path: root/dk_sdfe/DK

#------------------------------------------------------------------------------------------------------
#
#      PROJ implementations of current and legacy Danish coordinate systems
#
#------------------------------------------------------------------------------------------------------
#
#  This file is Work-In-Progress, and should not be used without great testing care. It is
#  currently provided for informational and testing purposes, but will in due course become
#  the official definition and implementation of transformations to and from Danish systems.
#
#  Revision history:
#  -----------------
#
#  2017-09-??  Initial setup.
#              Kristian Evers <kreve@sdfe.dk>
#
#  2017-11-03  Formal definitions of legacy systems,
#              New datum naming structure
#              Check up on all polynomial transformations.
#              Karsten Engsager, Thomas Knudsen <thokn@sdfe.dk>
#
#  2017-11-08  Clean up, introduce _TC32_TD32, add descriptions
#              Thomas Knudsen <thokn@sdfe.dk>
#
#  2017-12-08  Introduce the Femerbelt system, the Storstrom
#              projection, and a number of seldom-used legacy
#              systems.
#              Karsten Engsager, Thomas Knudsen <thokn@sdfe.dk>
#
#  2018-02-21  Check-up, streamline built-in self-tests, add a
#              number of comments and descriptions, preparing
#              for PROJ 5.0.0 release.
#              Thomas Knudsen <thokn@sdfe.dk>
#
#------------------------------------------------------------------------------------------------------


<metadata> +version=1.0.0 +origin=SDFE +lastupdate=2018-02-26


#------------------------------------------------------------------------------------------------------
#  Vertical datums
#------------------------------------------------------------------------------------------------------
<DVR90> proj=vgridshift grids=dk_sdfe_dvr90.tif            # current
<DNN>   proj=vgridshift grids=dk_sdfe_dnn.tif              # historical
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
#  UTM ETRS89:  The primary system for mapping
#------------------------------------------------------------------------------------------------------
<UTM32N> proj=utm zone=32 ellps=GRS80 units=m no_defs
<UTM33N> proj=utm zone=33 ellps=GRS80 units=m no_defs

<UTM32N_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:UTM32N
<UTM33N_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:UTM33N

<UTM32N_DNN> proj=pipeline step init=DK:DNN step init=DK:UTM32N
<UTM33N_DNN> proj=pipeline step init=DK:DNN step init=DK:UTM33N
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:UTM32N
tolerance   0.1 mm
accept      12 55
expect      691875.6321 6098907.8250
</gie>
#------------------------------------------------------------------------------------------------------


#------------------------------------------------------------------------------------------------------
#  DKTM ETRS89:  Used for construction tasks, where a scale factor close to unity is important
#------------------------------------------------------------------------------------------------------
<DKTM1> proj=etmerc lat_0=0 lon_0=9     k=0.99998 x_0=200000 y_0=-5000000 ellps=GRS80 units=m no_defs
<DKTM2> proj=etmerc lat_0=0 lon_0=10    k=0.99998 x_0=400000 y_0=-5000000 ellps=GRS80 units=m no_defs
<DKTM3> proj=etmerc lat_0=0 lon_0=11.75 k=0.99998 x_0=600000 y_0=-5000000 ellps=GRS80 units=m no_defs
<DKTM4> proj=etmerc lat_0=0 lon_0=15    k=1       x_0=800000 y_0=-5000000 ellps=GRS80 units=m no_defs

<DKTM1_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:DKTM1
<DKTM2_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:DKTM2
<DKTM3_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:DKTM3
<DKTM4_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:DKTM4

<DKTM1_DNN> proj=pipeline step init=DK:DNN step init=DK:DKTM1
<DKTM2_DNN> proj=pipeline step init=DK:DNN step init=DK:DKTM2
<DKTM3_DNN> proj=pipeline step init=DK:DNN step init=DK:DKTM3
<DKTM4_DNN> proj=pipeline step init=DK:DNN step init=DK:DKTM4

