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Index Page recpgr_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       recpgr_c ( Rectangular to planetographic )

       void recpgr_c ( ConstSpiceChar   * body,
                       SpiceDouble        rectan[3],
                       SpiceDouble        re,
                       SpiceDouble        f,
                       SpiceDouble      * lon,
                       SpiceDouble      * lat,
                       SpiceDouble      * alt       )

#### Abstract

       Convert rectangular coordinates to planetographic coordinates.

#### Required_Reading

       KERNEL
       NAIF_IDS
       PCK

#### Keywords

       CONVERSION
       COORDINATES
       GEOMETRY
       MATH

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       body       I   Body with which coordinate system is associated.
       rectan     I   Rectangular coordinates of a point.
       re         I   Equatorial radius of the reference spheroid.
       f          I   Flattening coefficient.
       lon        O   Planetographic longitude of the point (radians).
       lat        O   Planetographic latitude of the point (radians).
       alt        O   Altitude of the point above reference spheroid.

#### Detailed_Input

       body        is the name of the body with which the planetographic
                   coordinate system is associated.

                   `body' is used by this routine to look up from the
                   kernel pool the prime meridian rate coefficient giving
                   the body's spin sense. See the -Files and -Particulars
                   header sections below for details.

       rectan      are the rectangular coordinates of a point. Units
                   are arbitrary, except that the input `re' must be
                   expressed in the same units.

       re          is the equatorial radius of a reference spheroid.
                   This spheroid is a volume of revolution: its
                   horizontal cross sections are circular. The shape of
                   the spheroid is defined by an equatorial radius `re' and
                   a polar radius `rp'. Units of `re' must match those of
                   `rectan'.

       f           is the flattening coefficient =

                      (re-rp) / re

                   where `rp' is the polar radius of the spheroid, and the
                   units of `rp' match those of `re'.

#### Detailed_Output

       lon         is the planetographic longitude of the input point.
                   This is the angle between the prime meridian and the
                   meridian containing `rectan'. For bodies having
                   prograde (aka direct) rotation, the direction of
                   increasing longitude is positive west: from the +X
                   axis of the rectangular coordinate system toward the
                   -Y axis. For bodies having retrograde rotation, the
                   direction of increasing longitude is positive east:
                   from the +X axis toward the +Y axis.

                   The earth, moon, and sun are exceptions:
                   planetographic longitude is measured positive east for
                   these bodies.

                   The default interpretation of longitude by this
                   and the other planetographic coordinate conversion
                   routines can be overridden; see the discussion in
                   -Particulars below for details.

                   `lon' is output in radians. The nominal range of `lon' is
                   given by:

                      0  <  lon  <  2*pi
                         -

                   However, round-off error could cause `lon' to equal 2*pi.

       lat         is the planetographic latitude of the input point. For
                   a point P on the reference spheroid, this is the angle
                   between the XY plane and the outward normal vector at
                   P. For a point P not on the reference spheroid, the
                   planetographic latitude is that of the closest point
                   to P on the spheroid.

                   `lat' is output in radians. The range of `lat' is given
                   by:

                      -pi/2  <  lat  <  pi/2
                             -       -

       alt         is the altitude of point above the reference spheroid.

                   The units associated with `alt' are those associated
                   with the input `rectan' and `re'.

#### Parameters

       None.

#### Exceptions

       1)  If the body name `body' cannot be mapped to a NAIF ID code, and
           if `body' is not a string representation of an integer, the
           error SPICE(IDCODENOTFOUND) is signaled by a routine in the
           call tree of this routine.

       2)  If the kernel variable

              BODY<ID code>_PGR_POSITIVE_LON

           is present in the kernel pool but has a value other than one
           of

               'EAST'
               'WEST'

           the error SPICE(INVALIDOPTION) is signaled by a routine in the
           call tree of this routine. Case and blanks are ignored when
           these values are interpreted.

       3)  If polynomial coefficients for the prime meridian of `body' are
           not available in the kernel pool, and if the kernel variable
           BODY<ID code>_PGR_POSITIVE_LON is not present in the kernel
           pool, the error SPICE(MISSINGDATA) is signaled by a routine in
           the call tree of this routine.

       4)  If the equatorial radius is non-positive, the error
           SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call
           tree of this routine.

       5)  If the flattening coefficient is greater than or equal to one,
           the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in
           the call tree of this routine.

       6)  For points inside the reference ellipsoid, the nearest point
           on the ellipsoid to `rectan' may not be unique, so latitude may
           not be well-defined.

       7)  If the `body' input string pointer is null, the error
           SPICE(NULLPOINTER) is signaled.

       8)  If the `body' input string has zero length, the error
           SPICE(EMPTYSTRING) is signaled.

