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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

   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 
 
Wed Apr  5 17:54:41 2017