#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
#  Kp2000 ETRS89:  A predecessor to DKTM (see above). Kp2000 was never in widespread use.
#------------------------------------------------------------------------------------------------------
<KP2000B> proj=etmerc lat_0=0 lon_0=15  k=1       x_0=900000 y_0=0 ellps=GRS80 units=m no_defs
<KP2000J> proj=etmerc lat_0=0 lon_0=9.5 k=0.99995 x_0=200000 y_0=0 ellps=GRS80 units=m no_defs
<KP2000S> proj=etmerc lat_0=0 lon_0=12  k=0.99995 x_0=500000 y_0=0 ellps=GRS80 units=m no_defs

<KP2000B_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:KP2000B
<KP2000J_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:KP2000J
<KP2000S_DVR90> proj=pipeline step init=DK:DVR90 step init=DK:KP2000S

<KP2000B_DNN> proj=pipeline step init=DK:DNN step init=DK:KP2000B
<KP2000J_DNN> proj=pipeline step init=DK:DNN step init=DK:KP2000J
<KP2000S_DNN> proj=pipeline step init=DK:DNN step init=DK:KP2000S

#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# Storstrom Bridge Map Projection: lon_0=1152nt
#------------------------------------------------------------------------------------------------------
<SSBKP> proj=etmerc  ellps=GRS80
        lat_0=0      lon_0=11.86666666666666666667
        x_0=40000    y_0=-6013000
        k=1          units=m        no_defs
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# Danish Mercator ETRS89 lat_0=56 x_0=500000 -> y_0=-3716499.0435458627
#------------------------------------------------------------------------------------------------------
<DM> proj=merc lat_ts=56 lon_0=9 x_0=500000 y_0=-3716499.0435458627 ellps=GRS80 no_defs
<DMRC> DK:DM
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:DM
tolerance   0.1 mm
accept      12 55
expect      687178.31448147167  390074.81929540867
</gie>
#------------------------------------------------------------------------------------------------------







#------------------------------------------------------------------------------------------------------
#  Danish legacy systems - formal definitions
#------------------------------------------------------------------------------------------------------
#  These formal definitions are for illumination - not for computation.
#  Valid only for observations already measured in the relevant (legacy)
#  reference frame.
#
#  See below for the much more involved setups needed to go to and from
#  the legacy frames.
#------------------------------------------------------------------------------------------------------
# UTM ED50
<_UTM32_ED50_FORMAL> proj=utm zone=32 ellps=intl units=m no_defs
<_UTM33_ED50_FORMAL> proj=utm zone=33 ellps=intl units=m no_defs

# System Storebaelt (lon_0= 10 58 nt)
<_SB_FORMAL> proj=etmerc
            lat_0=0 lon_0=10.96666666666666667 k=0.999999
            x_0=500000 y_0=0 ellps=intl
            units=m  no_defs

# Denmark Sweden Bridge Project System Oeresund (ED50) (lon_0 = 12 48 nt)
<_DKS_FORMAL> proj=etmerc
             lat_0=0  lon_0=12.8  k=0.999999
             x_0=119000  y_0=-5895000 ellps=intl
             units=m no_defs

# Danish Mercator ED50
<_DM_FORMAL> proj=merc ellps=intl lat_ts=56 lon_0=9
            x_0=500000                              y_0=-3716499.0435879501
            overfitted_x_0=499919.274212 overfitted_y_0=-3716691.9921
            units=m no_defs

# Generalstabens lcc Jutland and Zealand (lon_0 = 2 12 nt, W positive)
<_GS_FORMAL>  proj=lcc lat_ts=56 lat_0=55 lon_0=2.2
             x_0=0    y_0=0   ellps=GS

# Generalstabens konform-koniske for Bornholm (lon_0 = -2 21 nt, W positive)
<_GSB_FORMAL> proj=lcc lat_1=56 lat_0=55 lon_0=-2.35 # lat_ts=56
             x_0=18831.460 y_0=5614.621 ellps=GS

# Koebenhavns Kommune
# <_KK_FORMAL>  proj=localcrd ellps=danish units=m no_defs
#------------------------------------------------------------------------------------------------------




