In article <3fc4e32c@news.povray.org>, "Carl Hoff" <hof### [at] wtnet> wrote:

> I think what I'm trying to do would keep all strait lines as strait lines
> after the transformation. 

That isn't the only constraint...


> Although lines that were parallel before the
> transformation might not be after. 

That is another constraint. Parallel lines must transform to parallel 
lines.


> I also think it should be invertible
> as long as the point where the z scaling factor becomes zero is
> outside the object.

It doesn't work that way...the transform has a singularity, which makes 
it non-invertible.


> > To bend a tube, use a little CSG.
> 
> I'm not trying to bend a tube either. 

Well, those were just examples of commonly desired transformations that 
are not possible.


> You know how a cone can be
> used to connect two spheres to make a shape like you'd get with a
> linear sphere_sweep.  I'm trying to connect these two spheres with a
> similar shape.
> 
> sphere {<0,0,0>,a1 scale <1,1,b1/a1>}
> sphere {<x0,0,0>a2 scale <1,1,b2/a2>}
> 
> Does that make it any clearer what I'm trying to do?

It sounds like you are looking for a supercone shape. Look in shapes.inc 
for a macro for creating these..though you may have a hard time fitting 
it to the capping ellipsoids. This transformation can not be done 
directly in POV, you have to use either an isosurface, process a mesh, 
or do it with CSG and existing primitives. The transformations possible 
in POV are scaling (including reflection), rotation, translation, 
shearing, and combinations of these.

http://mathworld.wolfram.com/AffineTransformation.html

-- 
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/

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