# Curvature calculation algorithms in Paraview

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 April 17, 2014, 08:46 Curvature calculation algorithms in Paraview #1 New Member   Ali Join Date: Dec 2012 Posts: 9 Rep Power: 6 Hi Guys Does any one know which algorithm(s) paraView uses to calculate the mean and Gaussian curvatures of a surface? Thank you

 May 6, 2014, 12:06 #2 New Member   Join Date: Feb 2012 Posts: 13 Rep Power: 7 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). openfoammaofnepo likes this.

 May 19, 2014, 12:52 #3 New Member   Ali Join Date: Dec 2012 Posts: 9 Rep Power: 6 Thank you Eric! actually it was very on time!

 August 2, 2014, 18:56 #4 Senior Member   Join Date: Jan 2013 Posts: 342 Rep Power: 7 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?

August 3, 2014, 07:26
#5
Senior Member

Join Date: Jan 2013
Posts: 342
Rep Power: 7
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
 Mean_Curvature.jpg (65.2 KB, 36 views)

 August 5, 2014, 17:47 #6 Senior Member   Join Date: Jan 2013 Posts: 342 Rep Power: 7 Seems nobody interests in this problem?

 July 20, 2017, 10:14 #7 New Member   Join Date: Feb 2012 Posts: 13 Rep Power: 7 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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