#### Files

       This routine expects a kernel variable giving body's prime
       meridian angle as a function of time to be available in the
       kernel pool. Normally this item is provided by loading a PCK
       file. The required kernel variable is named

          BODY<body ID>_PM

       where <body ID> represents a string containing the NAIF integer
       ID code for `body'. For example, if `body' is "JUPITER", then
       the name of the kernel variable containing the prime meridian
       angle coefficients is

          BODY599_PM

       The optional kernel variable

          BODY<body ID>_PGR_POSITIVE_LON

       also is normally defined via loading a text kernel. When this
       variable is present in the kernel pool, the prime meridian
       coefficients for `body' are not required by this routine. See the
       -Particulars section below for details.

#### Particulars

       Given the body-fixed rectangular coordinates of a point, this
       routine returns the planetographic coordinates of the point. The
       body-fixed rectangular frame is that having the X-axis pass
       through the 0 degree latitude 0 degree longitude direction, the
       Z-axis pass through the 90 degree latitude direction, and the
       Y-axis equal to the cross product of the unit Z-axis and X-axis
       vectors.

       The planetographic definition of latitude is identical to the
       planetodetic (also called "geodetic" in SPICE documentation)
       definition. In the planetographic coordinate system, latitude is
       defined using a reference spheroid. The spheroid is
       characterized by an equatorial radius and a polar radius. For a
       point P on the spheroid, latitude is defined as the angle between
       the X-Y plane and the outward surface normal at P. For a point P
       off the spheroid, latitude is defined as the latitude of the
       nearest point to P on the spheroid. Note if P is an interior
       point, for example, if P is at the center of the spheroid, there
       may not be a unique nearest point to P.

       In the planetographic coordinate system, longitude is defined
       using the spin sense of the body. Longitude is positive to the
       west if the spin is prograde and positive to the east if the spin
       is retrograde. The spin sense is given by the sign of the first
       degree term of the time-dependent polynomial for the body's prime
       meridian Euler angle "W":  the spin is retrograde if this term is
       negative and prograde otherwise. For the sun, planets, most
       natural satellites, and selected asteroids, the polynomial
       expression for W may be found in a SPICE PCK kernel.

       The earth, moon, and sun are exceptions: planetographic longitude
       is measured positive east for these bodies.

       If you wish to override the default sense of positive longitude
       for a particular body, you can do so by defining the kernel
       variable

          BODY<body ID>_PGR_POSITIVE_LON

       where <body ID> represents the NAIF ID code of the body. This
       variable may be assigned either of the values

          'WEST'
          'EAST'

       For example, you can have this routine treat the longitude
       of the earth as increasing to the west using the kernel
       variable assignment

          BODY399_PGR_POSITIVE_LON = 'WEST'

       Normally such assignments are made by placing them in a text
       kernel and loading that kernel via furnsh_c.

       The definition of this kernel variable controls the behavior of
       the CSPICE planetographic routines

          pgrrec_c
          recpgr_c
          dpgrdr_c
          drdpgr_c

       It does not affect the other CSPICE coordinate conversion
       routines.

#### Examples

       The numerical results shown for these examples may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       1) Find the planetographic coordinates of the point having Mars
          rectangular coordinates:

             X (km) =      0.0
             Y (km) =  -2620.678914818178
             Z (km) =   2592.408908856967

          (These input values have been chosen to create "simple" output
          values.)

          Use the PCK kernel below to load the required triaxial
          ellipsoidal shape model and orientation data for Mars.

             pck00008.tpc

          Example code begins here.

          /.
             Program recpgr_ex1
          ./

          #include <stdio.h>
          #include "SpiceUsr.h"

          int main()
          {
             /.
             Local variables
             ./
             SpiceDouble             alt;
             SpiceDouble             f;
             SpiceDouble             lat;
             SpiceDouble             lon;
             SpiceDouble             radii  [3];
             SpiceDouble             re;
             SpiceDouble             rectan [3];
             SpiceDouble             rp;

             SpiceInt                n;

             /.
             Load a PCK file containing a triaxial
             ellipsoidal shape model and orientation
             data for Mars.
             ./
             furnsh_c ( "pck00008.tpc" );

             /.
             Look up the radii for Mars.  Although we
             omit it here, we could first call badkpv_c
             to make sure the variable BODY499_RADII
             has three elements and numeric data type.
             If the variable is not present in the kernel
             pool, bodvrd_c will signal an error.
             ./
             bodvrd_c ( "MARS", "RADII", 3, &n, radii );

             /.
             Compute flattening coefficient.
             ./
             re  =  radii[0];
             rp  =  radii[2];
             f   =  ( re - rp ) / re;

