[vtkusers] Re: Max and Min Principal Curvature Using VTK.

[Goodwin Lawlor]

Dongqing Chen wrote:
> Hi, there:
>  
>    In vtk, there is no direct way to compute either max (kmax) or min 
> (kmin) principal curvature at each surface mesh point.
vtk5.0 (or CVS since July 2004) has methods:
SetCurvatureTypeToMaximum()
SetCurvatureTypeToMinimum()

which use the same equations below.

>   Now, I can use vtkCurvatures to obtain the Gaussian curvature (K) and 
> mean curvature (H) at the same point, then the two equations listed 
> below to calculate kmax and kmin.
>  
>    kmax=H+sqrt(H^2-K); kmin=H-sqrt(H^2-K).
>  
>   But some problems are generated accordingly:
>  
>  1). can kmax or kmin be a complex number, since H^2-K can not be 
> guaranteed to positive number or 0?
H^2-K is tested to see if its non-negative. If it is negative then k_max
and k_min are undefined and are set to 0. The isn't very satisfactory,
since k_max/k_min can be defined and have a value of 0...

>  2). if kmax or kmin could be a complex number, then we can not compare 
> complex mumbers to figure out which one is bigger?
It can't be complex
>  3). if my understanding is wrong in question 2), then kmax or kmin 
> means the absolute value of  | H+sqrt(H^2-K) | or  | H-sqrt(H^2-K)|?
>  4). Finally, if kmax or kmin is an absolute value, then how to come 
> up its direction?
The directions of the curvatures aren't calculated by this algorithm.
Other algorithms use an eigensolution and so the directions are the
eigenvectors and the curvatures are the eigenvalues

hth

Goodwin