[ali.ghaemi]

Hi Guys

Does any one know which algorithm(s) paraView uses to calculate the mean and Gaussian curvatures of a surface?

Thank you

[eric_albin]

Hi Ali,
Maybe it is a bit late but here is the answer:
http://www.vtk.org/doc/release/5.0/h....html#_details

For the Gaussian curvature, the angle deficit method is used (Gauss-Bonnet theorem). It is equal to 2pi minus the sum of the angles for the neighbor faces...
For the mean curvature, it computes a sum over the neighbor edges of the angle between the neighbor faces multiplied by the edge length.
I advice you to have a look to these papers:
- Gatzke & Grimm. Estimating curvatures on triangular meshes (2006).
- Dyn, Hormann, Sun-Jeong & David. Optimizing 3D Triangulations using Discrete Curvature Analysis (2001).

[ali.ghaemi]

Thank you Eric! actually it was very on time!

[openfoammaofnepo]

Dear All,

When we compute the Gaussian curvature using paraview, how is the sign (plus or minus or zero) of the curvature defined in paraview?

In my case, I have a 3D irregular closed iso-surface, assume there is one point P in the closed -iso-surface. Can the sign of curvature from paraview be used for identifying the convex or concave relate to that point P?

[openfoammaofnepo]

Hello,

I calculate the mean curvature using paraview. I am not sure if why it looks so fragmented. In my expectation, it curvature can be more smooth. Are yours also like my results in the attachment? Did I make some mistake to plot out the mean curvature?

Thank you very much OFFO

[openfoammaofnepo]

Seems nobody interests in this problem?

[eric_albin]

Hi,

I faced similar problems with curvatures within paraview.
The problem is not simple. First, I guess you generated a mesh representing the implicit surface using the 'isocontour' filter. The mesh extraction is done with a marching cube method. If you have a look to the mesh, you will see that it is very irregular. Using built-in discrete methods to compute curvature with such an irregular mesh is really inaccurate.

I am really sorry to tell you that you should not use built-in filters to compute curvatures. If you are interested, you can have a look to my paper : "Computational assessment of curvatures and principal directions of implicit surfaces from 3D scalar data".
I use an implicit method to compute curvatures at the nodes of the iso-contours extracted by the marching cube method. This is much more accurate because you do not use mesh points but your original 3D data to compute the curvature... I did this with my own python filter within ParaView to handle multi-files...