SpiceBoolean isrot_c ( ConstSpiceDouble m ,
SpiceDouble dtol )
Indicate whether a 3x3 matrix is a rotation matrix.
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.
m is a 3x3 matrix to be tested.
ntol is the tolerance for the norms of the columns
dtol is the 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 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.
1) If either of ntol or dtol is negative, the error
SPICE(VALUEOUTOFRANGE) is signaled. isrot_c returns the
value SPICEFALSE in this case.
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
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.
Ui = ------ , i = 1, 2, 3.
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.
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:
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 ]
[ code for the normal case goes here ]
N.J. Bachman (JPL)
H.A. Neilan (JPL)
-CSPICE Version 1.0.0, 16-AUG-1999 (NJB) (HAN)
indicate whether a matrix is a rotation matrix