#------------------------------------------------------------------------------------------------------
#  Legacy systems - actual transformations
#------------------------------------------------------------------------------------------------------
#
#  Technical implementation
#  -------------------------
#  Most of the transformations to and from the Danish legacy systems are based on a
#  7-parameter Helmert transformation, followed by a bivariate polynomial adjustment.
#
#  The Helmert transformation takes us from the current system (ETRS89) to a system that
#  is sufficiently close to the older systems to allow us to take the final steps using
#  the polynomial ("Horner") way.
#
#  In most cases, the intermediate system is formally ED50: The parameters produce the
#  least squares optimum route from ETRS89 to ED50. But due to the much more stable scale
#  factor of ETRS89, the ED50 coordinates computed using the Helmert step alone reveals
#  the large tensions in the ED50 net:  The Helmert transformed coordinates can be thought
#  of as "ED50 if ED50 had as good a scale factor as ETRS89".
#
#  To discern, we refer to the Helmert transformed datum as "Technical Datum 32",
#  TD32 - a 2D datum for computational use only. A TD32 coordinate transformed
#  to UTM zone 32, is referred to the "Technical Coordinate System 32, on the
#  TD32 datum", _TC32_TD32.
#
#  _TC32_TD32 is the step stone from which the bivariate Horner polynomials takes us the
#  final steps to the target system.
#
#  Naming convention
#  ------------------
#  The transformations to and from Danish legacy systems are named such that to go
#
#  FROM the current system (i.e. for the time being, GEO_ETRS89),
#  TO system X,
#  use the FORWARD method of the transformation accessed as +init=DK:X
#
#  and conversely, to go
#
#  FROM system X
#  TO the current system,
#  use the INVERSE method of the transformation accessed as +init=DK:X
#
#
#  Numerical example
#  ------------------
#  For example, one may transform data from GEO_ETRS89 to System 45 Bornholm
#  using the syntax
#
#      echo 15 55 0 0 | cct +init=DK:S45B
#
#  which will respond with
#
#      42915.059286989766000  37569.188021636372000   -33.327159059233963     0.000000000000000
#
#  And a forward-inverse roundtrip test can be implemented as:
#
#      echo 15 55 0 0 | cct +init=DK:S45B | cct -I +init=DK:S45B
#
#  Which results in this near perfect roundtrip:
#
#      14.999999999998458    55.000000000290619    -0.000000000931323     0.000000000000000
#
#  (the test point 15E, 55N is situated close to the south shore of Bornholm,
#   a few km south of the Pedersker village)
#
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
#  The primary step stone:  _TC32_TD32
#------------------------------------------------------------------------------------------------------
<_TC32_TD32>
    proj=pipeline no_defs
    step proj=cart ellps=GRS80
    step proj=helmert inv
         x = -81.0703   rx = -0.48488
         y = -89.3603   ry = -0.02436
         z =-115.7526   rz = -0.41321   s = -0.540645
         convention = coordinate_frame
    step proj=cart ellps=intl  inv      # Now: GEO_TD32
    step proj=utm  ellps=intl  zone=32  # And now: TC32_TD32 (UTM32 if ED50 was "perfect")
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:_TC32_TD32
tolerance   0.1 mm
accept      9.5 57 0 0
expect      530454.9998 6317704.6255

operation   init=DK:_TC32_TD32
tolerance   0.1 mm
accept      15 55 0 0
expect      883653.4932  6111473.4226
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> UTM32_ED50, valid for Denmark except Bornholm (i.e. west of 13E)
#------------------------------------------------------------------------------------------------------
<UTM32_ED50_L>
    proj=pipeline
    step init=DK:_TC32_TD32
    step init=dk_sdfe_DK_general.pol:TC32_L inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:UTM32_ED50_L
tolerance   40 mm
accept      9.5 57 0 0
expect      530455.2023  6317704.6465
</gie>



