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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_PJELPL orthogonally projects an ellipse onto a plane.

I/O


   Given:

      elin    a structure describing a SPICE ellipse.

              [1,1] = size(elin); struct = class(elin)

              The structure has the fields:

                 center:    [3x1 double]
                 semiMajor: [3x1 double]
                 semiMinor: [3x1 double]

      plane   a structure describing a SPICE plane.

              [1,1] = size(plane); struct = class(plane)

              The structure has the fields:

                  normal:     [3x1 double]
                  constant:   [1x1 double]

              are, respectively, a SPICE ellipse and a SPICE plane. The
              geometric ellipse represented by 'elin' is to be orthogonally
              projected onto the geometric plane represented by 'plane'.

   the call:

      elout = cspice_pjelpl( elin, plane )

   returns:

      elout   the SPICE ellipse that represents the geometric
              ellipse resulting from orthogonally projecting the ellipse
              represented by 'elin' onto the plane represented by 'plane'.

              [1,1] = size(elout); struct = class(elout)

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.

      %
      % Assign the values for plane/ellipse definition
      % vectors.
      %
      center  = [ 1,  1,  1 ]';
      vect1   = [ 2,  0,  0 ]';
      vect2   = [ 0,  1,  1 ]';
      normal  = [ 0,  0,  1 ]';

      %
      % Create a plane using a constant value of 0...
      %
      plane = cspice_nvc2pl( normal, 0 );

      %
      % ...and an ellipse.
      %
      elin = cspice_cgv2el( center, vect1, vect2 );

      %
      % Project the ellipse onto the plane.
      %
      elout = cspice_pjelpl( elin, plane );

      %
      % Output the ellipse in the plane.
      %
      fprintf( 'Center    :  %f  %f  %f\n', elout.center    )
      fprintf( 'Semi-minor:  %f  %f  %f\n', elout.semiMinor )
      fprintf( 'Semi-major:  %f  %f  %f\n', elout.semiMajor )

   MATLAB outputs:

      Center    :  1.000000  1.000000  0.000000
      Semi-minor:  0.000000  1.000000  0.000000
      Semi-major:  2.000000  0.000000  0.000000

Particulars


   Projecting an ellipse orthogonally onto a plane can be thought of
   finding the points on the plane that are `under' or `over' the
   ellipse, with the `up' direction considered to be perpendicular
   to the plane.  More mathematically, the orthogonal projection is
   the set of points Y in the plane such that for some point X in
   the ellipse, the vector Y - X is perpendicular to the plane.
   The orthogonal projection of an ellipse onto a plane yields
   another ellipse.

Required Reading


   For important details concerning this module's function, please refer to
   the CSPICE routine pjelpl_c.

   MICE.REQ
   ELLIPSES.REQ
   PLANES.REQ

Version


   -Mice Version 1.0.0, 11-JUN-2013, EDW (JPL)

Index_Entries


   project ellipse onto plane


Wed Apr  5 18:00:34 2017