Can someone please explain why Quadratics and Cubic splines are even necessary?
As far as I can figure from wikipedia and wolfram's mathworld they are both
just linear combinations of Bezier splines (someone please correct me if I am
wrong).

The math behing bezier splines seems a whole lot more simple as I learned it in
Hight school geometry as opposed to high school Algebra 2. Also if you look at
Photoshop or Illustrator when it somes to defining curve segements every thing
seems to be Bezier (again I may be wrong).

Can anyone explain the math behind cubics and quadratics?

Also i'm a little irked that spherical sweeps do not include a bezier spline
option, nore does the spline keyword. I can make a macro easily enough to
create a bezier sweep (see
http://www.anim8or.com/manual/3_object_editor.html#extrusion). But it would be
nice if the prism object had that type of functionality included.

Sorry for my rant. What can I say except that 3d studio max and any upgrades are
too expensive (or I'm too cheap), and it takes too long too learn (or I don't
have enought time to learn).

Anyone and everyones thoughts are welcome.

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"Woody" <nomail@nomail> wrote:
> Can someone please explain why Quadratics and Cubic splines are even necessary?

AFAIK they are simple to specify:  you just specify the in-between points,
rather than specifying the control points as well as is the case with bezier
splines.  The bezier spline requires 2 control points for each point specified
while in quadratic and cubic they are considered as the next and previous
points.

Hey, some people do it by hand rather than on inkscape! :)

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> Hey, some people do it by hand rather than on inkscape! :)


I guess I'll have to google "inkscape".

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"Woody" <nomail@nomail> wrote:
> > Hey, some people do it by hand rather than on inkscape! :)
>
>
> I guess I'll have to google "inkscape".

www.inkscape.org

excellent open-source vector drawing program.  Exports beziers as povray prisms.

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>> > Hey, some people do it by hand rather than on inkscape! :)
>>
>>
>> I guess I'll have to google "inkscape".
>
> www.inkscape.org
>
> excellent open-source vector drawing program.  Exports beziers as povray 
> prisms.
>
I like Spilin Editor for simple cubic splined lathes and prisms.
http://www.flashnet.it/users/fn027571/spil/main.html

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"Tim Attwood" <tim### [at] comcastnet> wrote:
> >> > Hey, some people do it by hand rather than on inkscape! :)
> >>
> >>
> >> I guess I'll have to google "inkscape".
> >
> > www.inkscape.org
> >
> > excellent open-source vector drawing program.  Exports beziers as povray
> > prisms.
> >
> I like Spilin Editor for simple cubic splined lathes and prisms.
> http://www.flashnet.it/users/fn027571/spil/main.html

But Still,, some of us like the manual control without using specialized
editors.

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Woody wrote:
> But Still,, some of us like the manual control without using specialized
> editors.

yeah, like wasting time in trial-and-error steps entering lots of points 
by hand as well as the always annoying internal points in the lathe... I 
find more fun to program in Brainf*ck...

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> yeah, like wasting time in trial-and-error steps entering lots of points 
> by hand as well as the always annoying internal points in the lathe... I 
> find more fun to program in Brainf*ck...

To be fair I must admit that sometimes I have done this manually
for cubic splines by sketching a profile onto graph paper then
entering the data. It's not really that hard to come up with a couple
extra control points when the rest are on the curve.

Bezier curves are a different matter, it's very difficult to visuallize
where all the control points should be without some feedback,
at least for complex curves. For simple curves they're just
tangent to the normal, with the magnitude controlling the flatness,
that's OK manually if the normal is along an axis.

There's really two ways to go about making a scene, one is
to do sketches on paper (or mentally if you can visualize well),
then try to make your scene match. Somethime text entry is a
fast way to put your picture into SDL.

The other method is to create your scene on the computer in
the first place, and modify it until it looks good. A GUI can
make this method fast, since it helps visualize the scene.

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"nemesis" <nam### [at] gmailcom> wrote:
> "Woody" <nomail@nomail> wrote:
> > Can someone please explain why Quadratics and Cubic splines are even necessary?
>
> AFAIK they are simple to specify:  you just specify the in-between points,
> rather than specifying the control points as well as is the case with bezier
> splines.  The bezier spline requires 2 control points for each point specified
> while in quadratic and cubic they are considered as the next and previous
> points.
>
> Hey, some people do it by hand rather than on inkscape! :)

That's the best way in my opinion since I'm bit of povray purist. It would be
nice if beziers were included as options in features where they are not
currently available (such as spherical sweeps), since beziers and linear
splines are alot easier to visualize (in my insignifigant opinion for what
little change that is worth). And since beziers require a lot less points than
a linear spline that looks otherwise identical, it seems to make sense.

Any chance of these getting into future POV Ray versions?

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Woody wrote:
> That's the best way in my opinion since I'm bit of povray purist. It would be
> nice if beziers were included as options in features where they are not
> currently available (such as spherical sweeps), since beziers and linear
> splines are alot easier to visualize (in my insignifigant opinion for what
> little change that is worth). And since beziers require a lot less points than
> a linear spline that looks otherwise identical, it seems to make sense.
> 
> Any chance of these getting into future POV Ray versions?

I'm not privy to why they aren't built into POV-Ray, but I have just 
recently put together a macro that creates a sphere sweep-like object 
along a bezier spline (including interpolation of radii).  I was 
planning on putting it up in the object collection with a set of macros 
sometime, but I can post it by itself sooner if there's any interest.

I've also been pondering how best to create a standalone spline-like 
macro using the same method.

-- 
-The Mildly Infamous Blue Herring

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