the ones with i<=j.  The rest follows from symmetry of
the Hessian.

Needless to say, this makes the Hessian assembly quite
a bit faster.

[[Imported from SVN: r8587]]

[[Imported from SVN: r8572]]

[[Imported from SVN: r8571]]

[[Imported from SVN: r8570]]

[[Imported from SVN: r8569]]

Because trace(sym(A)) == trace(A)

[[Imported from SVN: r8568]]

[[Imported from SVN: r8567]]

[[Imported from SVN: r8566]]

[[Imported from SVN: r8565]]

[[Imported from SVN: r8562]]

[[Imported from SVN: r8559]]

[[Imported from SVN: r8554]]

[[Imported from SVN: r8553]]

[[Imported from SVN: r8543]]

[[Imported from SVN: r8508]]

[[Imported from SVN: r8507]]

This change makes the localgeodesicfefunction test fail again.
So there must be a bug in the corresponding non-finite-difference
code.  Looking at simplex cases confirms me in this opinion.
But I don't find the bug...

[[Imported from SVN: r8463]]

[[Imported from SVN: r8462]]

[[Imported from SVN: r8409]]

implement the remaining curvature and bending terms for the energy gradient.  These are not working yet, though.

[[Imported from SVN: r8408]]

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]]

So far, the long form of the quadratic bending energy has been
implemented and tested, and it appears to do the right thing.

This is a snapshot commit.  The code remains out-commented until
it is finished.

[[Imported from SVN: r8403]]

[[Imported from SVN: r8385]]

[[Imported from SVN: r8384]]

[[Imported from SVN: r8376]]

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: r8369]]

[[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]]

[[Imported from SVN: r8364]]

we know the function value when calling evaluateDerivative.  So let's give that value to the method, to prevent it from recomputing it

[[Imported from SVN: r8363]]

To compute the derivative you need the function value (see my paper).
Therefore, it is computed as the first thing in the evaluateDerivative
method.  However, frequently, the assembler also needs the function value,
and also computes it.  Hence the function value is computed twice.
Since computing the function values takes quite a bit of time
this patch removes that redundancy, at the price of a slightly
more complicated API: if you happen to know the correct function
value when calling evaluateDerivative, you can now hand over the
value.  Then evaluateDerivative uses that value instead of recomputing it.

Short measurements have shown a speed increase between 25% and 45%.

[[Imported from SVN: r8362]]

Much nicer: I can have the surface and the director vector fields
all in one file.

[[Imported from SVN: r8361]]

The speed increase cause by the patch is, alas, hardly measurable.

[[Imported from SVN: r8360]]

[[Imported from SVN: r8353]]