Procedure

   surfnm_c ( Surface normal vector on an ellipsoid ) 

   void surfnm_c ( SpiceDouble        a,
                   SpiceDouble        b,
                   SpiceDouble        c,
                   ConstSpiceDouble   point[3],
                   SpiceDouble        normal[3] )

Abstract

   Compute the outward-pointing, unit normal vector at a point on
   the surface of an ellipsoid.

Required_Reading

   None.

Keywords

   ELLIPSOID
   GEOMETRY

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   a          I   Length of the ellipsoid semi-axis along the X-axis.
   b          I   Length of the ellipsoid semi-axis along the Y-axis.
   c          I   Length of the ellipsoid semi-axis along the Z-axis.
   point      I   Body-fixed coordinates of a point on the ellipsoid.
   normal     O   Outward pointing unit normal to ellipsoid at `point'.

Detailed_Input

   a           is the length of the semi-axis of the ellipsoid that is
               parallel to the X-axis of the body-fixed reference frame.

   b           is the length of the semi-axis of the ellipsoid that is
               parallel to the Y-axis of the body-fixed reference frame.

   c           is the length of the semi-axis of the ellipsoid that is
               parallel to the Z-axis of the body-fixed reference frame.

   point       is a 3-vector giving the bodyfixed coordinates of a point
               on the ellipsoid. In bodyfixed coordinates, the semi-axes
               of the ellipsoid are aligned with the X, Y, and Z-axes of
               the reference frame.

Detailed_Output

   normal      is the unit vector pointing away from the ellipsoid and
               normal to the ellipsoid at `point'.

Parameters

   None.

Exceptions

   1)  If any of the axes are non-positive, the error
       SPICE(BADAXISLENGTH) is signaled by a routine in the call tree
       of this routine.

Files

   None.

Particulars

   This routine computes the outward pointing unit normal vector to
   the ellipsoid having semi-axes of length `a', `b', and `c' from the
   point `point'.

Examples

   A typical use of surfnm_c would be to find the angle of incidence
   of the light from the sun at a point on the surface of an
   ellipsoid.

   Let q be a 3-vector representing the rectangular body-fixed
   coordinates of a point on the ellipsoid (we are assuming that
   the axes of the ellipsoid are aligned with the axes of the
   body fixed frame.) Let v be the vector from q to the sun in
   bodyfixed coordinates. Then the following code fragment could
   be used to compute angle of incidence of sunlight at q.

      surfnm_c   ( a, b, c, q, nrml );

      incidn = vsep_c ( v, nrml );

Restrictions

   1)  It is assumed that the input point is indeed on the ellipsoid.
       No checking for this is done.

Literature_References

   None.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)
   B.V. Semenov        (JPL)

Version

   -CSPICE Version 1.3.2, 01-NOV-2021 (JDR)

       Edited the header to comply with NAIF standard.

       Updated the documentation to refer to "reference frame" instead
       of "coordinate system" as per NAIF conventions.

   -CSPICE Version 1.3.1, 31-JAN-2008 (BVS)

       Removed '-Revisions' from the header.

   -CSPICE Version 1.3.0, 22-OCT-1998 (NJB)

       Made input vector const.

   -CSPICE Version 1.2.0, 08-FEB-1998 (NJB)

       Removed local variables used for temporary capture of outputs.

   -CSPICE Version 1.0.0, 25-OCT-1997 (NJB)

        Based on SPICELIB Version 1.2.0, 07-AUG-1996 (WLT)

Index_Entries

   surface normal vector on an ellipsoid