[vtkusers] how to create a torus ?

[Jan Ehrhardt]

Many thanks for your answers!

Indeed John, I need the surfaces to test the moment-based curvature
estimation.
I enhanced this approach by using the distance between the barycentre of
the neighbourhood and the tangential plane on the central point.
The code is really dirty, and I have actually no time to clean it up.
Please be 
patient. (But if you are realy interested in, send me a mail.)

For real world data the results are fantastic, if you choose the correct
radius R 
(size of the neighbourhood).
For my data (surface models of bones) I get nearly the same results for
a unsmoothed 
and "undecimated" polydata models and the smoothed and decimated
versions (both with 
the same radius).

But for the vtkSphereSource the results are surprisingly bad, and I
don't know why.

I tried the superquadric torus and all looks fine, but I have to go
deeper into that.
The idea is to use different resolutions and to add noise to the torus.
I hope that 
the results remain nearly the same.

Actually I have two problems:

1. An mathematical analysis of the moment-based curvature is realy hard
(for me),
because you have to compute the barycentre of a round part of the
surface.
But a 2D analysis for polylines is to find in 
U. Clarenz, G. Dziuk and M. Rumpf
"On generalized mean curvature flow in surface processing"

2. Actually I use all triangles with a distance smaller than R to the
centre. So
  I can get triangles, which are not connected with the central triangle
(triangles 
  on the other side of the surface). I found no algorithm to check the
connectivity, 
  which is fast enough.
 
Thanks Phillip, for the icosahedron ! 


Jan