quaternion: Added generalized construction from and conversion to Euler-angles

The particular rotation sequence is specified via the enumeration:

    //- Euler-angle rotation sequence
    enum rotationSequence
    {
        ZYX, ZYZ, ZXY, ZXZ, YXZ, YXY, YZX, YZY, XYZ, XYX, XZY, XZX
    };

and provided as an argument to the constructor from Euler-angles

    //- Construct a quaternion given the three Euler angles:
    inline quaternion
    (
        const rotationSequence rs,
        const vector& angles
    );

and conversion to Euler-angles:

    //- Return a vector of euler angles corresponding to the
    //  specified rotation sequence
    inline vector eulerAngles(const rotationSequence rs) const;

applications/test/quaternion/Test-quaternion.C

@@ -1,10 +1,43 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2011-2016 OpenFOAM Foundation
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Application
+    Test-quaternion
+
+Description
+    Test application for quaternions.
+
+\*---------------------------------------------------------------------------*/
+
 #include "quaternion.H"
 #include "septernion.H"
 #include "IOstreams.H"
 
 using namespace Foam;
 
-int main()
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+int main(int argc, char *argv[])
 {
     quaternion q(vector(1, 0, 0), 0.7853981);
     Info<< "q " << q << endl;
@@ -36,5 +69,32 @@ int main()
            *septernion(vector(0, 1, 0))).transform(v)
         << endl;
 
+    Info<< "Test conversion from and to Euler-angles" << endl;
+    vector angles(0.1, 0.2, 0.3);
+    for (int rs=quaternion::ZYX; rs<quaternion::XZX; ++rs)
+    {
+        if
+        (
+            mag
+            (
+                angles
+              - quaternion(quaternion::rotationSequence(rs), angles)
+               .eulerAngles(quaternion::rotationSequence(rs))
+            )
+          > SMALL
+        )
+        {
+            FatalErrorInFunction
+                << "Inconsistent conversion for rotation sequence "
+                << rs << exit(FatalError)
+                << endl;
+        }
+    }
+
+    Info<< "End\n" << endl;
+
     return 0;
 }
+
+
+// ************************************************************************* //