[Insight-users] Translation, Rotation and Scaling

[Ramón Casero Cañas]

Luis Ibanez wrote:
> Hi Ramon,
> 
> When you have Anisotropic Scaling and Rotation,
> that is equivalent to providing Shearing.
> 
> In other words, you can implement Shearing by
> composing Rotation and Anisotropic scaling.
> 
> Therefore, you cannot have a transform that has
> Anisotropic Scaling and Rotation but not Shearing.


Hi Luis,

Thanks for your reply. I hope I'm not digging a hole for myself :), but 
I think in this case the order of composition is important. I have 
attached 3 pictures to illustrate this.

orig.jpg is the original image.

I agree that if you have rotation followed by anisotropic scaling, in 
general you get shearing. For example, rotating the figure -45º, scaling 
the width by 1/2 and then rotating back (NB. not by 45º) produces the 
sheared figure orig-rotation-scaling.jpg.

However, if you have anisotropic scaling followed by rotation, then you 
cannot get shearing, as illustrated by figure orig-scaling-rotation.jpg.

Thus, there has to be a transformation with both anisotropic scaling and 
rotation but not shearing, hasn't it?

Best regards,

Ramon.

-- 
Ramón Casero Cañas, DPhil

Computational Biology, Computing Laboratory
University of Oxford
Wolfson Building, Parks Rd
Oxford OX1 3QD

tlf     +44 (0) 1865 610807
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