2 1
-expect  -222638.981586547 111319.490793274
-accept  -2 -1
-expect  -222638.981586547 -111319.490793274
+accept  2 1 0
+expect  6373287.27950247        222560.09599219 110568.77482092
+accept  2 -1 0
+expect  6373287.27950247        222560.09599219 -110568.77482092
+accept  -2 1 0
+expect  6373287.27950247        -222560.09599219 110568.77482092
+accept  -2 -1 0
+expect  6373287.27950247        -222560.09599219 -110568.77482092
 
 direction inverse
 accept  200 100
diff --git a/test/gie/more_builtins.gie b/test/gie/more_builtins.gie
index 20bffbd9..e21f0321 100644
--- a/test/gie/more_builtins.gie
+++ b/test/gie/more_builtins.gie
@@ -131,11 +131,11 @@ expect    12 55 0 0
 -------------------------------------------------------------------------------
 Finally test a pipeline with more than one init step
 -------------------------------------------------------------------------------
-operation proj=pipeline        step
-          init=epsg:25832 inv  step
-          init=epsg:25833      step
-          init=epsg:25833 inv  step
-          init=epsg:25832
+operation proj=pipeline
+          step init=epsg:25832 inv
+          step init=epsg:25833
+          step init=epsg:25833 inv
+          step init=epsg:25832
 -------------------------------------------------------------------------------
 accept    691875.63214  6098907.82501  0  0
 expect    691875.63214  6098907.82501  0  0