[vtkusers] vtkCurvatures: mean curvature

[Philippe Pouletaut]

Dear vtk users,

I am a user of slicer2 for application in biomechanics and I would like 
to ask
about two issues in the implementation of the class vtkCurvature:

(1) I don't understand how the curvature along an edge can be calculated by
                H(edge e) = length(e)*dihedral_angle(e).
In addition, curvature calculated using  this equation seems to give 1 / 
eps  scaled by a factor (a/(2pi)),
where eps is the radius of the osculating circle,
and a the aperture angle of the portion of circle.

In fact, I've tested the code for the case of portion of sphere of radius 1.
For a aperture angle value of the portion of sphere of 2pi/3, the code 
gives H = 0,3882.
For a = 4pi/3, H = 0,7054.
For a = 2pi (whole sphere), H = 1.

Could anyone explain me these different results?

(2) In the documentation of the curvature class, it is stated that we 
can use the computation of tensor
for H. But I don't know which integer for set in the statement :
SetComputeTensor (int)
Could anyone give me an example of program with the use of tensor?

Thanks in advance for your help,
sincerly yours.