[[Imported from SVN: r8559]]

[[Imported from SVN: r8558]]

[[Imported from SVN: r8557]]

[[Imported from SVN: r8556]]

[[Imported from SVN: r8555]]

[[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: r8460]]

[[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]]

[[Imported from SVN: r8404]]

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: r8402]]

[[Imported from SVN: r8401]]

[[Imported from SVN: r8400]]

[[Imported from SVN: r8399]]

[[Imported from SVN: r8385]]

[[Imported from SVN: r8384]]

[[Imported from SVN: r8381]]

[[Imported from SVN: r8380]]

[[Imported from SVN: r8378]]

[[Imported from SVN: r8377]]

[[Imported from SVN: r8376]]

New implementation properly handles the two sheets.

Now the TargetSpace test passes again.  Yay!

[[Imported from SVN: r8375]]

[[Imported from SVN: r8374]]

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]]

Which highlights the fact that the code was hacky in the first place:
These type conversion should not be necessary.  Will be fixed soon.

[[Imported from SVN: r8365]]