Index Page recpgr_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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

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

       re         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          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        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        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        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) will be signaled.

       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) will be signaled.  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) will be signaled.

       4) If the equatorial radius is non-positive, the error
          SPICE(VALUEOUTOFRANGE) is signaled.

       5) If the flattening coefficient is greater than or equal to one,
          the error SPICE(VALUEOUTOFRANGE) is signaled.

       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) The error SPICE(EMPTYSTRING) is signaled if the input
          string `body' does not contain at least one character, since the
          input string cannot be converted to a Fortran-style string in
          this case.

       8) The error SPICE(NULLPOINTER) is signaled if the input string
          pointer `body' is null.

#### 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

       Numerical results shown for this example may differ between
       platforms as the results depend on the SPICE kernels used as
       input 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.)

                #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 );
             }

          Output from this program should be similar to the following
          (rounding and formatting will differ across platforms):

             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:    3397
             Polar radius:         3375

          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
      ------------------------------------------------------------------
       3397.000      0.000      0.000       0.000      0.000       0.000
      -3397.000      0.000      0.000     180.000      0.000       0.000
      -3407.000      0.000      0.000     180.000      0.000      10.000
      -3387.000      0.000      0.000     180.000      0.000     -10.000
          0.000  -3397.000      0.000      90.000      0.000       0.000
          0.000   3397.000      0.000     270.000      0.000       0.000
          0.000      0.000   3375.000       0.000     90.000       0.000
          0.000      0.000  -3375.000       0.000    -90.000       0.000
          0.000      0.000      0.000       0.000     90.000   -3375.000

       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)
       H.A. Neilan     (JPL)
       B.V. Semenov    (JPL)
       W.L. Taber      (JPL)

#### Version

       -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

    Wed Apr  5 17:54:41 2017