[Insight-developers] Evaluators : Lagrange, Hermite, Bezier

[Miller, James V (CRD)]

Luis,

Why introduce another concept "Evaluators"? These are just functions. They
should cleanly in the FunctionBase design.  

Jim


-----Original Message-----
From: Luis Ibanez [mailto:luis.ibanez@kitware.com]
Sent: Friday, March 15, 2002 10:09 AM
To: insight-developers@public.kitware.com
Cc: Aljaz Noe
Subject: [Insight-developers] Evaluators : Lagrange, Hermite, Bezier


Hi,

In order to factorize some of the functionalities required
for FEM Cells and Elements we will need to implement
interpolator using multivariate Lagrange and Hermite
polynomials.  This is needed to support high order
elements and element with C1 continutity.

There is already have a MultivariateLegendrePolynomial
class that Jisung wrote for the MRIBias correction filter.

In OpenGL there is this kind of classes are called "Evaluators"
because they facilitate to evaluate the resulting interpolation
function using parametric coordinates.

The advantage of implementing a set of Evaluators is that
they will be used at the Cell level and at the Element level.
They can also be reused to create image interpolators by
succesively associating the voxels in a neigborhood with
the nodes required by the polynomials.  In the same way
that the current BSpline Image Interpolator is doing now.

Does somebody has interest creating classes along those
lines ?

We plan to create the following classes :

- ND Hermite polynomials
- ND Bezier
- ND Lagrange polynomials

and probably rework the current Multivartiate Legendre
polynomial to provide a common API.


  Luis.







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