gregjohn wrote:
> Just to restate, I have one transform that is, in effect,
> 
> #declare First_Trans= transform{
>  rotate foo1 translate bar1
>  rotate foo2 translate bar2
>  rotate foo3 translate bar3
>  rotate foo4 translate bar4
>  rotate foo5 translate bar5
>  rotate foo6 translate bar6
>  rotate foo7 translate bar7 }
> 
> Imagine all the transformations a big toe or index digit has to go
> through from
> the hip.  Up the spine, over to shoulder, etc. And then I've got one
> transform that describes, as a function of clock, a walk cycle, and
> another a run.

If you have always the same parameters (foo1 to foo7 and bar1 to bar7 in
you example), why do you not simply interpolate all these parameters
themselves (i.e. compute foo1 to foo7 and bar1 to bar7 depending on the
clock value and their start and end value) and compute the
transformation afterwards?

> Now if all transforms are matrices, then I'm guessing a complicated
> transform, too, is a matrix. Here's where it may be either incredibly
> stupid question or trivial implementation (three lines of SDL or for
> inclusion in povray 4.1).
> 
> Can you simply average all of the components of two different
> transforms and get
>  either a meaningful or smooth transition?

Consider the identity transform and a rotation around an axis by 180
degrees. What do you think is a meaningful transition in this case? In
which direction do you want to rotate? Or would you like to scale
instead of rotate, i.e. scaling along the plane normal to the axis by 1
to -1?
So, "meaningful" is not well defined in this situation. So it would
probably not happen what you intend.

And look also at this start-matrix
 1  0  0
 0  1  0
 0  0  1 
And the end-matrix
-1  0  0
 0 -1  0 
 0  0 -1
In this case you will encounter a matrix with only 0 as components,
which does not make much sense.

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