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<DIV><FONT face=Arial size=2>Hi, there:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> In vtk, there is no direct way to
compute either max (kmax) or min (kmin) principal curvature at each surface mesh
point. </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> 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.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> kmax=H+sqrt(H^2-K);
kmin=H-sqrt(H^2-K).</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> But some problems are generated
accordingly:</FONT></DIV>
<DIV><FONT face=Arial size=2> </FONT></DIV>
<DIV><FONT face=Arial size=2> 1). can kmax or kmin be a complex number,
since H^2-K can not be guaranteed to positive number or 0?</FONT></DIV>
<DIV><FONT face=Arial size=2> 2). if kmax or kmin could be a complex
number, then we can not compare complex mumbers to figure out which one is
bigger?</FONT></DIV>
<DIV><FONT face=Arial size=2> 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)|?</FONT></DIV>
<DIV><FONT face=Arial size=2> 4). Finally, if kmax or kmin is an absolute
value, then how to come up its direction?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> Thank a lot!</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Best Wishes</FONT></DIV>
<DIV><FONT face=Arial size=2>Dongqing Chen</FONT></DIV></BODY></HTML>