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API for coordinate conversion routines (geo.c)

Data structures:

  • DMS
    Structure holding degree, minutes & seconds.

  • ELLIPSOID
    Structure holding parameters and some precalculated constants for series for given ellipsoid.

  • HELMERT7
    Parameters for Helmert 7-parameters transformation, including precalculated rotation matrix.

  • PROJ
    Projection parameters for Gauss-Krueger/Transverse Mercator projections.

  • GEOGRA
    Structure holding geodetic/geographic coordinates (fi, la, h).

  • GEOUTM
    Structure holding geographic cartesian coordinates (x, y, H).

  • GEOCEN
    Structure holding geocentric cartesian coordinates (X, Y, Z).

  • AFT
    Structure holding affine transformation data (source and destination triangle coordinates and pre-calculated parameters for direct affine transformation for this triangle).

Global variables:

  • gid_wgs
    Selected geoid model on WGS84 (Slo2000 or EGM2008; via cmd-line or default).

  • hsel
    Selected type of output height (transformed height, copied height or geoid height; via cmd-line or default).

Initialization routines:

  • ellipsoid_init
    Initializes parameters and precalculate series' constants for 3 ellipsoids:

    • Bessel 1841
    • WGS84
    • GRS_80

  • params_init
    Initializes parameters for Helmert 7-parameters transformations, projection parameters (luckily both projections GK and TM are the same for Slovenia) and some geoid model data.

Supporting routines:

  • geoid_height
    Calculates geoid height from fi,la and given geoid id using bilinear interpolation. Both included geoid models (Slo2000 and EGM2008) cover only the area between:

    • N 45°15' – 47°00' in 1.0' steps (105 cells)
    • E 13°15' – 16°45' in 1.5' steps (140 cells)

    Missing values in Slo2000 geoid model (on Slovenia borders) are filled with the same value as current value.

  • coord_in_triangle
    Checks whether specified x,y coordinates (GK or TM) lie within or on borders of specified triangle (from AFT array). Algorithm first checks if the point is contained in a triangle bounding box, then performs the normal check and at the end an additional check, if the point lies on triangle borders (within ε distance).

  • xy2fila_ellips
    Transforms x,y,H coordinates (GK or TM) to fi,la,h on specified ellipsoid oid. Coordinates are first converted from relative to real coordinates according to projection, then fi and la are calculated. In the end geoid height for this point is used in calculating output h.

  • fila_ellips2xy
    Transforms fi,la,h coordinates to x,y,H (GK or TM) on specified ellipsoid oid. First the geoid height for given point is calculated, fi and la are converted to radians and then x and y are calculated. In the end the precalculated geoid height is used in calculating output h.

  • xyz2fila_ellips
    Transforms cartesian X,Y,Z coordinates to fi,la,h on specified ellipsoid oid using Bowring's algorithm. Output h is calculated via algorithm. In the end fi and la are converted from radians to degrees.

  • fila_ellips2xyz
    Transforms fi,la,h coordinates to cartesian X,Y,Z on specified ellipsoid oid. First fi and la are converted to radians, then X,Y and Z are calculated using ISO/DIS 19111:2001 algorithm.

  • xyz2xyz_helmert
    Transforms cartesian X,Y,Z coordinates to cartesian X,Y,Z using specified Helmert 7-parameters transformation using the following formula [Xo;Yo;Zo] = [Xt;Yt;Zt] + (1 + s)*R*[Xi;Yi;Zi], where R: rotation matrix.

Main conversion routines:

  • gkxy2fila_wgs
    Transforms Gauss-Krueger x,y,H coordinates on Bessel 1841 to fi,la,h on WGS84 using the following steps:

    • converts GK x,y,H on Bessel 1841 to fi,la,h on Bessel 1841 using xy2fila_ellips()
    • converts fi,la,h on Bessel 1841 to X,Y,Z on Bessel 1841 using fila_ellips2xyz()
    • converts X,Y,Z on Bessel 1841 to X,Y,Z on WGS84 using xyz2xyz_helmert()
    • converts X,Y,Z on WGS84 to fi,la,h on WGS84 using xyz2fila_ellips()

    In the end the correct height is calculated according to selected type of output height (transformed, copied or geoid height).

  • fila_wgs2gkxy
    Transforms fi,la,h coordinates on WGS84 to Gauss-Krueger x,y,H on Bessel 1841 using the following steps:

    • the geoid height for given point is calculated
    • converts fi,la,h on WGS84 to X,Y,Z on WGS84 using fila_ellips2xyz()
    • converts X,Y,Z on WGS84 to X,Y,Z on Bessel 1841 using xyz2xyz_helmert()
    • converts X,Y,Z on Bessel 1841 to fi,la,h on Bessel 1841 using xyz2fila_ellips()
    • converts fi,la,h on Bessel 1841 to GK x,y,H on Bessel 1841 using fila_ellips2xy()

    In the end the correct height is calculated according to selected type of output height (transformed, copied or geoid height).

