[Insight-developers] Inner product != Scalar product

[Luis Ibanez]

This message was too big for the list, so
the PDF file that was attached is now
checked in

InsightDocuments/Developer/Numerics/MetricTensor.pdf

Luis



-------Original Message------------------
Hi,

To better explain this we need some diagrams,
so I prepared a PDF file with some description
of the differences between the inner product and
the scalar product, the role of the Metric Tensor
and its relationship with covariant and contravariant
components.

All our conflicts are originated in our need for
affine transformations (or more complex transforms).
As soon as we abandon the orthogonal isometric
coordinate system, things are less trivial and some
reflexes have to be reanalized, like for example
using the inner product for computing the norm of
a vector.

The attached PDF file makes 53Kb, I'm cc'ing the
list but if the file is to big I'll better check
it in InsightDocuments.



-- 
Luis Ibanez                                      CB#:   7060
Research Assistan Professor                      phone: (919) 843 5436
Division of Neurosurgery                         fax:   (919) 966 6627
University of North Carolina at Chapel Hill      email: ibanez@cs.unc.edu
Chapel Hill, NC 27599-7060                       http://www.cs.unc.edu/~ibanez