Procedure

   void frame_c ( SpiceDouble x[3],
                  SpiceDouble y[3],
                  SpiceDouble z[3] ) 

Abstract

 
    Given a vector x, this routine builds a right handed 
    orthonormal frame x,y,z where the output x is parallel to 
    the input x. 
 

Required_Reading

 
   None. 
 

Keywords

 
    AXES,  FRAME 
 

Brief_I/O

 
    VARIABLE  I/O  DESCRIPTION 
    --------  ---  ------------------------------------------------ 
    x         I/O  Input vector. A parallel unit vector on output. 
    y          O   Unit vector in the plane orthogonal to x. 
    z          O   Unit vector given by x X y. 
 

Detailed_Input

 
 
    x      This vector is used to form the first vector of a 
           right-handed orthonormal triple. 
 

Detailed_Output

 
    x, 
    y, 
    z      form a right handed orthonormal frame, where x is 
           now a unit vector parallel to the original input 
           vector x.  There are no special geometric properties 
           connected to y and z (other than that they complete the 
           right handed frame). 
 

Parameters

 
    None. 
 

Exceptions

 
   Error Free.
 
   1) If x on input is the zero vector the ``standard'' frame (ijk) 
      is returned. 
 

Files

 
    None. 
 

Particulars

 
    Given an input vector x, this routine returns unit vectors x, 
    y, and z such that xyz forms a right-handed orthonormal frame 
    where the output x is parallel to the input x. 
 
    This routine is intended primarily to provide a basis for 
    the plane orthogonal to x.  There are no special properties 
    associated with y and z other than that the resulting xyz frame 
    is right handed and orthonormal.  There are an infinite 
    collection of pairs (y,z) that could be used to this end. 
    Even though for a given x, y and z are uniquely determined, users 
    should regard the pair (y,z) as a random selection from this 
    infinite collection. 
 
    For instance, when attempting to determine the locus of points 
    that make up the limb of a triaxial body, it is a straightforward 
    matter to determine the normal to the limb plane.  To find 
    the actual parametric equation of the limb one needs to have 
    a basis of the plane.  This routine can be used to get a basis 
    in which one can describe the curve and from which one can 
    then determine the principal axes of the limb ellipse. 
 

Examples

 
    In addition to using a vector to construct a right handed frame 
    with the x-axis aligned with the input vector, one can construct 
    right handed frames with any of the axes aligned with the input 
    vector. 
 
    For example suppose we want a right hand frame xyz with the 
    z-axis aligned with some vector v.  Assign v to z 
 
          z[0] = v[0]; 
          z[1] = v[1]; 
          z[2] = v[2]; 
 
    Then call frame_c with the arguments x,y,z cycled so that z 
    appears first. 
 
          frame_c (z, x, y); 
 
    The resulting xyz frame will be orthonormal with z parallel 
    to the vector v. 
 
    To get an xyz frame with y parallel to v perform the following 
 
          y[0] = v[0]; 
          y[1] = v[1]; 
          y[2] = v[2]; 
 
          frame_c (y, z, x); 
 

Restrictions

 
    None. 
 

Literature_References

 
    None. 
 

Author_and_Institution

 
    W.L. Taber      (JPL) 
    I.M. Underwood  (JPL) 
 

Version

 
   -CSPICE Version 1.0.0, 26-MAR-1999 (NJB)

Index_Entries

 
   build a right handed coordinate frame 
 

Link to routine frame_c source file frame_c.c