[Insight-users] difference between vector and covariantvector

[Luis Ibanez]

Hi Yannick,

A Vector describes the relative position between two points in space.

             Vector = Point1 - Point2


A CovariantVector describes the direction orthogonal to a surface.

          CovariantVector = Vector1 x Vector2

where "x" is a cross product of the two vectors.


CovariantVectors and Vectors behave differently under
Affine transformation. That is one of the reasons why
it is important to make a distinction between them in ITK.


For example:

  Gradients of functions are CovariantVectors (not Vectors).



    Regards,



        Luis



----------------------
yannick pannier wrote:
> Hi everybody,
> 
> I'm learning how to use ITK's library and I don't understand very well 
> the difference between itk::CovariantVector and itk::Vector classes.
> 
> The ITK's software guide say :
> 
> //  covariant vector differs from a vector in the way they behave
> //  under affine transforms, in particular under anisotropic
> //  scaling. If a covariant vector represents the gradient of a
> //  function, the transformed covariant vector will still be the valid
> //  gradient of the transformed function, a property which would not
> //  hold with a regular vector.
> 
> Does anyone could give me more explanations ?
> 
> Thanks,
> 
> Yannick
> 
> 
> _______________________________________________
> Insight-users mailing list
> Insight-users at itk.org
> http://www.itk.org/mailman/listinfo/insight-users
>