[vtkusers] about transformation in theory

David Gobbi dgobbi at atamai.com
Fri Aug 18 09:18:11 EDT 2006

Hi W,

When I wrote those functions, I based the math on how covariant vs.
contravariant vectors behave under coordinate transformations. My
sources were my old Physics notes and the CRC book "Standard
Mathematical Tables and Formulae" which has a nice section on tensor

A derivation of the formulas is given in the following paper:

Generalized 3D nonlinear transformations for medical imaging: an
object-oriented implementation in VTK
David G. Gobbi and Terry M. Peters
Computerized Medical Imaging and Graphics, vol. 27 (2003) pp. 255-265

- David

wwyang wrote:
> Hello,
> I'm reading the vtk source code in class vtkAbstractTransform about
> the functions:
> TransformNormalAtPoint(), TransformPoint() and TransformVectorAtPoint().
> I am very interested in the theory of those transforming which
> unfortunately is
> not explained in detail in the source code.
> Anybody can give me some advices about what technique papers or books
> i should read to
> understand them in theory.
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