             /.
             Do the conversion.
             ./
             rectan[0] =      0.0;
             rectan[1] =  -2620.678914818178;
             rectan[2] =   2592.408908856967;

             recpgr_c ( "mars", rectan, re, f, &lon, &lat, &alt );

             printf ( "\n"
                      "Rectangular coordinates:\n"
                      "\n"
                      "  X (km)                 = %18.9e\n"
                      "  Y (km)                 = %18.9e\n"
                      "  Z (km)                 = %18.9e\n"
                      "\n"
                      "Ellipsoid shape parameters:\n"
                      "\n"
                      "  Equatorial radius (km) = %18.9e\n"
                      "  Polar radius      (km) = %18.9e\n"
                      "  Flattening coefficient = %18.9e\n"
                      "\n"
                      "Planetographic coordinates:\n"
                      "\n"
                      "  Longitude (deg)        = %18.9e\n"
                      "  Latitude  (deg)        = %18.9e\n"
                      "  Altitude  (km)         = %18.9e\n"
                      "\n",
                      rectan[0],
                      rectan[1],
                      rectan[2],
                      re,
                      rp,
                      f,
                      lon / rpd_c(),
                      lat / rpd_c(),
                      alt                   );

             return ( 0 );
          }

          When this program was executed on a Mac/Intel/cc/64-bit
          platform, the output was:

          Rectangular coordinates:

            X (km)                 =    0.000000000e+00
            Y (km)                 =   -2.620678915e+03
            Z (km)                 =    2.592408909e+03

          Ellipsoid shape parameters:

            Equatorial radius (km) =    3.396190000e+03
            Polar radius      (km) =    3.376200000e+03
            Flattening coefficient =    5.886007556e-03

          Planetographic coordinates:

            Longitude (deg)        =    9.000000000e+01
            Latitude  (deg)        =    4.500000000e+01
            Altitude  (km)         =    3.000000000e+02

       2) Below is a table showing a variety of rectangular coordinates
          and the corresponding Mars planetographic coordinates. The
          values are computed using the reference spheroid having radii

             Equatorial radius:    3396.190
             Polar radius:         3376.200

          Note:  the values shown above may not be current or suitable
                 for your application.

          Corresponding rectangular and planetographic coordinates are
          listed to three decimal places.

          rectan[0]  rectan[1]  rectan[2]       lon       lat        alt
          --------------------------------------------------------------
           3396.190      0.000      0.000     0.000     0.000      0.000
          -3396.190      0.000      0.000   180.000     0.000      0.000
          -3406.190      0.000      0.000   180.000     0.000     10.000
          -3386.190      0.000      0.000   180.000     0.000    -10.000
              0.000  -3396.190      0.000    90.000     0.000      0.000
              0.000   3396.190      0.000   270.000     0.000      0.000
              0.000      0.000   3376.200     0.000    90.000      0.000
              0.000      0.000  -3376.200     0.000   -90.000      0.000
              0.000      0.000      0.000     0.000    90.000  -3376.200

       3) Below we show the analogous relationships for the earth,
          using the reference ellipsoid radii

             Equatorial radius:    6378.140
             Polar radius:         6356.750

          Note the change in longitudes for points on the +/- Y axis
          for the earth vs the Mars values.

          rectan[0]  rectan[1]  rectan[2]     lon       lat        alt
          ------------------------------------------------------------
           6378.140      0.000      0.000     0.000     0.000      0.000
          -6378.140      0.000      0.000   180.000     0.000      0.000
          -6388.140      0.000      0.000   180.000     0.000     10.000
          -6368.140      0.000      0.000   180.000     0.000    -10.000
              0.000  -6378.140      0.000   270.000     0.000      0.000
              0.000   6378.140      0.000    90.000     0.000      0.000
              0.000      0.000   6356.750     0.000    90.000      0.000
              0.000      0.000  -6356.750     0.000   -90.000      0.000
              0.000      0.000      0.000     0.000    90.000  -6356.750

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       C.H. Acton          (JPL)
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       H.A. Neilan         (JPL)
       B.V. Semenov        (JPL)
       W.L. Taber          (JPL)
       E.D. Wright         (JPL)

#### Version

       -CSPICE Version 1.0.2, 10-AUG-2021 (JDR)

           Edited header to comply with NAIF standard.

       -CSPICE Version 1.0.1, 23-JAN-2008 (EDW)

           Corrected typo in LAT range description, from:

                       -pi/2  <  LAT  <  pi
                              -       -

           to:

                       -pi/2  <  LAT  <  pi/2
                              -       -

       -CSPICE Version 1.0.0, 26-DEC-2004 (CHA) (NJB) (HAN) (BVS) (WLT)

#### Index_Entries

       convert rectangular to planetographic coordinates

#### Link to routine recpgr_c source file recpgr_c.c

    Fri Dec 31 18:41:11 2021