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isrot_c

 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

```   isrot_c ( Indicate whether a matrix is a rotation matrix )

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

```

#### Abstract

```   Indicate whether a 3x3 matrix is a rotation matrix.
```

```   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)
J. Diaz del Rio     (ODC Space)
H.A. Neilan         (JPL)
```

#### Version

```   -CSPICE Version 1.0.1, 03-AUG-2021 (JDR)

Edited the header to comply with NAIF standard.

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

#### Index_Entries

```   indicate whether a matrix is a rotation matrix
```
`Fri Dec 31 18:41:08 2021`