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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_SAELGV calculates the semi-axis vectors of an ellipse 
   generated by two arbitrary 3-vectors. 

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

I/O

   
   Given:
   
      vec1,
      vec2    two double precision 3-vectors that define an ellipse 
              (the generating vectors). The ellipse is the set of points 

                  center  +  cos(theta) vec1  +  sin(theta) vec2 
 
               where theta ranges over the interval (-pi, pi] and 
               center is an arbitrary point at which the ellipse 
               is centered.  An ellipse's semi-axes are 
               independent of its center, so the vector center 
               shown above is not an input to this routine.

               'vec1' and 'vec2' need not be linearly independent; 
               degenerate input ellipses are allowed.  
   
   the call:
   
      cspice_saelgv, vec1, vec2, smajor, sminor
   
   returns:
   
      smajor   the double precision semi-major axis 3-vector
               of the ellipse

      sminor   the double precision semi-minor axis 3-vector
               of the ellipse
   
   Note that 'vec1' and 'vec2' need to be linearly independent.
   

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.


      ;;
      ;; Define two arbitrary, linearly independent, vectors.
      ;;
      vec1 = [ 1.d, 1.d, 1.d ]
      vec2 = [ 1.d,-1.d, 1.d ]
   
      ;;
      ;; Calculate the semi-major and semi-minor axes of an
      ;; ellipse generated by the two vector.
      ;;
      cspice_saelgv, vec1, vec2, smajor, sminor
      print, smajor
      print, sminor
   
   IDL outputs for smajor:  
   
      1.4142136     -1.7634653e-16  1.4142136
   
   IDL outputs for sminor:
   
      2.3799435e-16  1.4142136      2.3799435e-16
   
   For this example, values on the order of 10E-16 equate to 0.d
   with regards to double precision round-off error.
   

Particulars


   We note here that two linearly independent but not necessarily 
   orthogonal vectors vec1 and vec2 can define an ellipse 
   centered at the origin:  the ellipse is the set of points in 
   3-space 
 
      center  +  cos(theta) vec1  +  sin(theta) vec2 
 
   where theta is in the interval (-pi, pi] and center is an 
   arbitrary point at which the ellipse is centered. 
 
   This routine finds vectors that constitute semi-axes of an 
   ellipse that is defined, except for the location of its center, 
   by vec1 and vec2.  The semi-major axis is a vector of largest 
   possible magnitude in the set 
 
      cos(theta) vec1  +  sin(theta) vec2 
 
   There are two such vectors; they are additive inverses of each 
   other. The semi-minor axis is an analogous vector of smallest 
   possible magnitude.  The semi-major and semi-minor axes are 
   orthogonal to each other.  If smajor and sminor are choices of 
   semi-major and semi-minor axes, then the input ellipse can also 
   be represented as the set of points 
 
      center  +  cos(theta) smajor  +  sin(theta) sminor 
 
   where theta is in the interval (-pi, pi]. 
 
   The capability of finding the axes of an ellipse is useful in 
   finding the image of an ellipse under a linear transformation. 
   Finding this image is useful for determining the orthogonal and 
   gnomonic projections of an ellipse, and also for finding the limb 
   and terminator of an ellipsoidal body. 

Required Reading


   ICY.REQ
   ELLIPSES.REQ

Version


   -Icy Version 1.0.1, 08-MAY-2008, EDW (JPL)

      Expanded description of input and output variables.

   -Icy Version 1.0.0, 16-JUN-2003, EDW (JPL)

Index_Entries

 
   semi-axes of ellipse from generating vectors 
 



Wed Apr  5 17:58:03 2017