Christoph Hormann <chr### [at] gmxde> wrote in
news:3E83121A.13AEC9A1@gmx.de: 

> 
> 
> 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):

I discarded the idea of using user defined pigment functions
as user defined vector functions some time ago, but I don't
remember why. (Maybe I didn't think of the "average trick".)

But it's nice if it really works.


> #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) }
>   )

You can write the above expression like this:

#declare fn_trans_avg = Vector_Function(fn_x, fn_y, fn_z)

(Just in case you didn't know.)


> 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.

But this would lead to incorrect result in many
cases. E.g. for rotations:

Interpolate between the rotations of a vector
<1, 0, 0> around the y-axis. First 90 degrees
and then 270 degrees.

The result of each rotation would be <0, 0, -1>
and <0, 0, 1>. And the average of this would
be (<0, 0, -1> + <0, 0, 1>)/2 = <0, 0, 0>, which
is clearly wrong. The result should have been
a rotation of (90 + 270)/2 = 180 degrees about
the y-axis, i.e. <-1, 0, 0>.


Tor Olav

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