Abstract

   CSPICE_EDPNT scales a point so that it lies on the surface of a specified
   triaxial ellipsoid that is centered at the origin and aligned
   with the Cartesian coordinate axes.

I/O

   Given:

      p        a non-zero point in three-dimensional space.

               [3,1] = size(p); double = class(p)

      a,
      b,
      c        respectively, the semi-axis lengths of a triaxial
               ellipsoid in the X, Y, and Z directions.

               [1,1] = size(a); double = class(a)
               [1,1] = size(b); double = class(b)
               [1,1] = size(c); double = class(c)

               The axes of the ellipsoid are aligned with the axes of the
               Cartesian coordinate system.

   the call:

      [ep] = cspice_edpnt( p, a, b, c )

   returns:

      ep       the result of scaling the input point `p' so that it lies on
               the surface of the triaxial ellipsoid defined by the input
               semi-axis lengths.

               [3,1] = size(ep); double = class(ep)

Parameters

   None.

Examples

   Any 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 surface intercept point on an ellipsoid having radii

          ( 3, 2, 1 )

      of the ray emanating from the origin and having direction
      vector

          ( 1, 1, 1 )


      Example code begins here.


      function edpnt_ex1()

         a    = 3.0;
         b    = 2.0;
         c    = 1.0;

         v    = [ 1.0, 1.0, 1.0 ]';

         [ep] = cspice_edpnt( v, a, b, c );

         fprintf( 'EP    =  %17.14f %17.14f %17.14f\n', ...
                                    ep(1), ep(2), ep(3) )

         %
         % Verify that `ep' is on the ellipsoid.
         %
         level =   (ep(1)/a) ^ 2 + (ep(2)/b) ^ 2 + (ep(3)/c) ^ 2;

         fprintf( 'LEVEL =  %17.14f\n', level )


      When this program was executed on a Mac/Intel/Octave5.x/64-bit
      platform, the output was:


      EP    =   0.85714285714286  0.85714285714286  0.85714285714286
      LEVEL =   1.00000000000000

Particulars

   This routine efficiently computes the ellipsoid surface point
   corresponding to a specified ray emanating from the origin.
   Practical examples of this computation occur in the Mice
   routines cspice_latsrf and cspice_srfrec.

Exceptions

   1)  If any of the target ellipsoid's semi-axis lengths is
       non-positive, the error SPICE(INVALIDAXES) is signaled by a
       routine in the call tree of this routine.

   2)  If `p' is the zero vector, the error SPICE(ZEROVECTOR) is
       signaled by a routine in the call tree of this routine.

   3)  If the level surface parameter of the input point underflows,
       the error SPICE(POINTTOOSMALL) is signaled by a routine in the
       call tree of this routine.

   4)  If any of the input arguments, `p', `a', `b' or `c', is
       undefined, an error is signaled by the Matlab error handling
       system.

   5)  If any of the input arguments, `p', `a', `b' or `c', is not of
       the expected type, or it does not have the expected dimensions
       and size, an error is signaled by the Mice interface.

Files

   None.

Restrictions

   None.

Required_Reading

   MICE.REQ

Literature_References

   None.

Author_and_Institution

   J. Diaz del Rio     (ODC Space)

Version

   -Mice Version 1.0.0, 09-AUG-2021 (JDR)

Index_Entries

   scale point to lie on ellipsoid