#------------------------------------------------------------------------------------------------------
# GEO_ETRS89 -> GEO_ED50, valid for Denmark except Bornholm
#------------------------------------------------------------------------------------------------------
<GEO_ED50_L>  proj=pipeline
              step init=DK:UTM32_ED50_L
              step proj=utm zone=32 ellps=intl units=m no_defs inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:GEO_ED50_L
tolerance   40 mm
accept      9.5 57 0 0
expect      9.501323491951883   57.000587965055587
accept      12 55  0 0
expect      12.001173940  55.000628676      # Authoritative value, obtained from KMSTrans2
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> UTM32_ED50, Bornholm
#------------------------------------------------------------------------------------------------------
<UTM32_ED50_B> proj=pipeline  ellps=GRS80
     step init=DK:_TC32_TD32
     step init=dk_sdfe_DK_bornholm.pol:UTM32_ED50_B     # no inv here, due to polynomial swap in DK_bornholm.pol
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:UTM32_ED50_B
tolerance   30 mm
accept      15 55 0 0
expect      883654.5767  6111474.6515    # Authoritative value, obtained from KMSTrans2
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> UTM33_ED50, Bornholm
#------------------------------------------------------------------------------------------------------
<UTM33_ED50_B> proj=pipeline  ellps=GRS80
     step init=DK:UTM32_ED50_B
     step proj=utm zone=32 ellps=intl units=m no_defs inv
     step proj=utm zone=33 ellps=intl units=m no_defs
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:UTM33_ED50_B
tolerance   30 mm
accept      15 55 0 0
expect      500071.1125   6094991.2120    # Authoritative value, obtained from KMSTrans2
</gie>
#------------------------------------------------------------------------------------------------------


#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> GEO_ED50, Bornholm
<GEO_ED50_B>  proj=pipeline  ellps=GRS80
    step init=DK:UTM32_ED50_B
    step proj=utm zone=32 ellps=intl units=m no_defs inv
<ED50_B>  init=DK:GEO_ED50_B
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:GEO_ED50_B
tolerance   30 mm
accept      15 55 0 0
expect      15.001111641   55.000603892    # Authoritative value, obtained from KMSTrans2
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> System45
#------------------------------------------------------------------------------------------------------
<S45B>  proj=pipeline no_defs
        step   init=DK:_TC32_TD32
        step   init=dk_sdfe_DK_bornholm.pol:TC32_B inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:S45B
tolerance   40 mm
accept      15 55 0 0
expect      42915.0596  37569.1876    # Authoritative value, obtained from KMSTrans2
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> System 34 Jutland
#------------------------------------------------------------------------------------------------------
<S34J>  proj=pipeline  ellps=GRS80
        step   init=DK:_TC32_TD32
        step   init=dk_sdfe_DK_jutland.pol:TC32_L inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:S34J
tolerance   40 mm
accept      9.5 57 0 0
expect      263190.2497  286078.3847
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> System 34 Zealand
#------------------------------------------------------------------------------------------------------
<S34S>  proj=pipeline  ellps=GRS80
        step   init=DK:_TC32_TD32
        step   init=dk_sdfe_DK_zealand.pol:TC32_L inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:S34S
tolerance   40 mm
accept      12.5 55.7 0 0
expect      76425.6474  143042.0038
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# System Storebaelt (Great Belt system)
#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> System Storebaelt (The Great Belt System)
#------------------------------------------------------------------------------------------------------
<SB> proj=pipeline  no_defs
        step init=DK:UTM32_ED50_L
        step init=dk_sdfe_DK_bridges.pol:UTM32_ED50_L inv   # tol = 0.5 mm
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:SB
tolerance   30 mm
accept      11 55.3 0 0
expect      502194.1051  6130826.4745
accept      10.891109758 55.319726643 0 0
expect      495280.2216  6133024.6786

