[vtkusers] Curvature based one moments

[Jan Ehrhardt]

Hi Phillip. Hi folks,

I have implemented an measure for the curvature of an object, based on
the first moment of the neighbourhood of an triangle. Maybe this is of
interest.
I do the following:
- Compute the center and area of each triangle
- for each triangle center C
    determine all triangles within an sphere of radius R
    compute the center of mass M for this neighbourhood
    determine the distance D between C and M
- end for

D is near 0 for flat surface areas and high for edges and corners. R is
an implicite smoothing factor.
Here are some pictures for the same surface generated with marching
cubes before and after triangle decimation:
R=3
http://www.medinf.mu-luebeck.de/~ehrhardt/images/vhf_curvature_moment_dc_r3.jpg
http://www.medinf.mu-luebeck.de/~ehrhardt/images/vhf_curvature_moment_full_r3.jpg
R=5
http://www.medinf.mu-luebeck.de/~ehrhardt/images/vhf_curvature_moment_dc_r5.jpg
http://www.medinf.mu-luebeck.de/~ehrhardt/images/vhf_curvature_moment_full_r5.jpg

You can compare with former results using Phillips vtkCurvature classes:
In http://www.medinf.mu-luebeck.de/~ehrhardt/images/vhf_curvature_dc.jpg
and
http://www.medinf.mu-luebeck.de/~ehrhardt/images/vhf_curvature_full.jpg

The difference between decimated and not decimated surface-version is
much less, using the moments-method.
The edges (acetabular rim for example) are very pronounced.

But there is something to do:
I have to ensure, that all triangles within the sphere Radius are
connected with the central triangle.
Does anyone know a fast and easy implementable method ? (Using the vtk
connectivity-Filter out of the box
is far too slow).

Regards,
	Jan