WARNING: These methods implement the projection in quaternion
space.  This is NOT the canonical projection in matrix space.

This is necessary to compute H1 errors in matrix space.

When switching to the double covered quaternion pair, the
corresponding distance was not computed correctly

Needed for projection-based finite elements.

This patch also adds a unit test.  So far this test passes.

This fixes a dubious compiler error.

[[Imported from SVN: r9871]]

[[Imported from SVN: r9846]]

[[Imported from SVN: r9845]]

[[Imported from SVN: r9588]]

We normalize unit vectors again in the constructor and the assignment operator.
This makes sure we never drift away from the unit sphere, and it also allows
us to init unit spheres with any value in R^n and be sure we obtain a unit
vector.  This makes the test pass again.  Leaving the projection out didn't
really make a measurable difference anyway.

[[Imported from SVN: r9574]]

The old implementation used quaternion multiplication to transport
the argument to the Lie algebra, and use the standard formula there.
However, one may as well use the formula for the unit sphere in R^4,
which is much simpler, and also faster.  I fact, this patch gives
a few percent of speedup for the overall code.

[[Imported from SVN: r9562]]

There is one copy which takes FieldVector<T,4> as its second argument.
Since EmbeddedTangentVector ( = Quaternion<T>) derives from FieldVector<T,4>,
that second implementation should work in all cases.

[[Imported from SVN: r9560]]

The methods 

Rotation<T,3> exp(const Rotation<T,3>& p, const EmbeddedTangentVector& v) 

and

otation<T,3> exp(const Rotation<T,3>& p, const Dune::FieldVector<T,4>& v)

do literally the same.  So they should be next to each other in the code.

[[Imported from SVN: r9559]]

This effectively means that we use another prolongation of the distance 
function on M into the surrounding space.  Since the prolongation does not
matter this patch should not change the algorithm behavior.  However, it
shaves off a few norm calculations and division.  I cannot really measure
any difference though.

A possible effect of this is that while all values should remain on the
manifold, they may start to 'drift away' due to numerical artifacts.
So we may have to add an occasional renormalization step eventually.

[[Imported from SVN: r9558]]

When using the classes with ADOL-C, T becomes an 'adouble',
which is a non-trivial type.  However, the convexityField
is constexpr (and with a reason -- otherwise we could write
the initialization together with the declaration), and
constexpr and non-trivial types don't work together.

[[Imported from SVN: r9444]]

Because ADOL-C doesn't like calls to sqrt(0), obviously.
The use of sqrt(x) for small x can be avoided completely
using modified series expansions, because the overall
function exp is differentiable even at x=0.

[[Imported from SVN: r9426]]

Makes for a more precise Hessian matrix when using automatic differentiation.

[[Imported from SVN: r9425]]

[[Imported from SVN: r9424]]

Because ADOL-C cannot handle the latter

[[Imported from SVN: r9386]]

[[Imported from SVN: r9385]]

[[Imported from SVN: r9384]]

And use it in the test.

This patch uses the new 'constexpr' macro.  Hence it is C++11 only.

[[Imported from SVN: r9195]]

[[Imported from SVN: r8972]]

with respect to the quaternion coordinates.  Or, in other words,
the second derivative of the map from quaternions to 
orthogonal matrices.

[[Imported from SVN: r8407]]

New implementation properly handles the two sheets.

Now the TargetSpace test passes again.  Yay!

[[Imported from SVN: r8375]]

The new implementation should take proper care of the two-sheet structure.

I am writing 'should' here: it still fails the test sometimes,
but then the result appears to be close enough to think rounding errors
are responsible.

[[Imported from SVN: r8373]]

The new implementation properly handles the double-sheet structure

[[Imported from SVN: r8372]]

don't keep a private implementation of derivativeOfArcCosSquared -- use the one from UnitVector instead

[[Imported from SVN: r8371]]

Properly taking into account the two-sheet covering structure

[[Imported from SVN: r8370]]

[[Imported from SVN: r8368]]

Now it properly handles the situation that p and q may be on
different sheets of the double cover.

[[Imported from SVN: r8367]]

[[Imported from SVN: r8366]]

This is safer, because calling the constructor implicitly
can lead to unwanted quaternion normalization.
(happened to me...)

[[Imported from SVN: r8344]]

Even though multiplication of Rotations is the same thing
as multiplication of Quaternions, in the first case the
output is a Rotation class, and in the second on a Quaternion
class.

[[Imported from SVN: r8343]]

[[Imported from SVN: r8342]]

[[Imported from SVN: r8333]]

[[Imported from SVN: r8329]]