  • gkxy2tmxy
    Transforms Gauss-Krueger x,y,H coordinates on Bessel 1841 to Transverse Mercator n,e,H on WGS84 using the following steps:

    • converts GK x,y,H on Bessel 1841 to fi,la,h on Bessel 1841 using xy2fila_ellips()
    • converts fi,la,h on Bessel 1841 to X,Y,Z on Bessel 1841 using fila_ellips2xyz()
    • converts X,Y,Z on Bessel 1841 to X,Y,Z on WGS84 using xyz2xyz_helmert()
    • converts X,Y,Z on WGS84 to fi,la,h on WGS84 using xyz2fila_ellips()
    • converts fi,la,h on WGS84 to TM n,e,H on WGS84 using fila_ellips2xy()

    In the end the correct height is calculated according to selected type of output height (transformed, copied or geoid height).

  • tmxy2gkxy
    Transforms Transverse Mercator n,e,H coordinates on WGS84 to Gauss-Krueger x,y,H on Bessel 1841 using the following steps:

    • converts TM n,e,H on WGS84 to fi,la,h on WGS84 using xy2fila_ellips()
    • converts fi,la,h on WGS84 to X,Y,Z on WGS84 using fila_ellips2xyz()
    • converts X,Y,Z on WGS84 to X,Y,Z on Bessel 1841 using xyz2xyz_helmert()
    • converts X,Y,Z on Bessel 1841 to fi,la,h on Bessel 1841 using xyz2fila_ellips()
    • converts fi,la,h on Bessel 1841 to GK x,y,H on Bessel 1841 using fila_ellips2xy()

    In the end the correct height is calculated according to selected type of output height (transformed, copied or geoid height).

  • gkxy2tmxy_aft
    Transforms Gauss-Krueger x,y,H coordinates on Bessel 1841 to Transverse Mercator n,e,H on WGS84 using affine/triangle-based transformation with 899 reference virtual tie points (already built-in).

    Input height is copied to the output height.

  • tmxy2gkxy_aft
    Transforms Transverse Mercator n,e,H coordinates on WGS84 to Gauss-Krueger x,y,H on Bessel 1841 using affine/triangle-based transformation with 899 reference virtual tie points (already built-in).

    Input height is copied to the output height.

  • tmxy2fila_wgs
    Transforms Transverse Mercator n,e,H coordinates on WGS84 to fi,la,h on WGS84 using the following steps:

    • converts TM n,e,H on WGS84 to fi,la,h on WGS84 using xy2fila_ellips()

    In the end the correct height is calculated according to selected type of output height (only copied or geoid height possible).

  • fila_wgs2tmxy
    Transforms fi,la,h coordinates on WGS84 to Transverse Mercator n,e,H on WGS84 using the following steps:

    • converts fi,la,h on WGS84 to TM n,e,H on WGS84 using fila_ellips2xy()

    In the end the correct height is calculated according to selected type of output height (only copied or geoid height possible).

  • gkxy2fila_wgs_aft
    Transforms Gauss-Krueger x,y,H coordinates on Bessel 1841 to fi,la,h on WGS84 using affine/triangle-based transformation:

    • converts GK x,y,H on Bessel 1841 to TM n,e,H on WGS84 using gkxy2tmxy_aft()
    • converts TM n,e,H on WGS84 to fi,la,h on WGS84 using tmxy2fila_wgs()

    Correct height is calculated in tmxy2fila_wgs() according to selected type of output height (only copied or geoid height possible).

  • fila_wgs2gkxy_aft
    Transforms fi,la,h coordinates on WGS84 to Gauss-Krueger x,y,H on Bessel 1841 using affine/triangle-based transformation:

    • converts fi,la,h on WGS84 to to TM n,e,H on WGS84 using fila_wgs2tmxy()
    • converts TM n,e,H on WGS84 to GK x,y,H on Bessel 1841 using tmxy2gkxy_aft()

    Correct height is calculated in fila_wgs2tmxy() according to selected type of output height (only copied or geoid height possible).

Additional routines:

  • xy2fila_ellips_loop
    Transforms x,y,H coordinates (GK or TM) to fi,la,h on specified ellipsoid oid using loop search over fi,la coordinates. This search is currently implemented only for GK zone 5 (Slovenia). Loop using fila_ellips2xy() ends when precision is good enough or fi,la,h are not found. In the end geoid height for this point is used in calculating output h.

  • fila_ellips2xy_loop
    Transforms fi,la,h coordinates to x,y,H (GK or TM) on specified ellipsoid oid using loop search over x,y coordinates. This search is currently implemented only for GK zone 5 (Slovenia). First the geoid height for given point is calculated, then loop using xy2fila_ellips() is executed until precision is good enough or fi,la,h are not found. In the end the precalculated geoid height is used in calculating output h.

These two routines are included for curiosity only.

Supporting libraries:

  • shapelib v1.3.0
    The Shapefile C Library provides routines needed for reading and writing ESRI Shapefiles (.shp) and the associated attribute files (.dbf):

    • SHPOpen, DBFOpen, SHPGetInfo, SHPCreate, DBFCloneEmpty, SHPComputeExtents, SHPWriteObject, DBFWriteTuple, ...