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Curvature calculation algorithms in Paraview

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Old   April 17, 2014, 08:46
Default Curvature calculation algorithms in Paraview
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Ali
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Hi Guys

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

Thank you
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Old   May 6, 2014, 12:06
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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).
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Old   May 19, 2014, 12:52
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Thank you Eric! actually it was very on time!
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Old   August 2, 2014, 18:56
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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?
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Old   August 3, 2014, 07:26
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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
Attached Images
File Type: jpg Mean_Curvature.jpg (65.2 KB, 36 views)
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Old   August 5, 2014, 17:47
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Seems nobody interests in this problem?
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Old   July 20, 2017, 10:14
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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...
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