Which is the type returned by the derivativeOfProjection method.

[[Imported from SVN: r10067]]

This is needed for projection-based finite elements.

The code in this patch has not been tested yet.

[[Imported from SVN: r9887]]

[[Imported from SVN: r9886]]

[[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]]

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]]

[[Imported from SVN: r9449]]

[[Imported from SVN: r9448]]

I can't make up my mind whether I want 'ctype' or 'field_type'

[[Imported from SVN: r9447]]

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]]

[[Imported from SVN: r9397]]

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: r8369]]

It makes it difficult to be sure that an explicitly
requested type is really handed over to every place.

While we are at it: reverse the order of the template
parameters.  Now first comes the type, then the dimension.
This is more like FieldVector and friends, and hence
should be less confusing.

[[Imported from SVN: r8148]]

[[Imported from SVN: r8145]]

[[Imported from SVN: r8034]]

[[Imported from SVN: r7374]]

[[Imported from SVN: r7313]]

[[Imported from SVN: r7225]]

[[Imported from SVN: r7205]]

[[Imported from SVN: r7196]]

[[Imported from SVN: r7195]]

[[Imported from SVN: r7134]]

[[Imported from SVN: r7090]]

bugfix in thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument.  Now it produces the same result as the fd approximation at least in for S^1

[[Imported from SVN: r7066]]

[[Imported from SVN: r7053]]

[[Imported from SVN: r7052]]

[[Imported from SVN: r7051]]

[[Imported from SVN: r7050]]

[[Imported from SVN: r7049]]

[[Imported from SVN: r7048]]

[[Imported from SVN: r7033]]

[[Imported from SVN: r6501]]

[[Imported from SVN: r6496]]

[[Imported from SVN: r6450]]

[[Imported from SVN: r6437]]

export the manifold dimension as 'dim'.  The main class template parameter had to change names for this

[[Imported from SVN: r6433]]

The first dim rows contain an orthonormal frame of the tangent space
as before.  The new rows contain an orthonormal frame of the
normal bundle.

[[Imported from SVN: r6432]]

[[Imported from SVN: r6424]]

[[Imported from SVN: r6388]]