direction   inverse
accept      502194.1051  6130826.4745 0 0
expect      11 55.3
accept      495280.2216  6133024.6786 0 0
expect      10.891109758 55.319726643
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# Denmark Sweden Bridge Project System Oeresund (ED50) (lon_0 = 12 48 nt)
#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> Denmark Sweden Bridge Project System (ED50)
#------------------------------------------------------------------------------------------------------
<DKS>  proj=pipeline  no_defs
       step   init=DK:S34S
       step   init=dk_sdfe_DK_bridges.pol:S34S inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:DKS
tolerance   30 mm
accept      12.7  55.66 0 0
expect      112779.7960  275908.0748   # Authoritative value, obtained from KMSTrans2
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> Generalstabens System, except Bornholm
#------------------------------------------------------------------------------------------------------
<GS>  proj=pipeline  ellps=GRS80
    step   init=DK:UTM32_ED50_L
    step   init=dk_sdfe_DK_general.pol:GS
#------------------------------------------------------------------------------------------------------
<GEO_GS> proj=pipeline  ellps=GRS80
    step   init=DK:GS
    step   init=DK:GS_FORMAL inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:GS
tolerance   30 mm
accept      8.998706228455516 55.999371897298793  0  0
expect      85938.0998  112123.5083
accept      10  57 0 0
expect      22859.7375 222752.8941
direction   inverse
accept      22859.7375 222752.8941 0 0
expect      10  57
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> Generalstabens System Bornholm
#------------------------------------------------------------------------------------------------------
# Implemented as a 4th order complex polynomium going from UTM33_ED50
# to System GS Bornholm. The datum shift from ETRS89 to ED50 is done
# in the UTM33_ED50_B step.
#
# The complex polynomium partially implements a further datum shift,
# to System GS Bornholm, partially carries out the conformal mapping
# from UTM to the Lambert Conformal Conic, which is the formal basis
# of the GS systems.
#------------------------------------------------------------------------------------------------------
<GSB>  proj=pipeline  ellps=GRS80
    step   init=DK:UTM33_ED50_B
    step   init=dk_sdfe_DK_bornholm.pol:GSB
#------------------------------------------------------------------------------------------------------
<GEO_GSB> proj=pipeline  ellps=GRS80       #
    step   init=DK:GSB
    step   init=DK:_GSB_FORMAL inv
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:GSB
tolerance   30 mm
accept      15  55 0 0
expect      14063.5412  5598.3811
direction inverse
accept      14063.5412  5598.3811 0 0
expect      15  55
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# Koebenhavns Kommune Koordinatsystem
#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> System Koebenhavns Kommune
#------------------------------------------------------------------------------------------------------
<KK>  proj=pipeline no_defs
      step   init=DK:S34S
      step   init=dk_sdfe_DK_zealand.pol:KK
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:KK
tolerance   30 mm
accept      12.5  55.7 0 0
expect     -133514.7527  79977.9650   # Authoritative value, obtained from KMSTrans2
direction  inverse
accept     -133514.7527  79977.9650  0 0
expect      12.5  55.7
</gie>
#------------------------------------------------------------------------------------------------------







#------------------------------------------------------------------------------------------------------
# System Ostenfeld (South Jutland, Part of Germany before 1920)
#
# NOT READY YET
#------------------------------------------------------------------------------------------------------
# <OS_FORMAL> proj=localcrd ellps=bessel units=m no_defs
#------------------------------------------------------------------------------------------------------
# ETRS89 (Geodetic) -> System Ostenfeld
#------------------------------------------------------------------------------------------------------
<OS>  proj=pipeline ellps=GRS80
    step   init=DK:S34J
    step   init=dk_sdfe_DK_jutland.pol:OS
    step   proj=axisswap order=2,1
#------------------------------------------------------------------------------------------------------
<gie>
operation   init=DK:OS
tolerance   30 mm
accept      9  55 0 0
expect      59184.3614  -14910.8690  # KMSTrans2
direction   inverse
accept      59184.3614  -14910.8690  0 0
expect      9  55
</gie>
#------------------------------------------------------------------------------------------------------



#------------------------------------------------------------------------------------------------------
# Missing: Danske Mercator ED50 & Vertical reference frame transformations
#------------------------------------------------------------------------------------------------------