Tor Olav Kristensen wrote:
> 
> Christoph Hormann <chr### [at] gmxde> wrote in
> news:3E82C325.E3BF946C@gmx.de:
> ...
> > With transform functions you could easily interpolate between two
> > transforms but the tricky thing is you can't use the functions to
> > transform regular objects.  This of course leads to the idea of function
> > based transforms - this would be an interesting new feature.
> 
> I don't understand what you mean by "function based transforms".
> 
> Please explain (and if possible give an example of a problem
> that it would solve that is not possible to solve in a "good"
> way with POV-Ray v3.5).

Well, as i said you currently can't use functions in transforms, therefore
you can't do much with it.  But as you know you can use transforms in
functions:

function { transform { ... } }

So you can declare two different transform functions and average them
(since current vector function support is limited too you have to use a
pigment function for that):

#declare fn_trans1=function { transform { ... } }
#declare fn_trans2=function { transform { ... } }

#declare fn_x = function { 0.5*(fn_trans1(x, y, z).x + fn_trans2(x, y,
z).x) }
#declare fn_y = function { 0.5*(fn_trans1(x, y, z).y + fn_trans2(x, y,
z).y) }
#declare fn_z = function { 0.5*(fn_trans1(x, y, z).z + fn_trans2(x, y,
z).z) }

#declare fn_trans_avg=
  Vector_Function(
    function { fn_x(x, y, z) },
    function { fn_y(x, y, z) },
    function { fn_z(x, y, z) }
  )

The 'Vector_Function()' macro uses the average pigment trick to combine
three float functions to one vector function.  This macro is included in
megapov's 'mechsim.inc' include file although the version coming with
megapov 1.0 is broken.

> (IIRC: "interpolating" between _any_ two arbitrary matrix
> transformations are not a well defined problem.)

This is surely correct but for situations like this the transforms to
interpolate between are not so different so this method probably leads to
acceptable results.

Christoph

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