[vtkusers] Max and Min Principal Curvature Using VTK.

[Dongqing Chen]

Hi, there:

   In vtk, there is no direct way to compute either max (kmax) or min (kmin) principal curvature at each surface mesh point. 

  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?
 2). if kmax or kmin could be a complex number, then we can not compare complex mumbers to figure out which one is bigger?
 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?

 Thank a lot!

Best Wishes
Dongqing Chen
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