> In article<4cebdf3f$1@news.povray.org>,
> Thomas A. Fine<fin### [at] head-cfaharvardedu>  wrote:
>> I thought (and maybe this is where I'm wrong) that a cubic b-spline curve
>> was nothing more than a bunch of bezier curves strung together with
>> endpoints joined (and actually removed, being represented by the midpoints
>> of adjacent control points).  But this does not yield a curve that matches
>> the original letter shape.  It's close, but the curves are too sharp near
>> the control points and too flat near the mid-points.
>>
>> Is my assumption about the relationship between cubic b-splines and
>> beziers wrong?  Or is povray's sphere_sweep b_spline just some other kind
>> of curve?  Or am I on the right track, but just making some mistake in
>> representing the data in the appropriate order?
>
> As it turns out, I was wrong about what "cubic b-spline" means.  I'm
> still not entirely clear, and it seems like it may mean different things
> to different people, but I think what I had in mind was actually a
> cubic bezier spline, which is not the same thing.
>
> And furthermore, I don't even think it's possible.  Or if it is, I haven't
> been able to wrap my head around it.  I think the problem is that cubic
> b-splines are always C2 continuous, but quadratic b-splines are usually
> only C1 continuous.  But I haven't seeen this explicitly confirmed anywhere.
>
> So what I'm doing now is converting the TrueType quadratic b-spline into
> a collection of cubic beziers, and converting each bezier into a separate
> sphere_sweep.
>
> This works!  Except that I'm finding sphere_sweep to be extremely unstable.
> The curve segments randomly blow up in spectacular ways, spewing extra
> pixels far and wide.  I'm not talking about the documented black specks on
> the curve.  I'm talking about plotting the curve far far away from where the
> curve should be plotted.  Is there a known bug here that I could fix by
> upgrading my 3.6.1 macports install?
>
> I'm thinking I might need to go with the excellent suggestion from bart of
> just decomposing the thing into spheres and cylinders.  This works great
> for 2-D drawing. Unfortunately, shading makes seams really obvious so I'll
> need to use vastly more increments than I would need in 2-D drawing.  But
> it's better than abstract pixel explosions.
>
> 	tom

Long known problem when usint version 3.6.1.

Thing is that sphere_sweep is buggy in 3.6.
They behave beter in version 3.7.
Although version 3.7 is still in beta stage, it's prety robust, you only 
have to update it when a new subversion comes up.



Alain

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