Christoph Hormann <chr### [at] gmxde> wrote in
news:3E836145.921A71E8@gmx.de: 

> 
> 
> Tor Olav Kristensen wrote:
>> 
>> [...]
>> 
>> But then POV-Ray would need to examine the
>> vector function in order to make sure that
>> it does not represent a non-linear trans-
>> formation.
>> 
>> And if it is only allowed to be a linear
>> transformation, then I think that it will
>> only be useful within isosurfaces, pigments
>> and maybe patterns.
>> 
>> I suspect that this would not allow for new
>> types of transformations. It would only make
>> it easier to do certain transformation (that
>> are already possible today).
>> 
>> Or am I wrong about all this ?
> 
> I have no idea what you are talking about.  A transform can always be
> seen as a function -  you put in a vector and get out a vector. 
> Nothing prevents you to use an arbitrary vector function for that and
> not just a transformation matrix. 
...

Then we are talking about exactly the same thing.

You said that a vector function transformation should
not be able to deform a box; such a transformation of
a box should always result in a box. From this I
reasoned that this would mean that that transformation
step would be linear.(*)

I'm just questioning if allowing for such vector
functions to be used as transformations will introduce
any new possibilities outside isosurfaces and pigments.

Don't misunderstand me. I think we really need vector
functions, but I just don't understand how they can be
so useful in transformations if non-linear trans-
formations with them aren't allowed.


Tor Olav


(*) One could construct transformations that are non-
linear and that will preserve _some_ boxes as boxes
through the transformation. E.g.:

VectorFunction(x, y, z) { <select(x, -x, x)*x, y, z> }

(But I think that many boxes will be deformed by
this transformation.)

Another non-linear transformation function that
comes to my mind are this:

VectorFunction(x, y, z, w) { <x/w, y/w, z/w> }

This would be a useful 4D vector to 3D vector
transformation.

But I am having trouble coming up with 3D to 3D
transformations that are non-linear and that will
guarantee that all boxes are preserved as boxes.

Do you have any examples ?

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