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isrot_c
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Procedure
Abstract
Required_Reading
Keywords
Brief_I/O
Detailed_Input
Detailed_Output
Parameters
Exceptions
Files
Particulars
Examples
Restrictions
Literature_References
Author_and_Institution
Version
Index_Entries

Procedure

   SpiceBoolean isrot_c ( ConstSpiceDouble    m   [3][3],
                          SpiceDouble         ntol,
                          SpiceDouble         dtol       )

Abstract

 
   Indicate whether a 3x3 matrix is a rotation matrix. 
 

Required_Reading

 
   ROTATION 
 

Keywords

 
   ERROR 
   MATRIX 
   ROTATION 
 

Brief_I/O

 
   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   m          I   A matrix to be tested. 
   ntol       I   Tolerance for the norms of the columns of m. 
   dtol       I   Tolerance for the determinant of a matrix whose 
                  columns are the unitized columns of m. 
 
   The function returns the value SPICETRUE if and only if m is 
   a rotation matrix. 
 

Detailed_Input

 
   m              is a 3x3 matrix to be tested. 
 
   ntol           is the tolerance for the norms of the columns 
                  of m. 
 
   dtol           is the tolerance for the determinant of a matrix 
                  whose columns are the unitized columns of m. 
 

Detailed_Output

 
   The function returns the value SPICETRUE if and only if m is found 
   to be a rotation matrix.  The criteria that m must meet are: 
 
 
      1) The norm of each column of m must satisfy the relation 
 
            1. - ntol  <   || column ||   <  1. + ntol. 
                       -                  - 
 
      2) The determinant of the matrix whose columns are the 
         unitized columns of m must satisfy 
 
            1. - dtol  <   determinant   <  1. + dtol. 
                       -                 - 

Parameters

 
   None. 
 

Exceptions

 
   1)  If either of ntol or dtol is negative, the error 
       SPICE(VALUEOUTOFRANGE) is signaled.  isrot_c returns the 
       value SPICEFALSE in this case. 
 

Files

 
   None. 
 

Particulars

 
   This routine is an error checking "filter"; its purpose is to 
   detect gross errors, such as uninitialized matrices.  Matrices 
   that do not pass the tests used by this routine hardly qualify as 
   rotation matrices.  The test criteria can be adjusted by varying 
   the parameters ntol and dtol. 
 
   A property of rotation matrices is that their columns form a 
   right-handed, orthonormal basis in 3-dimensional space.  The 
   converse is true:  all 3x3 matrices with this property are 
   rotation matrices. 
 
   An ordered set of three vectors V1, V2, V3 forms a right-handed, 
   orthonormal basis if and only if 
 
      1)   || V1 ||  =  || V2 ||  =  || V3 ||  =  1 
 
      2)   V3 = V1 x V2.  Since V1, V2, and V3 are unit vectors, 
           we also have 
 
           < V3, V1 x V2 > = 1. 
 
           This quantity is the determinant of the matrix whose 
           columns are V1, V2 and V3. 
 
   When finite precision numbers are used, rotation matrices will 
   usually fail to satisfy these criteria exactly.  We must use 
   criteria that indicate approximate conformance to the criteria 
   listed above.  We choose 
 
      1)   |   || Vi ||  -  1   |   <   ntol,  i = 1, 2, 3. 
                                    - 
 
      2)   Let 
 
                     Vi 
              Ui = ------ ,   i = 1, 2, 3. 
                   ||Vi|| 
 
           Then we require 
 
              | < U3, U1 x U2 > - 1 |  <  dtol; 
                                       - 
 
           equivalently, letting U be the matrix whose columns 
           are U1, U2, and U3, we insist on 
 
              | det(U) - 1 |  <  dtol. 
                              _ 

Examples

 
   1)  We have obtained an instrument pointing matrix C from a 
       C-kernel, and we wish to test whether it is in fact a 
       rotation matrix.  We can use isrot_c to check this: 
 
          #include "SpiceUsr.h"
               .
               .
               .
          /.
          Obtain pointing matrix: 
          ./
          ckgp_c ( inst, timein, tol, ref, c, &timout, &found );
 
            
          /.
          Verify that c is a rotation: 
          ./
          
          if ( !isrot_c( c ) )
          {
          
             [ perform exception handling ] 
          
          }
          else
          {
          
             [ code for the normal case goes here ] 
             
          }
            
 

Restrictions

 
   None. 
 

Literature_References

 
   None. 
 

Author_and_Institution

 
   N.J. Bachman   (JPL) 
   H.A. Neilan    (JPL) 
 

Version

 
   -CSPICE Version 1.0.0, 16-AUG-1999 (NJB) (HAN)

Index_Entries

 
   indicate whether a matrix is a rotation matrix 
 
Wed Apr  5 17:54:37 2017