[vtkusers] Computing curvature of a surface

[Jan Ehrhardt]

Moin Moin,

thanks very much for any help. I have tried Phillipps classes with a
pre-4.0 version
and it works fine. Special thanks to Phillipp !

Now I have a new problem:
I have a surface-representation of an object, i.e. generated with
marching cubes and a 
second surface-representation after applying the triangle decimation
algorithm.
Now I compute the mean curvatures for both surfaces and the curvatures
significantly differ
(but the  minimal and maximal mean curvature is the same for both
surfaces).

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
a visualization of the curvatures with scalar-range [-0.1, 0.1] is
schown.

Is it possible to compute something like a "normalized curvature"
independent from the
triangle resolution and  small local variations (maybe caused by
discretisation artefakts).

Regards,
	Jan

"Philipp.Batchelor" wrote:
> 
> 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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