[vtkusers] Computing curvature of a surface

[Philipp.Batchelor]

Yes,

it's a funny coincidence that I hadn't been touched my curvature
code for a long time, but have been working this week on  the  changes to make it compatible
with the way vtk4.x handles Scalars. (Not without struggle, as my post
on Monday shows). Also, I'm trying to add a new method to compute curvatures, based
on principal curvatures, which also computes a curvature tensor, but this is untested yet.
Note that the filter was written quite a while ago, when I was still learning
vtk, and is certainly not up the vtk coding standards. 

In short: Gauss curvature is the angle defect at a vertex.
          Mean curvature, edge length x dihedral angle at edge.

You can have a look at the main loops is the method GetK() and GetH()
of the filter, and copy-paste that if it is more convenient.


----------------------------------
Dr Philippe Batchelor
King's College London  	
London	SE1 9RT

phone: 	+44 207 955 4223
fax:	+44 207 955 4532
----------------------------------

"Andrew J. P. Maclean" wrote:
> 
> It has all been done for you!
> 
> Look at:
> http://www-ipg.umds.ac.uk/p.batchelor/curvatures/curvatures.html
> 
> Philipp Batchelor also supplies some vtk Classes to do it:
> His comments are:
> " This a VTK C++ class, a subclass of vtkPolyDataToPolyDataFilter, as
> input it takes a triangulated PolyData, and the output is the same
> PolyData, with the desired curvatures a scalars. This is chosen by the
> method vtkCurvatures::SetCurvatureType(i), with i = 0 for , i = 1 for
> for . i = 2 should give both, but I haven't used it very much in that
> way. Note thata as the computation of angles uses the acos, asin, and
> atan2 functions, the curvatures are double.
> Warning As mentioned above: the mean curvature requires an oriented
> surface, so typically, the surface should have gone through a
> vtkTriangleFilter and vtkPolyDataNormals. This is quite restrictive, in
> particular none of the definitions really requires triangles, I just did
> it for convenience. If you'd want to suggest modifications, don't
> hesitate to email me.
> 
> I use the class in a local library, so that the curvature class can be
> used in Tcl. I normally use VTK 3.1, on a Sun Ultra-30, with the Sun
> compiler.
> 
> As they are relatively small files, they are provided directly: Download
> vtkCurvatures.h and DownloadvtkCurvatures.cxx "
> 
> Andrew
> 
> ___________________________________________
> Andrew J. P. Maclean
> Postal:
> Australian Centre for Field Robotics
> The Rose Street Building J04
> The University of Sydney  2006  NSW
> AUSTRALIA
> 
> Room:  106
> Phone: +61 2 9351 3283
> Fax:   +61 2 9351 7474
>        http://www.acfr.usyd.edu.au/
> 
> ___________________________________________
> 
> -----Original Message-----
> From: vtkusers-admin at public.kitware.com
> [mailto:vtkusers-admin at public.kitware.com] On Behalf Of Jan Ehrhardt
> Sent: Wednesday, 3 July 2002 18:11
> To: vtkusers
> Subject: [vtkusers] Computing curvature of a surface
> 
> hi folks,
> 
> I have the following problem: I want to register two polygonal surfaces
> using nonlinear transformations.
> I have implemented an algorithm similar to andresens and nielsen
> "geometry constrained diffusion".
> This works like ICP but for nonlinear transformations.
> Actually, I match the nearest points on the two surfaces.
> The idea is not only to use the spatial distance but also the normal
> vektors and curvature of the points
> to identify corresponding points.
> The normals caan I compute using vtkPolyDataNormals, but how to compute
> the curvature of the surface points?
> Concrete:
> I have an polydata surface (no associated image or scalar values!).
> How can I compute the curvature for each point (triangle vertex) from
> the polydata ?
> Curvature means min and max curvature and /or gaussian curvature.
> 
> Regards and many thanks for ANY help,
> 
> Jan
> 
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