I see the algorithm now.  A torus is not really a good curve-fit for a
straight-ish curve, but cylinders would not work since they don't bend at
all.  If you want undilations, like when you specify the starting tangent,
the effect is intentional and beautiful, and the spline just specifies the
positions of the links, not the overall shape.

I suppose a shape that is to a parabola as a torus is to a circle would be
good for curve fitting, making a smooth curve with very few segments.

"Chris Colefax" <chr### [at] tagpovrayorg> wrote in message
news:3a662d5d@news.povray.org...
> John M. Dlugosz <joh### [at] dlugoszcom> wrote:
> > Chris, you sure make it look easy!
> >
> > I still don't understand what causes this.  Look at this low-count
version
> > (attached).  I jumped to the conclusion that the ripples are caused by
> > having too few torus segments, and each ripple is one such segment.
But,
> > they are regularly spaced, not bunched in the curved part.  So that's
not
> > it, is it?
> >
> > When reading your tutorial, I had also assumed that the purpose of using
> the
> > torii was as a curve-fit for one segment, but now I don't understand how
> > that can be, since a torus only has one curve everywhere (making it
> > ellipitical, as I had been thinking, would distort the cross-section of
> the
> > pipe, too).
>
> No, the torus pipe macro does not attempt to do any curve fitting.
Instead,
> it simply joins each pair of adjacent spline points with a circular arc,
> maintaining the continuity of curvature from one arc to the next
(regardless
> of the spline's curvature).  For the very first arc, we need a tangent, a
> starting direction.  By default, the initial tangent of the spline is
used,
> and with a suitable spline steps value this can create reasonably
accurate,
> fast rendering, completely smooth splines (example #1 in the attached
> image).
>
> The next two examples use the same number of spline steps, but with
> different initial torus tangent options.  Depending on how this is
specified
> and the number of spline steps, rippling can occur as in the middle
example.
> This rippling is precisely the effect I used in the previous renderings in
> this thread, and this is why I wrote the torus pipe spline macro to behave
> as it does.
>
> If you want to use the torus pipe spline macro to smoothly follow a
spline,
> I'd suggest starting with a spline steps value equal to the number of
spline
> segments, and increasing it from there in multiples of the number of
> segments.  Otherwise, I'd again suggest blob splines (see the squid
recently
> posted under "More fun with spline objects") as an alternative.
>
>
>

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